# #math

In this video I recap on estimating the sum of a series based on whether it converges by the Integral Test, Comparison Test, or the Alternating Series Tests. If a series is convergent by the Integral Test, we can estimate its sum by first finding an estimate of the size of its remainder. Since an integral is formed by an infinite set of rectangles, the remainder can be estimated based on whether the rectangles are above or below the curve. From this, we can estimate the sum of the series for the integral test.

If a series is convergent by the Comparison Test, we can estimate its sum by estimating the sum of the series it is being compared to. For example, if a series is less than another series that happens to converge by the integral test, we can use the sum estimate for the integral test.

If a series is convergent by the alternating series test, we can apply the alternating series estimation theorem. This theorem states that the absolute value of the remainder of the n-th partial sum of a series is less than the next positive term of the series. This can be seen visually since each subsequent term is larger than the difference between the sum and any given partial sum.

The timestamps of key parts of the video are listed below:

- Question 7: 0:00
- (a) Integral Test sum estimation: 0:27
- Estimating the size of the remainder: 1:47
- Remainder estimate for the integral test: 6:57
- (b) Estimating sum using the Comparison Test: 8:25
- (c) Estimating sum of alternating series: 15:02
- Visualization of the alternating series estimation theorem: 16:31

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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1 week ago
1 week, 1 day ago
1 week, 3 days ago

In this video I quickly recap on absolutely and conditionally convergent series. An absolutely convergent series is such that the absolute value of all the terms of a series is convergent. Since the absolute value of all the terms means that the series sums up to its maximum size, if it is absolutely convergent then it means it is also convergent. On the other hand, if a series is convergent but NOT absolutely convergent, then it is said to be conditionally convergent. This arises from positive and negative terms canceling out.

The timestamps of key parts of the video are listed below:

- Question 6: 0:00
- (a) Absolutely convergent series: 0:14
- (b) Absolutely convergent series are convergent: 0:56
- (c) Conditionally convergent series: 1:12

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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1 week, 4 days ago
1 week, 4 days ago

In this video I recap on 7 different types of tests for determining if an infinite series converges or diverges. The first is the Test for Divergence which states that if the limit of the sequence of terms does not approach 0, then the series is divergent. The second is the Integral Test, which states that the series is only convergent if its corresponding integral is also convergent. The third is the Comparison Test, which states that a series is convergent if every term of its sequence is smaller than that of a known convergent series. The fourth is the Limit Comparison Test, which states that if the limit of the ratio of the terms of 2 sequences is equal to a finite number c that is greater than 0, then either both series converge or both diverge. The fifth is the Alternating Series Test, which states that if the absolute value of all the terms of an alternating series is less than each subsequent term, and their limit approaches 0, then the alternating series is convergent. The sixth is the Ratio Test, which states that if the limit of the absolute value of the ratio of the n + 1 term divided by the n-th term is equal to a finite number less than 1, then the series is convergent. The seventh test is the Root Test, which states that if the n-th root of the absolute value of the n-th term is equal to a finite number less than 1, then the series is convergent.

Note that for all the tests listed, they have similar conditions for when the series is divergent, or in the case of the Ratio and Root Tests, where the tests are inconclusive when the limits equal to 1.

The timestamps of key parts of the video are listed below:

- Question 5: 0:00
- (a) Test for Divergence: 0:22
- (b) Integral Test: 1:25
- (c) Comparison Test: 3:32
- (d) Limit Comparison Test: 4:43
- (e) Alternating Series Test: 5:28
- (f) Ratio Test: 8:01
- (h) Root Test: 9:23

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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1 week, 5 days ago

In this video I go over a quick recap on how the sum of a series affects the limit of its terms and its partial sums. If an infinite series sums up to 3, then this must mean that the terms of the series all approach the limit of 0 while the limit of the partial sums approach 3. In other words, the limit of the sequence of partial sums is equal to the sum of the infinite series.

The timestamps of key parts of the video are listed below:

- Question 4: 0:00
- Solution: 0:47
- Limits of the sequence vs partial sums: 1:06

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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1 week, 6 days ago

Contact email: [email protected]

Link to A+ Notes for Beginning Algebra

2 weeks, 3 days ago

In this video I go over a quick review of geometric series and p-series and show the circumstances for when they are convergent. A geometric series has all the terms being a constant number multiplied by a common ratio starting from the power of 0 and incrementing by 1 for each successive term. The series is convergent and equal to the (first term) / (1 - common ratio) when the absolute value of the common ratio is less than 1. I also show a geometric interpretation of the geometric series using similar triangles.

A p-series is of the form 1/n^p and it is convergent when p is greater than 1 and divergent for all other values.

The timestamps of key parts of the video are listed below:

- Question 3: 0:00
- Solution to (a): Geometric series: 0:28
- Geometric representation via similar triangles: 2:04
- Solution to (b): p-Series: 4:51

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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2 weeks, 4 days ago

In this video I review bounded and monotonic sequences as well as the monotonic sequence theorem. A bounded sequence is one in that is bounded above and bounded below. A sequence is bounded above if there is a number that is less than every term in the sequence. Likewise, a sequence bounded below is if there is a number that is larger than every term in the sequence. A monotonic sequence is either always increasing or always decreasing. The monotonic sequence theorem, which I covered in my earlier video, states that a bounded, monotonic sequence is always convergent.

The timestamps of key parts of the video are listed below:

- Question 2: 0:00
- Solution to (a): Bounded sequence: 0:22
- Solution to (b): Monotonic sequence: 1:33
- Solution to (c): Monotonic sequence theorem: 2:51

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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2 weeks, 5 days ago

In this video I go over a quick review of what convergent sequences and convergent series are. A sequence is just a list of numbers, and it is said to be convergent if its limit approaches a specific number as the number of terms gets large. A series is a summation of a sequence, and it is said to be convergent if the limit of the n-th partial sum of the sequence approaches a specific real number. I compare the definitions for when a both the sequence and series converge to the number 3.

The timestamps of key parts of the video are listed below:

- Question 1: 0:00
- Solution to Part (a): Convergent sequence: 0:39
- Solution to Part (b): Convergent series: 2:29
- Solution to Part (c): Limit of sequence equals 3: 4:31
- Solution to Part (d): Limit of series equals 3: 4:59

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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2 weeks, 6 days ago

In this video I derive the formula for projecting 3D coordinates onto a 2D screen using similar triangles. First I plot out the coordinates in 3D and then draw a straight line from the point where we are projecting the coordinates and onto the x = 0 plane. The point of projection can be thought of as the point at which our camera or eyes are located at, thus the resulting 2D projection maintains 3D perspective from that specific point. Drawing a second line passing through the z coordinates of the 3D line, we can see two similar triangles. Either of the similar triangles can be used to obtain identical formulas for the y and z projection coordinates. Note that in this projection derivation, I project the x coordinates to x = 0 and the camera or eyes location is at x = 1000. Epic stuff!

The timestamps of key parts of the video are listed below:

- Projecting 3D coordinates to 2D coordinates: 0:00
- Two Similar Triangles: 2:45
- Determining the formula for the y and z projection: 4:41
- 3D to 2D projection formula: 8:53

This video was taken from my earlier video listed below:

- Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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3 weeks, 6 days ago

A simple introduction to graphing Sine, Cosine and Tan Functions is shown. These functions are cyclical and are used in many real world applications so it is very important to understand there graphs.

- PDF video notes: https://1drv.ms/b/s!As32ynv0LoaIirUG-gzUSzPRcTN9oQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/trigonometry-graphing-sin-cos-tan-functions

Related Videos:

Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Exact Trigonometry Ratios Part 2: Examples: http://youtu.be/rgeJxcAphSw .

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3 weeks, 6 days ago

Link to A+ Notes for Beginning Algebra

Contact email: [email protected]
Timestamps
0:00 Intro
2:06 Dividing by a number by multiplying by its reciprocal
4:08 Division involving mixed numbers
14:00 Word Problems
23:29 Discussion of Exercises and Solutions

3 weeks, 6 days ago

In this video I project a 3D rectangle onto a 2D screen, while also removing a segment of a line that is behind the rectangle so that it maintains its 3D perspective. I first project the given 3D rectangle coordinates using the 3D to 2D projection equation I derived earlier. Then, I determine the point of intersection of the 3D rectangle and 3D line. The next point that is needed is the point of intersection of the projected 2D line and the bottom portion of the projected 2D rectangle. Once I solve for these, I use GeoGebra to plot the projected line while removing the portion that is behind the rectangle. The resulting 3D chart is truly amazing! https://www.geogebra.org/calculator/twezjbu5

The timestamps of key parts of the video are listed below:

- Question 4: Projecting a 3D rectangle to 2D: 0:00
- Solution: Graphing out the rectangle and its projection in GeoGebra: 1:04
- Remove the portion of the line behind the rectangle: 6:12
- Find point of intersection of the 3D line and rectangle: 7:15
- Determining the equation of the plane of the rectangle: 7:47
- Cross product to get the plane normal vector: 15:48
- Calculating the equation of the plane: 21:12
- Plugging in the line equation into the rectangle equation: 27:03
- Graphing the intersection point in GeoGebra: 32:18
- Finding the point of intersection of the projected line and rectangle: 35:03
- Vector equation of bottom right portion of projected rectangle: 38:08
- Equating the projected line equation with the bottom right rectangle line equation: 41:07
- Calculating the point of intersection of projected line and rectangle: 47:10
- Graphing it all out in GeoGebra: 50:30

This video was taken from my earlier video listed below:
p
- Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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4 weeks ago

Mirrored from / Original Video Source: Redacted - https://www.youtube.com/watch?v=SHLClkdrhes

My Channels:
NotMSM - https://rumble.com/c/c-2594130
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4 weeks ago
4 weeks ago
4 weeks ago

Coincidence ?

