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Table of Computer Drawn Quadric Surfaces

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First published at 03:01 UTC on March 29th, 2024.

#math
#geometry
#science

Math Easy Solutions

MES

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In this video I go over a table of 6 basic quadric surfaces with computer-drawn graphs: ellipsoid, elliptic paraboloid, hyperbolic paraboloid, cone, hyperboloid of one sheet, and a hyperboloid of two sheets. I also discuss their formulas and what happens when the variables change. All the shown graphs are symmetric about the z-axis but the equations can be modified to make it symmetric about a different axis. I have plotted all these surfaces on the GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec

Computers typically draw these surfaces by using 2D traces along vertical planes spaced at even intervals. Parts of the graph (those in the background) are then removed using hidden line removal techniques: https://youtu.be/JS1bbyvdhsA

Time stamps:

- Computer-Drawn Graphs of Quadric Surfaces: 0:00
- Table 1: Six Basic Quadric Surfaces 0:37
- Ellipsoid: 1:04
- Elliptic Paraboloid: 1:30
- Hyperbolic Paraboloid: 2:00
- Cone: 3:08
- Hyperboloid of One Sheet: 4:20
- Hyperboloid of Two Sheets: 4:50

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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