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Graphing a Hyperbolic Paraboloid in 3D

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First published at 22:20 UTC on March 26th, 2024.

#math
#geometry
#science

Math Easy Solutions

MES

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In this video I graph a hyperbolic paraboloid, which is a surface that has vertical traces being parabolas, and horizontal traces being hyperbolas. After first obtaining the traces in 2D, I draw them out in 3D, and then combine them all together to form what looks like a horse's saddle. I also graph the hyperbolic paraboloid using the GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec

Time stamps:

- Example 5: Hyperbolic Paraboloid: 0:00
- Solution: Obtaining the traces: 0:10
- Drawing the family of traces: 1:41
- Vertical parabolas in x = k planes: 1:57
- Vertical parabolas in y = k planes: 5:50
- Horizontal hyperbolas in z = k planes: 9:08
- Better graphs from my Calculus book: 16:02
- Fitting traces together to form a Hyperbolic Paraboloid: 17:30
- Better graph from Calculus book: 20:06
- Graphing in GeoGebra: 20:17

Full video below:

- Cylinders and Quadric Surfaces: https://youtu.be/k4EyLr4uOUA
- HIVE video notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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