1 month ago

Here we have Donkey Kong jr. Math, NES, playthrough.

1 month ago

Lesson 32 Percents, pre Algebra, basic math skill

Contact email: [email protected]

Link to A+ Notes for Beginning Algebra

Link to Textbook Discussion, Practice problems, Solutions

1 month ago

Lesson 33 Percents and Decimals, pre Algebra, basic math skill

Contact email: [email protected]

Timestamps
0:00 Intro
0:30 General relationship between decimals and percents
1:14 Change percent to decimal
5:51 Change decimal to percent
8:17 Solving problems involving percents

Link to A+ Notes for Beginning Algebra

Link to Textbook Discussion, Practice problems, Solutions

1 month ago

In this video I quickly go over how to verify if our 3D to 2D projection is correct, which I do so by adding sight lines in GeoGebra. These "sight lines" are just lines drawn connecting the coordinates of the camera and the projected points on the screen. If these sight lines intersect our clipped points along the 3D line, then it means our projection is indeed correct. This is because the clipped points are simply projected along a straight line from the camera to the screen. In the amazing GeoGebra 3D graphing calculator, we can quickly create sight lines by using the line segment function: https://www.geogebra.org/calculator/twezjbu5

The timestamps of key parts of the video are listed below:

- Question 3: Verifying the Projection with Sight Lines: 0:00
- Solution: 0:18
- Adding sight lines with GeoGebra: 1:31

This video was taken from my earlier video listed below:

- Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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1 month ago

In this video I first derive the formula for projecting a 3D point to a 2D screen and then apply that formula to the 3D line from the previous question. To project a 3D image onto a 2D screen, we just have to draw a line extending from the camera or viewpoint that intersects our desired point and extends to the screen. Then applying similar triangles, we can derive the projected coordinates for the y and z coordinates; note that the x-coordinates in this case all get projected to x = 0. Next we apply the derived formula to the clipped 3D line points from Question 1 to obtain the projected coordinates on the 2D screen. And as always, I graph this all out using the amazing GeoGebra 3D graphing calculator: https://www.geogebra.org/calculator/twezjbu5

The timestamps of key parts of the video are listed below:

- Question 1: Projecting Clipped 3D Line to 2D: 0:00
- Solution: Deriving 3D to 2D projection equation: 0:12
- Applying similar triangles: 7:18
- Projecting the clipped points of the 3D line: 10:51
- Graphing with GeoGebra: 14:31

This video was taken from my earlier video listed below:

- Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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1 month ago

In this video I go over Question 1 of the Laboratory Project: Putting 3D in Perspective and this time determine the points at which a 3D line needs to be clipped before it is projected onto a 2D screen. To do this, I first obtain the equations of the 4 clipping planes which project from the point of view of the camera or eyes and unto the vertices of the projected screen. Then we can plug in the equation of the 3D line into each linear equation of the planes and obtain points at which the line and planes intersect. Graphing this out in the amazing GeoGebra 3D graphing calculator, it becomes clear that the line only needs to be clipped at the left and top clipping planes. This is an important exercise in the mathematics of projecting 3D images onto 2D screens, which are used throughout computer graphics programming.

Here is a link to GeoGebra if you want to play around with the projection: https://www.geogebra.org/calculator/twezjbu5

The timestamps of key parts of the video are listed below:

- Laboratory Project: Putting 3D in Perspective: 0:00
- Question 1: Clipping a 3D Line: 2:08
- Solution: Graphing out the question in GeoGebra: 2:38
- We need 4 clipping planes: 4:35
- Recap on the equations of lines and planes: 6:58
- Vector and Parametric Equations of the 3D line: 8:17
- Equation of the right clipping plane: 12:21
- Note on simplified vectors: 21:49
- Linear equation of the right clipping plane: 22:49
- Plugging in equation of a line into the equation of a plane: 24:30
- Plotting our right clipping plane in GeoGebra: 30:49
- Equation of the top clipping plane: 32:47
- Plugging in equation of a line into the equation of a plane: 40:46
- Equation of the left clipping plane: 47:13
- Plugging in L into the plane equation: 50:42
- Equation of the bottom clipping plane: 58:52
- Plugging in L into the plane equation: 1:01:04
- Summary: Line is clipped at left and top clipping planes: 1:03:08

This video was taken from my earlier video listed below:

- Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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1 month ago

In this video I go over the mathematics involved in computer graphics programming in order to clip and project a 3D image onto a 2D screen while still maintaining 3D perspective. This was taken from my Stewart Calculus book in the Laboratory Project titled Putting 3D in Perspective. Computer graphics programmers have to somehow display 3D images stored in memory onto a 2D screen for users to observe. To do this, the 3D images need to be projected from a point at which the camera or eye is viewing and then onto a 2D screen behind the object, while maintaining perspective. To do this, the equations of 4 clipping planes are first needed to be obtained to clip off the portions of image that will be beyond the projection. In this Project, I derive the clipping plane equations, as well as equations of a 3D line and 3D rectangle, and their their projected formulas. I also go over the concept of "hidden line rendering" to remove objects that are behind other 3D objects, thus saving computing power by not needing to project them onto the screen. And as always, I use the amazing GeoGebra 3D graphing calculator to plot out all the projections, and which you can play around with in this link: https://www.geogebra.org/calculator/twezjbu5

The topics covered as well as their timestamps are listed below.

- Introduction: 0:00
- Calculus Book Reference: 1:00
- Sections in Calculus Book Chapter: 1:14
- Topics to Cover: 2:02
- Laboratory Project: Putting 3D in Perspective: 2:54
- 4 Questions: 5:03
- Question 1: 8:10
- Equation of the 3D line: 13:00
- Equation of the Right Clipping Plane: 18:22
- Equation of the Top Clipping Plane: 38:49
- Equation of the Left Clipping Plane: 53:15
- Equation Bottom Clipping Plane: 1:04:55
- Summary: 1:09:10
- Question 2: 1:10:54
- Projecting 3D on to 2D: 1:12:13
- Question 3: 1:27:31
- Question 4: 1:29:39
- Point of Intersection of the Line and Rectangle: 1:36:56
- Point of Intersection of the Projected Line and Projected Rectangle: 2:04:43
- Graphing it All Out in GeoGebra 3D Graphing Calculator: 2:20:10
- Outro: 2:23:31

- PDF video notes: https://1drv.ms/b/s!As32ynv0LoaIirBjY_SU7z2CXBOG1A
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK
- Full Vectors and the Geometry of Space series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ

Related Videos:

- Vectors and the Geometry of Space: Equations of Lines and Planes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes .

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1 month, 1 week ago

In this video I go over a very unique problem on showing that the n-th partial sum of the harmonic series is NOT an integer. The harmonic series is the sum of the terms 1/i where i is a positive integer. To show that the partial sum is not an integer, we require some truly outside-of-the-box thinking, which fortunately for us is made easier with the given hint. To prove this, we first assume that the partial sum IS an integer and then observe what happens to 2 similar equations. The first is the multiplication of (the product of all odd integers less than or equal to n) * (the largest power of 2 that is less than or equal to n) * (partial sum). The second equation is the same as the first but with the assumption that the partial sum is an integer. After going over some very unique mathematical reasoning, I show that the left side of the equation is always odd while the right side is always even. This is a contradiction and thus the partial sum can not be an integer! Pretty epic brain twister!

The timestamps of key parts of the video are listed below:

- Problem 26: Partial Sum of Harmonic Series is NOT an Integer: 0:00
- Solution: 2:27
- Right side of hint equation is even: 4:16
- Left side of hint equation is odd: 7:23
- Checking when r is less than k: 13:41
- Checking when r = k: 16:56
- Summary: Partial Sum of Harmonic Series is NOT an integer: 20:45

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 1 week ago

Comparing oneself to High End-Figurines

Numberdamus369 is noticing some people are trying to compare themselves to these high-end figures. Do not put yourself in that position. None of us are on the same level as them. Nor do we want to be on that level. These groups are invitation only and none of us are invited to be in it. The only thing you are invited to is to check out thenumberdamus369.com for more videos on never seeing sports, politics, and world events the same again. Love your family, friends and most importantly. Love Christ. Do not love or worship idols. Those who continue to worship idols will have a very rude awakening coming to them because what the Devil does best that regular people are very bad at doing or nowhere near the same level as these cats are. Is knowing how to Plan, Plot, Strategize and Organize their next decisions. Do not value materialistic possessions more than Christ or your family and friends.

2. Do not put information out regarding your family or job status.
These videos are not about you, family, mental state, or job.
So don’t go throw each other under the bus. Your family, neighbor. Former classmates etc. Are not the problem. By bringing up something that is not related to content in the video one has already lost from the beginning.

