Click to copy, then share by pasting into your messages, comments, social media posts and websites.
Click to copy, then add into your webpages so users can view and engage with this video from your site.
Report Content
We also accept reports via email. Please see the Guidelines Enforcement Process for instructions on how to make a request via email.
Thank you for submitting your report
We will investigate and take the appropriate action.
Discovery Project: The Geometry of a Tetrahedron
In this video I go over the Discovery Project titled The Geometry of a Tetrahedron. Discovery Projects are advanced math problems in each chapter of my calculus book, and this one is part of the Vectors and Geometry of Space chapter. This project involves 3 Questions regarding the tetrahedron, which is a triangular pyramid. The first question involves finding the areas of each triangular face using the Cross Product. The second question involves finding the volume of a tetrahedron when written in coordinate vector form. And the third question involves deriving the 3D version of the Pythagorean Theorem, which is: the 3 triangular areas squared at a vertex sum up to equal the square of the opposite triangular area!
The topics covered as well as their timestamps are listed below.
- Introduction: 0:00
- Calculus Book Reference: 0:56
- Sections in Calculus Book Chapter: 1:12
- Topics to Cover: 2:03
1. Discovery Project: The Geometry of a Tetrahedron: 2:25
2. 3 Questions: 3:05
- Question 1: 5:00
- Question 2: 34:59
- Solution to Part (a): 36:10
- The Equation of a Plane: 41:20
- The Distance from a Point to a Plane: 45:31
- Solution to Part (b): 52:43
- Question 3: 1:05:35
Download video notes: https://1drv.ms/b/s!As32ynv0LoaIicNsAiLSiBI1ivS39w?e=V33CkF
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
View video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T
View the full Vectors and the Geometry of Space series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ
Related Videos:
The Cross Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
The Dot Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product
Complex Numbers as Rotation Matrices: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices
Vectors: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
3D Coordinate Systems: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems .
------------------------------------------------------
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: [email protected]
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
Category | Education |
Sensitivity | Normal - Content that is suitable for ages 16 and over |
Playing Next
Related Videos
Introduction to Biology: Etymology and History
1 day, 15 hours ago
Jeff Behary's Electrotherapy Museum Full of Restored Tesla Coils
6 days, 14 hours ago
Warning - This video exceeds your sensitivity preference!
To dismiss this warning and continue to watch the video please click on the button below.
Note - Autoplay has been disabled for this video.