3. All content in videos is take it or leave it material.
Numbers are not up for debate, discussion, advice, or
medical advice especially from those who have no due diligence on doing research prior to throwing up words on a comment hoping it sticks. Quit being a person who argues over a ham sandwich coming with 1 slice of ham instead of 2 its still a ham sandwich take it or leave it.

4. If one makes it obvious that they are offended or
chooses to be insulted by content that never insulted them or anyone in the first place. Numberdamus369 will make more videos on that subject. Numberdamus369 does find it funny seeing how emotionally weak some people are. All the numberdamus369 is doing is showing numbers it’s a different way of looking at things that is not attached to emotions or EGO. Numberdamus369 is letting you know in plain sight here that one’s ignorance or arrogance will be used against them. We don’t control the outcome and circumstances to the situations that these people, groups, government etc created to begin with. So why is one choosing to be insulted over something they have no control over?
Without the Noun person place or thing there is nothing to talk about. The Noun creates everything.

Insults

Quick reminder if one chooses to insult Numberdamus369 over the showing of numbers just know that you already lost once you insult.

Numberdamus369 does find it funny when people go right on to personally attack Numberdamus369 because there is no intelligence or intellectual abilities to back up the claims. Numbers didn’t insult one chooses to be insulted by numbers.

1 month, 1 week ago

In this video I go over an interesting math problem which involves differentiating 3 power series to find relationships among them in order to show the given equation is true. In order to differentiate power series, we first need to determine if the series are convergent, which I do so using the Ratio Test. Next we can differentiate the given equation and using our obtained relationships, can show that the equation equals a constant. Plugging in x = 0 into the equation, we can thus simply solve for this constant, and thus prove our given equation.

The timestamps of key parts of the video are listed below:

- Problem 25: 0:00
- Solution: Using the Ratio Test to determine convergence: 1:33
- Term by Term Differentiation: 8:35
- Differentiating the desired equation: 14:42
- Determining the constant that equals to the desired equation: 20:09

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 2 weeks ago

In this video I go over an in-depth derivation to determine an explicit formula for the n-th Fibonacci number. The Fibonacci sequence is the sequence of terms where the previous 2 numbers are added together. Prior to making this video, I had not known there was an explicit formula to determine any given number in the Fibonacci sequence. The derivation involves first determining the Maclaurin series for the given function by writing it out as a power series. Doing so yield the coefficients of the Maclaurin series to be just the Fibonacci numbers. The next part of the derivation is to solve for the series of the given function again but this time using a different method, by using partial fractions. This yields two partial fractions that are in the form of the sum of a convergent geometric series. Replacing the partial fractions with their corresponding Geometric series, simplifying the result, and comparing with our prior Maclaurin series, I note that we have in fact an explicit formula for the n-th Fibonacci number. Absolutely amazing and mind-boggling stuff!

The timestamps of key parts of the video are listed below:

- Problem 24: Series involving Fibonacci series: 0:00
- Solution to (a): The function as a Maclaurin series: 1:37
- Comparing coefficients of powers of x: 7:25
- Each coefficient is equal to the n-th Fibonacci number: 11:27
- Solution to (b): Explicit formula for the n-th Fibonacci number: 13:06
- Completing the square: 13:32
- Writing f(x) as partial fractions: 21:41
- Summary of f(x) as partial fractions: 29:13
- Partial fractions are in the form of the sum of a convergent geometric series: 35:15
- Simplifying the resulting series: 43:52
- Explicit formula for the n-th Fibonacci number: 49:24

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 2 weeks ago

In this video I show that the series whose terms are reciprocals of positive integers, excluding the digit 0, has a sum that is less than 90. This is a very interesting problem as it shows how seemingly arbitrary series can have very simple solutions. To solve this problem, I first group the terms of the series such that each group has the same number of digits in the denominator. Next, I count the number of terms in each grouping and find a general formula for the n-th group. I also note that each term (besides the first one) is less than 1/10^(n-1). From this we can write a formula for the sum of the infinite series, which turns out to be a convergent geometric series. This means we can simply use our formula for the convergent geometric series and obtain our final answer, which is the series is less than 90. Epic stuff!

The timestamps of key parts of the video are listed below:

- Problem 23: Sum of reciprocals of positive integers without the digit 0: 0:00
- Solution: Group the terms into number of digits: 0:25
- Each term is less than 1/10^(n-1): 5:26
- Max sum of each grouping: 7:18
- Sum of series is less than a convergent geometric series: 9:06
- Sum of series is less than 90: 10:35

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 2 weeks ago

In this video I construct an infinite series of right triangles rotated about a single point and show that the central angle diverges to infinity as the number of triangles approach infinity. To show this, I first construct a table determining the base lengths of each triangle using the Pythagorean Theorem to obtain a formula for the n-th triangle base. From this we can obtain the angle as a formula involving the inverse tangent trigonometric function. Applying the Limit Comparison Test with a diverge p-series, I show, using L'Hospital's Rule, that the angle series diverges, hence the angle approaches infinity as the number of triangles approach infinity. This means that the series of triangles makes infinitely many turns around the central point.

The timestamps of key parts of the video are listed below:

- Problem 22: Spiraling Triangles: 0:00
- Solution: Repeating Pythagorean Theorem: 1:16
- Formula for n-th Triangle: 5:16
- Limit Comparison Test: 8:57
- Comparing with a Divergent p-series: 10:21
- Applying the Limit Comparison Test with our original series: 14:36
- Recap on tan(x): 18:59
- Applying L'Hospital's Rule: 20:56
- The angle of the triangles diverges to infinity: 22:30
- Recap on the derivative of arctan(x): 23:11

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 2 weeks ago

In this video I find the solutions of an infinite Maclaurin cosine series when it equals to zero. Although we aren't given that the series is a Maclaurin cosine series, we can see this to be the case by looking at our table of common Maclaurin series and replacing the x terms with -x^2. Given the periodic nature of the cosine function, we get an infinite number of solutions as a function of any given integer. I also include an important note at the end of the video about keeping track of the negative signs when transforming functions, something that my Calculus book solutions manual forgot to do!

The timestamps of key parts of the video are listed below:

- Problem 21: 0:00
- Solution: Case where x ≥ 0 is not a solution: 0:31
- Maclaurin series for cos x : 1:24
- Solutions for cos x = 0: 4:54
- Solutions for f(x) = 0: 7:38
- Note on the Solutions Manual: 9:32

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 3 weeks ago

In this video I go over a pretty amazing infinite series and show, after an extensive math proof, that it equals to ln 2. The series is sum of the infinite terms that follow the pattern 1/(1*2) + 1/(3*4) + 1/(5*6) + ... etc., and somehow this equals to the simple answer of ln 2 or natural log of 2. While the proof is complicated, fortunately the problem has 4 parts to provide the steps to solving for the proof. The steps involve writing a geometric series as an integral and then determining an inequality from solving the definite integral from x = 0 to x = 2 which includes ln 2 in the result. Rearranging the inequality and we obtain our final answer of ln 2. Amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 20: 0:00
- Solution to (a): 1:48
- Solution to (b): 6:55
- Solution to (c): 11:54
- Solution to (d): 20:44
- Final answer: Sum of series is ln 2: 25:52

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 3 weeks ago

1 month, 3 weeks ago

In this video I go over the sum of an infinite series that can be solved by noting it is just the Maclaurin series for inverse tan for the angle π/6. Using exact trigonometric ratios, by splitting an equilateral triangle and applying the Pythagorean Theorem, I show that tan(π/6) = 1/sqrt(3). This means that the inverse tan or arctan(1/sqrt(3)) = π/6. Plugging this value into our earlier Maclaurin series for tan(x), we obtain a formula that includes are given series in the Problem, which we can solve fairly easily.

The timestamps of key parts of the video are listed below:

- Problem 19: 0:00
- Solution: Maclaurin series for arctan(x): 0:19
- Exact trig ratios triangle for tan(π/6) 2:45
- Series for arctan(1/sqrt(3)): 5:19
- Alternate form of the solution: 12:40

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 3 weeks ago

The problem we face is the younger generations are not being taught to do math, let alone to think. The overpopulation scam will gain in popularity and the fear will overcome the logic as usual. Then the dangerous order followers will gladly for a few bucks help kill off humanity.

1 month, 3 weeks ago

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1 month, 4 weeks ago

Click the link below to watch the full video.
https://youtu.be/n_cXrPPZaQc?si=bRQvmE7RHwYYTtnu

1 month, 4 weeks ago

In this video I solve for the center of a polygonal spiral that is constructed by drawing a line connecting, at first, the midpoint points of the sides of a square and then connecting the midpoints of the previous lines forming an infinite spiral. I then use mathematical induction to prove the given formula for the x terms, and do the same for similar y terms. Taking the limit as n approaches infinity, I show am able to determine the center of the polygonal spiral. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 18: Polygonal Spiral: 0:00
- Solution to (a): Equation for x terms: 2:24
- Using mathematical induction: 6:52
- Summarizing all the induction terms: 16:43
- Similarly, we can solve for the y terms: 19:45
- Solution to (b): Solving for the x coordinate at infinity: 23:00
- Solving for the y coordinate at infinity: 27:44
- Final answer: Coordinates at infinity: 28:58

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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1 month, 4 weeks ago

In this video I go over a pretty amazing math problem on finding the sum of a series that is defined by a simple recursive formula, and it somehow turns out to be the number e! A recursive function is such that it depends on a previous version of itself, hence each new iteration modifies the previous value before it. In this problem, a sequence is defined recursively and by using the principle of mathematical induction, I show that as the series approaches an infinite number of terms the sum of the series approaches the number e. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 16: Recursive Sequence: 0:00
- Solution: 0:56
- Mathematical induction: 6:45
- Solving for the general case: 7:52
- Series is equal to the number e: 14:05

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months ago

In this video I determine the limit that the area of an infinite number of circles that can be packed inside an equilateral triangle. I represent this area as a ratio of the area of the circles divided by the area of the triangle. To solve this problem, I first determine an expression for the radius of the circles in terms of the length of the triangle. I then count up the number of circles, and determine the equation of the area of n circles. Then, I plug in the length of the triangle as a function of the triangle's area. This then obtains a division of the area of the circles divided by the area of the triangles. Taking the limit as n, the number of rows of circles, approaches infinity, we then obtain the limit we were asked to find. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 15: Packing infinite circles inside an equilateral triangle: 0:00
- Solution: Area of an Equilateral Triangle: 1:24
- Area of the circles: 4:34
- Length in terms of 4 radii: 8:48
- Length in terms of n radii: 10:16
- Solving for radius in terms of the length: 13:06
- Counting the number of circles: 13:44
- Total area of the circles: 15:20
- Limit of area of circles divided by area of triangle: 20:02

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months ago

In this video I solve the division of two p-series and perform some truly amazing algebraic manipulations to simplify and solve the problem. I start off by realizing that the division involves absolutely convergent 2 p-series since p is greater than 1. If a series is absolutely convergent than it is also convergent, that is the alternating positive and negative signs won't affect the convergence. I perform some truly amazing algebraic manipulations on the top series to get it in the form of the bottom one, and which results in obtaining our starting expression. After some cancellations, we can then obtain a final simplified answer. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 14: 0:00
- Solution: 0:46
- NEXT LEVEL algebraic manipulation: 2:42
- Final answer: 11:31

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months ago

In this video I determine the volume of an infinite string of beads formed by rotating an exponential and trigonometric function about the x-axis. The presence of the sine trig function means that the resulting 3D solid shape has nodes with a value of 0, hence forms what appears to be beads on a string. I first use the formula for disks to determine the volume of one bead, and then use an online integral calculator to solve the resulting volume integral. To calculate the total volume of the infinite number of beads, I do so using 2 methods. The first is simply expanding out the series and realizing it has a telescoping sum, which obtains our answer. The second method involves rewriting the volume of the n-th bead in the form of a Geometric Series, and I show that it is convergent and hence we can plug in our geometric series sum formula to obtain the total volume. I also play around with the amazing GeoGebra graphing calculator and discuss how to graph in 3D using the formula of a circle and our given function as the radius. Epic stuff!

The timestamps of key parts of the video are listed below:

- Problem 13: Rotating a curve to form a 3D string of beads: 0:00
- Solution to Part (a): Volume of the n-th bead: 1:01
- Graphing in 3D with GeoGebra Graphing Calculator: 1:49
- Formula for disks: 6:27
- Using an online integral calculator: 11:19
- Solution to Part (b): Total Volume of Beads: Method 1: Telescoping Sum: 17:36
- Method 2: Geometric Series: 23:48

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months ago

In this video I go over the famous Book Stacking Problem, and show that it is possible to stack books that extend infinitely far away from the table! To do this you have to stack such that the first book extends 1/2 from the second book which extends 1/4 from the third which extends 1/6 from the 4th, and so one. Then the center of mass of the stack of books can be determined and shown to be still above the table, which means the books won't tip over. Lastly, I show that the series of distances 1/2 + 1/4 + 1/6 + ... etc. is a divergent Harmonic series, which means that the distance keeps extending out to infinity as we add more books. Try this yourself and let me know how many books, or playing cards, you can stack up!

The timestamps of key parts of the video are listed below:

- Problem 12: Book Stacking Problem: 0:00
- Solution: Book extending completely off the table: 1:57
- Center of mass of the stack of books: 7:20
- Center of mass doesn't extend past the table: 17:02
- Books can extend infinitely far via the divergent Harmonic series: 18:42

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 1 week ago

In this video I go over an infinite series that involves natural logarithms and can be solved by rearranging it into a form that allows for a Telescoping Sum to be applied. Recall that the Telescoping Sum is such that an infinite series has all terms cancel out except the first and the last term. When we rearrange, using log rules, the series, we see that it can be rewritten into terms whose individual terms are separate by an integer; which means they will cancel out with each successive series addition. Truly remarkable stuff!

The timestamps of key parts of the video are listed below:

- Problem 11: 0:00
- Solution: Simplifying using Logarithm Rules 0:18
- Telescoping Sum: 6:11
- Sum is - ln 2: 10:29

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 1 week ago

In this video I go over a seemingly complicated infinite limit and solve it by first considering a special simpler case. I show the simpler case is true and then follow the same steps to show the general case is also true. This type of problem solving technique is called "Using Analogy" and is very useful at getting a starting point when looking at problems that appear complicated. For example, if a question involves large numbers, we can start off by solving it for smaller numbers and hopefully it will give clues as to how to solve it for bigger numbers.

The timestamps of key parts of the video are listed below:

- Problem 10: 0:00
- Solution: Using an analogy: 0:56
- Special cases, k = 1 and k = 2: 2:15
- General case: 8:10
- Limit is equal to 0: 14:26

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 1 week ago

Whew, at first the topic was impenetrable to me. No-one actually EXPLAINS what I explain here, anywhere I looked. And I might be wrong. I tried many different ways, in the same way children learn, when they are not placed in child-prisons where they are forced to MEMORISE stuff to pass exams, with NO real interest in generating UNDERSTANDING, let alone the PERSONAL ABILITY TO LEARN. So let me know, if you know your Binary math : )

2 months, 1 week ago

In this video I go over the sum of an infinite series that involves taking multiple derivatives of the Geometric Series. Starting off with the Geometric Series for x^n, we can apply the derivative to it for its radius of convergence, as derived from my earlier video on Power Series. When taking derivatives, the Radius of Convergence remains the same but we still have to determine the endpoints separately. The series with the terms (n^3)x^n has a radius of convergence equal to 1 and diverges at the endpoints, that is it diverges at x = 1 and x = -1.

The timestamps of key parts of the video are listed below:

- Problem 9: 0:00
- Solution: Start with a Geometric Series: 0:20
- Differentiating with Quotient Rule: 6:42
- Radius of Convergence is 1: 16:40
- Checking for convergence at the endpoints: 18:18
- Endpoints diverge: 21:09

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 1 week ago

This is a must watch video, seriously...very short...no excuse, you MUST watch it...just too good to miss 3 mins but like a photo, worth a thousand words...no, worth a BILLION words...seriously ...

2 months, 1 week ago

In this video I derive a similar formula as in Problem 7 but this time use arccot or inverse cotangent. I then use that formula, as well as the useful method of the Telescoping Sum, to determine the sum of a series involving arccot and show that it equals to π/2.

The timestamps of key parts of the video are listed below:

- Problem 8: 0:00
- Solution to Part (a): 0:30
- Solution to Part (b): 18:11

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 1 week ago

In this video I go over a very long problem that involves first determining several arctan formulas and then using them to determine the value of the π up to 7 decimal places. One such formula is named after mathematician John Machin (1680 - 1751) whom used it to determine π correct to 100 decimal places well before the invention of computers. This method also involves using the Maclaurin series for arctan or inverse tan which I had derived in my earlier videos. With modern computers however, the value of π has been calculated to trillions of decimal places!

The timestamps of key parts of the video are listed below:

- Problem 7: 0:00
- Solution to Part (a): 2:10
- Solution to Part (b): 16:42
- Solution to Part (c): 24:24
- Solution to Part (d): 38:00
- Solution to Part (e): 50:06
- Solution to Part (f): Calculating π: 55:58

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 2 weeks ago

2 months, 3 weeks ago

In this video I go over a sequence which involves rotating triangles around a point and determining the limit of the inner angle of the triangles. To solve this I first use the Pythagorean Theorem to determine the square of the distance of one of the sides of the triangles, and then simplify it by noting it includes a geometric sum. Given that the other triangle side keeps doubling, we can thus determine a formula of the inner angle. Using exact trigonometric ratios, we can determine that the limit of the angle approaches 60 degrees.

The timestamps of key parts of the video are listed below:

- Problem 4: Find the Limit of the Angle in the Triangle: 0:00
- Solution: 1:31
- Pythagorean Theorem for the Square of the Length: 4:14
- Geometric Sum: 10:37
- Finite Geometric Sum: 12:34
- Calculating the Angle: 17:14
- Exact Trigonometric Ratios: 23:40
- Angle Approaches 60 Degrees: 25:22

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 4 weeks ago

In this video I go over a two-part problem that involves proving a trigonometric identity and then using that identity to find the sum of an infinite series. The trig identity involves a half angle tangent function. The infinite series involves solving with a telescoping sum and applying L'Hospital's Rule.

The timestamps of key parts of the video are listed below:

- Problem 3: 0:00
- Solution to (a): Prove the Trig Identity: 0:34
- Solution to (b): Sum of Series: 5:19
- Telescoping Sum: 11:39
- Applying L'Hospital's Rule: 21:29
- Putting it All Together: 24:30

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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2 months, 4 weeks ago

In this video I go over determining where a function, that is given in the form of a limit as n approaches infinity, is continuous. I solve this by using the problem-solving strategy of taking cases, in this case where the absolute value of x is less than 1, equal to 1, and greater than 1. Using our limit laws, as well as our previous r^n series, I show that the function is continuous for all values of x except at +/- 1.

The timestamps of key parts of the video are listed below:

- Problem 2: Where is f continuous?: 0:00
- Case (i): |x| is less than 1: 0:32
- Case (ii): |x| = 1: 4:27
- Case (iii): |x| is greater than 1: 6:21
- Putting it all together: 8:42

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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3 months ago

In this video I go over the Problems Plus example questions for the Infinite Sequences and Series chapter from my calculus book as well as provide a quick recap on Taylor and Maclaurin Series. The Problems Plus sections of my Stewart calculus book are much more difficult than typical problems, and require very good problem solving skills. In this example, I go over the sum of the infinite series (x+2)^n / (n+3)!. The solution to this problem involves comparing with the known Maclaurin series for the exponential function, and then modifying it to match our given example.

The timestamps of key parts of the video are listed below:

- Example: Find the Sum of the Series: 0:00
- Recap on Taylor Series: 0:29
- Example Looks Like Maclaurin Series for Exponential Function: 6:39
- Modifying Exponential Series to Match Example: 7:53
- Example Series Involves the Exponential Series Missing First 3 Terms: 13:28

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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3 months ago

Can anyone tell me what the design on the new ONE EURO coin represents? I find it oddly disturbing : )

3 months ago

watch the rest in my recently YouTube upload . This is the link https://youtu.be/D2v729rgHns?si=ULoVd4nyHJFCdTRc

3 months ago

We are a passionate team of ex-MOE Primary and Secondary school teachers and curriculum specialists. We specialize in Primary PSLE Mathematics and Science as well as Secondary GCE O-level E-Math, A-math and Chemistry.

3 months, 2 weeks ago

This is part 1 of the series on Transformations of Functions and in this video I look at transforming a basic function by vertically or horizontally shifting it. This is very useful for graphing and also to better understand how equations are written and their corresponding graphs.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiodo45BXtkWowIxNmw

Related Videos:

Transformations of Functions Part 2: Horizontal Stretching and Reflecting: http://youtu.be/8sUgreHjTt8
Transformations of Functions - Graphing Sine and Cosine Example: http://youtu.be/9stMcSBo2mo .

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3 months, 3 weeks ago

In this video I start off with the linear equation of a plane and go backwards to show that, if at least one of a, b, and c are not zero, then the equation does indeed represent a plane. I show this by first assuming a is not equal to zero and writing the d term as (a d/a). Then I rewrite the equation as a dot product and simplify it further to show that it is just the vector equation of a plane. This is a good exercise and checkup on our earlier derivation of the linear equation of a plane.

The timestamps of key parts of the video are listed below:

- Exercise 1 + Hint: 0:00
- Solution: 0:46
- Rewriting Equation as a Dot Product: 1:55
- Obtaining a Vector Equation of a Plane: 3:54

This video was taken from my earlier video listed below:

- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes

Related videos:

Vectors and the Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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3 months, 3 weeks ago

In this video I go over determining the distance between skew lines, which are lines that are not parallel and don't intersect. To determine this, we can first interpret the skew lines as being on two parallel planes. This just means that we need to determine a single normal vector that is perpendicular to both skew lines. Then, we can simply determine a point on the skew line / parallel plane and use our point-to-plane distance formula. I double check this, as per usual, with the amazing GeoGebra 3D graphing calculator. Note that GeoGebra uses a distance formula that requires knowing both equations of the parallel planes, which I determine the second equation at the end of the video. Here is the link to the GeoGebra calculator so you can play around with it: https://www.geogebra.org/calculator/kccatfbp

The timestamps of key parts of the video are listed below:

- Example 10: Distance Between Skew Lines: 0:00
- Applying the Distance Formula Between a Point and a Plane: 8:08
- Graphing with GeoGebra 3D Graphing Calculator: 12:32
- GeoGebra Distance Formula Requires Equations of Both Planes: 14:47

This video was taken from my earlier video listed below:

- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes

Related videos:

Vectors and the Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

------------------------------------------------------

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3 months, 3 weeks ago

In this video I go over an example on determining the distance between two parallel planes. The first step is to find a point on one of the planes and then next is to simply apply the distance formula between a point to a plane that I derived in my earlier video. I also double check the distance by calculating it using the amazing GeoGebra 3D graphing calculator, which you can play around with here: https://www.geogebra.org/calculator/zmwhau8b

The timestamps of key parts of the video are listed below:

- Example 9: Distance Between Parallel Planes: 0:00
- Applying the Distance Formula from a Point to a Plane: 1:57
- Calculating Distance with GeoGebra 3D Graphing Calculator: 6:35

This video was taken from my earlier video listed below:

- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes

Related videos:

Vectors and the Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

------------------------------------------------------

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3 months, 3 weeks ago

FULL LIVE STREAM: Mulberries, Math, Garden, Comics, Gambling, Entheogens, Consciousness, Food, Money, Investing [ASMR]
https://www.bitchute.com/video/Epjbwq2KYsD6/

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4 months ago

And God will make the guilty pay.

Retards always commit the strawman fallacy "You say math is bad!?"

No. I love math. It enabled me to fly across the world because airplanes require math to have been designed. What I hate is having to learn math I do not need to know.

"You stink at math!"

Yeah, 'cause I don't need that math in my life. Your AD HOMINEM fallacy proves you stink at logic.

4 months, 1 week ago

Sen. Brad Pfaff (D-Onalaska) went on the radio to bash the Republican tax cut plan and promote Gov. Evers’ 10% middle class tax cut plan.

The Republican plan would cut rates across all tax brackets. Evers’ plan would give a 10% tax cut only to individuals making \$100,000 or less and married couples making \$150,000 or less.

He argued that a married couple making \$150,000 would get a \$15,000 cut under Evers’ plan. That would only be true if they were paying 100% of their income in taxes.

A couple making \$150,000 currently pays about \$7,540 in Wisconsin state income taxes (gross). 10% would be \$754. (Under the Republican plan, that same couple should get a 14% cut).

5 months ago

A new set of low test scores by American 13-year-olds say quite a bit about the U.S. education system and can be attributed to both the missed education due to the misguided COVID lockdowns as well as the overall deliberate dumbing-down of our public schools. Dr. Jerome Corsi delves into this issue as a recent NAEP test given in Fall 2023 which focused on basic skills resulted in13-year-olds scoring an average of 256 out of 500 in reading, and 271 out of 500 in math, down from average scores of 260 in reading and 280 in math three years ago.
Also, while defenders of child transgender surgeries and puberty blockers flourish in the US, some European nations are reversing their formerly kiddie-trans treatment-friendly policies.

Dr. Corsi also breaks down:
The Dying US Housing Market
The Latest Climate Change Wealth Redistribution Scheme
The lack of results and action post-Durham ReportGet Dr. Corsi's new book with Swiss America

CEO Dean Heskin, How the Coming Global Crash Will Create a Historic Gold Rush: https://www.thetruthcentral.com/how-the-coming-global-crash-will-create-a-historic-gold-rush/

Follow Dr. Jerome Corsi on Twitter: @corsijerome1
Our website: https://www.thetruthcentral.com

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5 months, 1 week ago

5 months, 2 weeks ago

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5 months, 2 weeks ago

It is interesting when people are faced by the math.

Help Support the Channel:
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6 months, 1 week ago

I just share videos for the most these days. All created equal until we're not. I never thought to have to question the life of lies until a few decades ago, just lived my life. Now they keep acting like they have a right to tell me and others what we can say, I find that comical.
When a white person does a horrid crime many of us say kill it. When a black person commits a crime they get a riot and gofundme.
I still believe in the Constitution as written and no place in it says I have to pay attention to any of what these so called freak 'influencers' say is good for anyone's life. I do hope one day to see justice, at least in my dreams.

6 months, 1 week ago

VIDEO, Part1: Why You Should Never Drink Coca-Cola, Part 1: Coke Has a High Acidity Level With a pH of 2.5–2.7
https://www.bitchute.com/video/YAXi4yMdey4P/

Full Live Stream: Mapping Out Global Conflicts, Part 5: California, Sudan, Turkey, China, Europe (Geopolitics 24:42)
https://www.bitchute.com/video/z6qO3hag1yJ2/

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6 months, 1 week ago

Would you believe it if it you were told that understanding math is your birthright? Math is the language of the Universe and EVERYONE should be a math genius.

Jason Shurka had the privilege of having a very real conversation with Robert Edward Grant, and that conversation will not disappoint. This interview was one of the most thought provoking and important interviews seen in a long time. Starting with ancient Egyptians and changing directions in ways that one couldn't predict!

This interview is free for all on UNIFYD TV because of how powerful the message is. UNIFYD TV is a censorship-free, ad-free platform that is for the people, built by the people.

Watch this interview now on UNIFYD TV and become a member to unlock a jam-packed library full of interviews, meditations, courses and MORE just like this!
More information, interviews and so much more (7 day FREE TRIAL)
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6 months, 3 weeks ago

Full Live Stream: Happy 420 Live Stream Held on Thursday, April 20, 2023 [ASMR]
https://www.bitchute.com/video/qkjmlpwiGv1q/

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6 months, 3 weeks ago

Full Live Stream: Happy 420 Live Stream Held on Thursday, April 20, 2023 [ASMR]
https://www.bitchute.com/video/qkjmlpwiGv1q/

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PLAYLIST: ASMR Math

PLAYLIST: The Language of Mathematics

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***CRYPTO***
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
Doge (DOGE): D83vU3XP1SLogT5eC7tNNNVzw4fiRMFhog

Peace.

chycho

http://www.chycho.com

6 months, 3 weeks ago

Check out Aegora: https://aegora.jp/

First two hours or so are a good recap discussion about Euclid so far, and a
preview of where we're going. The third hour or so is an interesting, more
general discussion, the locus of which is the "measuring-your-goals" problem,
and how so many problems in the managerialist economy are downstream of this
simple epistemic mistake.

Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI44.html
GeoGebra: (none yet)

Discussion references:

Book 3 Prop 35: https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/propIII35.html
Book 3 Prop 35 lazy Geogebra: https://www.geogebra.org/m/w7nwsccg
MLB the Show glitches: https://youtube.com/playlist?list=PLeV-0tFYTT3EApfV0CEpY35wcYfQR7pH7
Ben Sparks math lover video: https://youtu.be/FFftmWSzgmk

00:00:00 Introduction
00:03:34 Back, reading proposition
00:20:04 The Roman Rapist Mindset, and Euclid versus FQA
00:24:24 The visual Euclidean algorithm
00:26:54 Rape of the Sabine Women
00:28:44 Craig speaks, shape rotators versus wordcels
00:31:24 The water glass thing
00:34:04 Craig ate breakfast today so he's not hungry, space walk
00:39:04 the math discord and my transition story
00:42:54 back to euclid
00:46:19 Roman therapy
00:48:14 No straight guy would be an effective OnlyFans whore pimp, extractive versus productive
00:55:54 Elon Musk is the ideal male
01:01:44 Chord product theorem (Book 3 Prop 35), future plans, and being rigorlicious
01:16:54 If the universe is a simulation, it's programmed by pajeets; MLB The Show; Wildberger meta-numbers
01:24:34 Baudrillard was right and mathematics is wrong
01:30:04 Continuing with Euclid
01:37:34 Euclid's broken parallel copy procedure; arrisu to bobbu; Euclid's original sin; iterated function systems
02:14:34 Arch appears; why Arch loves The Founder; Razib Khan
02:20:59 Is grooming good or bad?
02:22:04 Academia is the worst possible setting for creative work
02:25:34 The cup of water thing; Did Arch eat breakfast?; Craig Cannon on Gungans; MAID
02:40:34 French perfectionist culture; show your imperfect work
02:51:34 The measuring-your-goals problem; Daddy issues
03:08:34 Money is too cheap right now; crypto
03:15:34 Arch out
03:18:34 Aegora; my plan when I become dictator
03:22:04 Putin is demilitarizing the west
03:31:34 Fake sign language interpreters

Where to find me:

BitChute: https://www.bitchute.com/doctorajaykumar/
Blog: https://zxq9.com/archives/author/doctorajaykumar
Gab: https://gab.com/DoctorAjayKumar
GitLab: https://gitlab.com/DoctorAjayKumar
GeoGebra: https://www.geogebra.org/u/doctorajaykumar
Odysee (main): https://odysee.com/@DoctorAjayKumar
Odysee (podcast): https://odysee.com/@BigBlackCannon
Locals: https://orangepill.locals.com/
Minds: https://www.minds.com/doctorajaykumar/
Rumble (main): https://rumble.com/c/c-906055
Rumble (podcast): https://rumble.com/c/c-765395
Website: ht

7 months, 1 week ago

Understanding how to write the equation is most of the work. Once you have that, you solve for the unknown, using logarithms and of course inverse logs. Even if someone had this in college or high school, they likely forgot it. It's not difficult, but fewer than one in 10,000 people in the general population can do this level of math. To teach, is to learn twice, so help someone out by explaining this to them. Start with a question. See the blank stare. They don't understand. So explain it.

7 months, 2 weeks ago

"Math, Religion and Spirituality"
Enjoy this clip from Episode 657 of the #TinFoilHatPod with @samtripoli & Special Guests: Mark & Jonathan Emerson http://algebravictory.org/
Watch the full episode on Rokfin.com & tip some #RAEToken! https://rokfin.com/post/130956/657-The-War-On-Math-With-Mark-and-Jonathan-Emerson

7 months, 3 weeks ago

VIDEO SEGMENT: "Silicon Valley Bank Collapse, What To Know: SVB Bonds, Interest Rates, Bank Runs & Colorful People"
https://www.bitchute.com/video/zxLuS2gNl7PI/

▶️ Guilded Server: https://www.guilded.gg/chycho

PLAYLIST: Math, Drop in Tutoring Sessions: One-on-One Online Math Tutoring Sessions

PLAYLIST: ASMR Math

PLAYLIST: Personal Finance

***SUPPORT***
▶️ Patreon: https://www.patreon.com/chycho
▶️ Paypal: https://www.paypal.me/chycho
▶️ Substack: https://chycho.substack.com/
▶️ Subscribe Star: https://www.subscribestar.com/chycho
▶️ Streamlabs at: https://streamlabs.com/chycholive
▶️ ...and crypto, see below.

VIDEO: Watch This Video to Understand Current Events, Geopolitics, the Markets, Investing & more [ASMR, M1]
https://www.patreon.com/posts/47915415

VIDEO: Understanding Wall Street & the Action on GameStop: WallStreetBets, What it All Means (Live Segment)
https://www.patreon.com/posts/understanding-on-46870917

ARTICLE: 20 banks that are sitting on huge potential securities losses — as was SVB
https://www.marketwatch.com/story/20-banks-that-are-sitting-on-huge-potential-securities-lossesas-was-svb-c4bbcafa

FORUM POST: Nothing to see here, just a good olde fashioned Bank Run

INFO: SVB Securities Chief Administrative Officer Joseph Gentile

COLORFUL PEOPLE: Lulz from the SVB Website
https://www.2ndsmartestguyintheworld.com/p/lulz-from-the-svb-website

***WEBSITE***
▶️ Website: http://www.chycho.com

***LIVE STREAMING***
▶️ Twitch: https://www.twitch.tv/chycholive

***VIDEO PLATFORMS***
▶️ BitChute: https://www.bitchute.com/channel/chycho
▶️ Rumble: https://rumble.com/c/chycho
▶️ Odysee: https://odysee.com/\$/invite/@chycho:6
▶️ Twitch: https://www.twitch.tv/chycholive

***FORUM***
▶️ Guilded Server: https://www.guilded.gg/chycho

***SOCIAL MEDIA***
▶️ Minds: https://www.minds.com/chycho
▶️ Gab: https://gab.ai/chycho
▶️ Vk: https://vk.com/id580910394
▶️ Parler: https://parler.com/#/user/chycho
▶️ Gettr: https://gettr.com/user/chycho

***AUDIO/PODCASTS***
▶️ SoundCloud: https://soundcloud.com/chycho

***CRYPTO***
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
Doge (DOGE): D83vU3XP1SLogT5eC7tNNNVzw4fiRMFhog

Peace.

chycho

http://www.chycho.com

***PLAYLISTS***

Live Streams (Twitch)

Bitcoin, Blockchain, ICOs and Cryptocurrencies

Politics/Economics (Political Economy, Personal Finance)

ASMR - Autonomous Sensory Meridian Response

The Language of Mathematics

Math in Real Life

Peace,

chycho

http://www.chycho.com

.

8 months, 1 week ago

Full Live Stream: Investing & Personal Finance: SVB, Bank Runs, Inflation, Interest Rates, Crypto, CBDC, Collapse ASMR
https://www.bitchute.com/video/Lw3S4e9R6koc/

▶️ Guilded Server: https://www.guilded.gg/chycho

PLAYLIST: ASMR Math

PLAYLIST: ASMR - Autonomous Sensory Meridian Response

***SUPPORT***
▶️ Patreon: https://www.patreon.com/chycho
▶️ Paypal: https://www.paypal.me/chycho
▶️ Substack: https://chycho.substack.com/
▶️ Subscribe Star: https://www.subscribestar.com/chycho
▶️ Streamlabs at: https://streamlabs.com/chycholive
▶️ ...and crypto, see below.

***WEBSITE***
▶️ Website: http://www.chycho.com

***LIVE STREAMING***
▶️ Twitch: https://www.twitch.tv/chycholive

***VIDEO PLATFORMS***
▶️ BitChute: https://www.bitchute.com/channel/chycho
▶️ Rumble: https://rumble.com/c/chycho
▶️ Odysee: https://odysee.com/\$/invite/@chycho:6
▶️ Twitch: https://www.twitch.tv/chycholive

***FORUM***
▶️ Guilded Server: https://www.guilded.gg/chycho

***SOCIAL MEDIA***
▶️ Minds: https://www.minds.com/chycho
▶️ Gab: https://gab.ai/chycho
▶️ Vk: https://vk.com/id580910394
▶️ Parler: https://parler.com/#/user/chycho
▶️ Gettr: https://gettr.com/user/chycho

***AUDIO/PODCASTS***
▶️ SoundCloud: https://soundcloud.com/chycho

***CRYPTO***
▶️ As well as Cryptocurrencies:
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
Doge (DOGE): D83vU3XP1SLogT5eC7tNNNVzw4fiRMFhog

Peace.

chycho

http://www.chycho.com

8 months, 1 week ago

Full Live Stream: Investing & Personal Finance: SVB, Bank Runs, Inflation, Interest Rates, Crypto, CBDC, Collapse ASMR
https://www.bitchute.com/video/Lw3S4e9R6koc/

▶️ Guilded Server: https://www.guilded.gg/chycho

***SUPPORT***
▶️ Patreon: https://www.patreon.com/chycho
▶️ Paypal: https://www.paypal.me/chycho
▶️ Substack: https://chycho.substack.com/
▶️ Subscribe Star: https://www.subscribestar.com/chycho
▶️ Streamlabs at: https://streamlabs.com/chycholive
▶️ ...and crypto, see below.

***WEBSITE***
▶️ Website: http://www.chycho.com

***LIVE STREAMING***
▶️ Twitch: https://www.twitch.tv/chycholive

***VIDEO PLATFORMS***
▶️ BitChute: https://www.bitchute.com/channel/chycho
▶️ Rumble: https://rumble.com/c/chycho
▶️ Odysee: https://odysee.com/\$/invite/@chycho:6
▶️ Twitch: https://www.twitch.tv/chycholive

***FORUM***
▶️ Guilded Server: https://www.guilded.gg/chycho

***SOCIAL MEDIA***
▶️ Minds: https://www.minds.com/chycho
▶️ Gab: https://gab.ai/chycho
▶️ Vk: https://vk.com/id580910394
▶️ Parler: https://parler.com/#/user/chycho
▶️ Gettr: https://gettr.com/user/chycho

***AUDIO/PODCASTS***
▶️ SoundCloud: https://soundcloud.com/chycho

***CRYPTO***
▶️ As well as Cryptocurrencies:
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
Doge (DOGE): D83vU3XP1SLogT5eC7tNNNVzw4fiRMFhog

Peace.

chycho

http://www.chycho.com

8 months, 1 week ago

date of the very first C19 injection given to the public:
DEC 8, 2020 = 12 8 2020 = (12+8=20) 2020 can be rewritten as 202020 or XX XX XX in Roman numerals
XX represents the human female chromosome - is it a coincidence that the C19 injections cause sterility and miscarriages?
Dec 8 2020 was not just a random date chosen to start culling the world's population.

DAN 12:11  “And from the time that which is continual is taken away, and the abomination that lays waste is set up, is one thousand two hundred and ninety days."

" that which is continual" is human rebirth, regeneration & reproduction, and it is "taken away" by the injectable venom which is the "abomination that lays waste" which contains human stem cells from aborted fetuses, rotted animal cells, heavy metals, synthetic DNA, nanotech, hydra worms, etc.

I pity the fool who fell for this cheap trick because the injected will not go unpunished.

8 months, 3 weeks ago

Full Live Stream: ASMR Math Tutoring #83: Homeschooling, Political Mathematics, Trigonometry [SEE NOTE, CORRECTION]
https://www.bitchute.com/video/ouZxSrWDQhSc/

PLAYLIST: Trigonometry

PLAYLIST: Personal Finance

▶️ Guilded Server: https://www.guilded.gg/chycho

VIDEO: Personal Finance: Timing Markets, Time Frame, Risk Tolerance, Investing, Fractals [ASMR Math]
https://youtu.be/gJlOsjs4ZQU

PLAYLIST: ASMR Math

***SUPPORT***
▶️ Patreon: https://www.patreon.com/chycho
▶️ Paypal: https://www.paypal.me/chycho
▶️ Substack: https://chycho.substack.com/
▶️ Subscribe Star: https://www.subscribestar.com/chycho
▶️ Streamlabs at: https://streamlabs.com/chycholive
▶️ ...and crypto, see below.

***WEBSITE***
▶️ Website: http://www.chycho.com

***LIVE STREAMING***
▶️ Twitch: https://www.twitch.tv/chycholive

***VIDEO PLATFORMS***
▶️ BitChute: https://www.bitchute.com/channel/chycho
▶️ Rumble: https://rumble.com/c/chycho
▶️ Odysee: https://odysee.com/\$/invite/@chycho:6
▶️ Twitch: https://www.twitch.tv/chycholive

***FORUM***
▶️ Guilded Server: https://www.guilded.gg/chycho

***SOCIAL MEDIA***
▶️ Minds: https://www.minds.com/chycho
▶️ Gab: https://gab.ai/chycho
▶️ Vk: https://vk.com/id580910394
▶️ Parler: https://parler.com/#/user/chycho
▶️ Gettr: https://gettr.com/user/chycho

***AUDIO/PODCASTS***
▶️ SoundCloud: https://soundcloud.com/chycho

***CRYPTO***
▶️ As well as Cryptocurrencies:
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
Doge (DOGE): D83vU3XP1SLogT5eC7tNNNVzw4fiRMFhog

Peace.

chycho

http://www.chycho.com

***PLAYLISTS***

Live Streams (Twitch)

Bitcoin, Blockchain, ICOs and Cryptocurrencies

Politics/Economics (Political Economy, Personal Finance)

ASMR - Autonomous Sensory Meridian Response

The Language of Mathematics

Math in Real Life

Show and Tell (Collections)

In Conversation with chycho: Q&A

Peace,

chycho

http://www.chycho.com

.

8 months, 3 weeks ago

NOTE - CORRECTION: I Read the percentage data incorrectly from the website. The percentages are actually:
Lib: 32.6%, Con: 33.7%, NDP: 17.8%, Q: 7.6%, G: 2.3%, PPC: 5.0%
https://newsinteractives.cbc.ca/elections/federal/2021/results/

Full Live Stream: ASMR Math Tutoring #83: Homeschooling, Political Mathematics, Trigonometry [SEE NOTE, CORRECTION]
https://www.bitchute.com/video/ouZxSrWDQhSc/

▶️ Guilded Server: https://www.guilded.gg/chycho

VIDEO: ASMR Math: Election Statistics: California & Donald Trump, Understanding "Tyranny of the Majority"

***SUPPORT***
▶️ Patreon: https://www.patreon.com/chycho
▶️ Paypal: https://www.paypal.me/chycho
▶️ Substack: https://chycho.substack.com/
▶️ Subscribe Star: https://www.subscribestar.com/chycho
▶️ Streamlabs at: https://streamlabs.com/chycholive
▶️ ...and crypto, see below.

***WEBSITE***
▶️ Website: http://www.chycho.com

***LIVE STREAMING***
▶️ Twitch: https://www.twitch.tv/chycholive

***VIDEO PLATFORMS***
▶️ BitChute: https://www.bitchute.com/channel/chycho
▶️ Rumble: https://rumble.com/c/chycho
▶️ Odysee: https://odysee.com/\$/invite/@chycho:6
▶️ Twitch: https://www.twitch.tv/chycholive

***FORUM***
▶️ Guilded Server: https://www.guilded.gg/chycho

***SOCIAL MEDIA***
▶️ Minds: https://www.minds.com/chycho
▶️ Gab: https://gab.ai/chycho
▶️ Vk: https://vk.com/id580910394
▶️ Parler: https://parler.com/#/user/chycho
▶️ Gettr: https://gettr.com/user/chycho

***AUDIO/PODCASTS***
▶️ SoundCloud: https://soundcloud.com/chycho

***CRYPTO***
▶️ As well as Cryptocurrencies:
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
Doge (DOGE): D83vU3XP1SLogT5eC7tNNNVzw4fiRMFhog

Peace.

chycho

http://www.chycho.com

***PLAYLISTS***

Live Streams (Twitch)

Bitcoin, Blockchain, ICOs and Cryptocurrencies

Politics/Economics (Political Economy, Personal Finance)

ASMR - Autonomous Sensory Meridian Response

The Language of Mathematics

Math in Real Life

Show and Tell (Collections)

In Conversation with chycho: Q&A

Peace,

chycho

http://www.chycho.com

.

8 months, 3 weeks ago

math tricks

8 months, 3 weeks ago

NOTE - CORRECTION: I Read the percentage data incorrectly from the website. The percentages are actually:
Lib: 32.6%, Con: 33.7%, NDP: 17.8%, Q: 7.6%, G: 2.3%, PPC: 5.0%
https://newsinteractives.cbc.ca/elections/federal/2021/results/

▶️ Guilded Server: https://www.guilded.gg/chycho

***SUPPORT***
▶️ Patreon: https://www.patreon.com/chycho
▶️ Paypal: https://www.paypal.me/chycho
▶️ Substack: https://chycho.substack.com/
▶️ Subscribe Star: https://www.subscribestar.com/chycho
▶️ Streamlabs at: https://streamlabs.com/chycholive
▶️ ...and crypto, see below.

TIMESTAMPS:
- Snack for Today: Munching on Pomegranates (1:40-3:29)
- CensorTube Shadow-banning: You Want to Be on BitChute, Rumble and Odysee (3:30-5:00)
- Some Random Discussion
- Education Advice: Removed Children from Centralized Indoctrination Centers, Schools Destroying Children's Lives & Their Future Prospects (19:39-23:45)
- Fruit Picking Season Is Coming
- Decentralize Schooling, Destruction of Education: Woke Indoctrination Is Destroying Our Societies (25:46-31:14)
- Political Mathematics: Canadian Elections and the Illusion of Democracy [ASMR Math] (31:24-57:49)
- Protecting Our Societies from "Tyranny of the Majority": Understanding Democracy, Protecting the Minority (34:04-35:43)
- Protecting the Minority from the Majority, "Tyranny of the Majority": China & Indie Population vs the World Example [ASMR Math] (51:43-56:53)
- You Can Not Necessary Trust "the Science", We Need Data Integrity (1:00:32-1:02:09)
- Some Random Discussion
- Introduction to Trigonometry [ASMR Math] (1:16:07-2:04:12)

Playlist: Trigonometry

PLAYLIST: Investing & Personal Finance

PLAYLIST: Pomegranates (How to Eat )

VIDEO: Harvesting and Drying Mint

VIDEO: ASMR Math: Election Statistics: California & Donald Trump, Understanding "Tyranny of the Majority"

ARTICLE: Anomalies, Prisons, and Geophysics: How Governments Use Data and How to Stop Them
https://chycho.blogspot.com/2012/06/anomalies-prisons-and-geophysics-how.html

https://chycho.blogspot.com/2010/01/language-of-mathematics-table-of.html

https://chycho.blogspot.com/2015/03/asmr-math-introduction-and-table-of.html

***WEBSITE***
▶️ Website: http://www.chycho.com

***LIVE STREAMING***
▶️ Twitch: https://www.twitch.tv/chycholive

***VIDEO PLATFORMS***
▶️ BitChute: https://www.bitchute.com/channel/chycho
▶️ Rumble: https://rumble.com/c/chycho
▶️ Odysee: https://odysee.com/\$/invite/@chycho:6
▶️ Twitch: https://www.twitch.tv/chycholive

***FORUM***
▶️ Guilded Server: https://www.guilded.gg/chycho

***SOCIAL MEDIA***
▶️ Minds: https://www.minds.com/chycho
▶️ Gab: https://gab.ai/chycho
▶️ Vk: https://vk.com/id580910394
▶️ Parler: https://parler.com/#/user/chycho
▶️ Bitclout: https://bitclout.com/u/chycho
▶️ Gettr: https://gettr.com/user/chycho

***AUDIO/PODCASTS***
▶️ SoundCloud: https://soundcloud.com/chycho

***MARKETPLACE***
▶️ Ebay Page: https://www.ebay.ca/usr/chycho

***CRYPTO***
▶️ As well as Cryptocurrencies:
Bitcoin (BTC): 1Peam3sbV9EGAHr8mwUvrxrX8kToDz7eTE
Bitcoin Cash (BCH): 18KjJ4frBPkXcUrL2Fuesd7CFdvCY4q9wi
Ethereum (ETH): 0xCEC12Da3D582166afa8055137831404Ea7753FFd
Ethereum Classic (ETC): 0x348E8b9C0e7d71c32fB2a70DcABCB890b979441c
Litecoin (LTC): LLak2kfmtqoiQ5X4zhdFpwMvkDNPa4UhGA
Dash (DSH): XmHxibwbUW9MRu2b1oHSrL951yoMU6XPEN
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chycho

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Early Childhood Education: How to Teach Counting, Adding, Multiplication, Subtracting and Division

ASMR - Autonomous Sensory Meridian Response

The Language of Mathematics

Math in Real Life

8 months, 3 weeks ago

Are you struggling to understand Calculus, Algebra, or other Mathematics-related topics? Then Matchmaticians is the perfect platform for you! Matchmaticians is a California-based company that provides easy access to inspiring mathematical help. So whether you're stuck on Calculus derivatives or algebra equations, this platform can provide the answers and solutions for homework questions you need in no time.

At Matchmaticians, users can ask or answer math questions with ease. The questioner chooses a deadline and offers a bounty for receiving a complete answer before the deadline. If the answer gets disputed, it will be reviewed by a Matchmatician's judge. This process guarantees quick and accurate solutions so students can get through their college coursework without getting stuck on a particular topic.

Matchmaticians allows users to view public questions that have already been answered. Another great feature is that 20% of the sales bounty will be deposited into the questioner's and answerer's Matchmaticians accounts. So not only does this platform provide a great learning opportunity for students, but it also offers a reward for those who contribute to it.

Overall, online Matchmaticians provide an easy and convenient way for students to get help with their studies without spending too much time or money. With its fast and accurate solutions, rewarding system, and variety of options available - it's no surprise why this platform has become so popular among students. So if you're stuck on Calculus, Algebra, or any other subject - check out Matchmaticians for the help you need!

8 months, 3 weeks ago

Mirrored video, I did not make this video!

Alright, so this video (video only, no audio) shows some interesting proportions and calculations in regard to the Earth, Sun, and Moon.

Coincidence?

If anyone knows who made this video, if there are more in the series, please leave a comment. Thank you.

9 months, 1 week ago

your sister or singing might be flat ...but not the Earth
flat foot sally ...she died one sunday morning went out on the sea...never came back...riding the waves...she forgot her sextant...

9 months, 2 weeks ago

Full Live Stream: Tectonics, Earthquakes & Mapping Out Global Conflicts: Geology, Geophysics & Geopolitics [ASMR]
https://www.bitchute.com/video/dOxOldvKeKrq/

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The Language of Mathematics

Math in Real Life

9 months, 2 weeks ago

Video Description: In this video, Brandon Peterson talks about the MIRACLE that is the King James Bible and the MATHEMATICAL PERFECTION that is that book in the English language. Accompanied by Jason Walters and Robert Breaker, they look at a plethora of what some might call: "coincidences," but taken as a sum together, that PROVE without a doubt that GOD'S FINGERPRINTS are all over that book! And, he has given us his PERFECT WORD! A MUST-SEE VIDEO for all Christians, in order to see that GOD ONLY WROTE ONE BIBLE!!! And, any other versions that claims to be "God's word" is found "wanting" and "defective" and doesn't measure up to God's perfect standard!

ABC's of Salvation:

Admit you have made mistakes and ask forgiveness. "For all have sinned, and come short of the glory of God" - Romans 3:23

Believe that Jesus Died on the cross and rose again for you. "For God so loved the world that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." - John 3:16

Confess and commit yourself to a life of following Jesus. "That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved." - Romans 10:9

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9 months, 2 weeks ago

Archaix web site: https://archaix.com/
Archaix Community site: https://archaix.wiki/
Archaix Books: https://ebay.us/yyiqXo
Old 1700-1900 Books: https://ebay.us/oMJuGN
Source: https://youtu.be/XI_L3iPWcDE?t=3460

9 months, 2 weeks ago

Archaix web site: https://archaix.com/
Archaix Community site: https://archaix.wiki/
Archaix Books: https://ebay.us/yyiqXo
Old 1700-1900 Books: https://ebay.us/oMJuGN

"Over two years ago in my video the Archaix Paradox I explained that there is an anomaly in the structuring of our arithmetic.

Anyone can replicate this exercise to produce the exact same results, and can even choose any number they want. For controls, we can choose any number up to 10,000 [higher numbers are merely reduplications of lower numbers]. The formula is simple.

Subtract every number starting with the one you chose from its reverse, dropping the integer and only focusing on the number itself. Analyzing numbers as they reflect back on themselves. In the pinned comment and description box I posted this transcript and example of the formula so all can see and replicate.

For example, I choose 4798.

4798-8974 = 4176
4176-6714= 2538
2538-8352= 5814
5814-4185= 1629
1629-9261= 7632
7632-2367= 5265
5265--5625= 360
360-063= 297
297-792 = 495
495-594 = 99
99-99 = 0

I had chose 4798. But you can choose any number you want to from 2 to 10,000. Sticking with this formula you will find that 99% of all numbers will collapse to 0. Some will collapse almost instantly, others will go through several permutations like my example here. But 99% of them WILL collapse to zero.

So what of the 1% that don’t collapse to zero?

And herein lies the mystery. The 1% that do not collapse to zero will collapse to 2178. There are no exceptions.

The formula is simple and demonstrates that 99% of all numbers collapse to 0 upon reflection. But the 1% that don’t collapse to 2178.

So what’s so special about 2178? Let’s use the formula on 2178.

2178-8712= 6534.
6534-4356= 2178.

An unending loop. A reset, or reboot encoded within our arithmetic. A phenomenon that has never been addressed by the scientific community. Further, the reflective permutations of 2178 as seen here are all multiples of 2178-

4356 is 2178 x 2
6534 is 2178 x 3
8712 is 2178 x 4

A simple formula that can be replicated by everyone leads us to a number that does not collapse, but loops indefinitely, while all other numbers collapse to zero using the exact same formula. Therefore we have a demonstrable anomaly that has never been priorly discovered nor explained.

My interpretation is that we exist within a kind of mathematical construct, that it is limited, a sort of anti-arithmetic but patterned holographically and moored through a single ingress/egress point at the looping barrier that is 2178. Meaning, those who are inside this false mathematical Construct when this time comes are inside a system that perpetually resets or reboots, the holography starting its historical programming all over again.

But this revelation about the properties of 2178 leads us to another data set..."

9 months, 3 weeks ago

10 months ago