Exercise 3: Manually Graphing the Projection of the Trefoil Knot onto the xy-Plane https://youtu.be/2_Zp2N35lYQ

In this video I manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I also plot the trefoil knot in 3D using the amazing GeoGebra graphing calculator as well as the new Desmos' graphing calculator. 

#math #trefoilknot #geogebra #desmos #calculus

Example 7: Using Computers (GeoGebra) to Draw Space Curves https://youtu.be/aBuDScugCXA

In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroidal spiral, trefoil knot, and a twisted cubic.

#math #3D #spacecurves #GeoGebra #calculator

Problems Plus 6: Largest Sphere in a Sphere https://youtu.be/uefSE-rXFw4

In this video I find the largest sphere that passes through a given point while every point inside is also inside a larger sphere.

A Hyperbolic Paraboloid Can Be Generated by Straight lines https://youtu.be/-nxmXc1GD-U

In this video I show that a hyperbolic paraboloid can be generated entirely by two sets of lines, thus classifying it as a Ruled Surface. The only quadric surfaces that are ruled surfaces are cylinders, cones, and hyperboloids of one sheet.

Applications of Quadric Surfaces: Telescopes, Car Headlights, Microphones, Nuclear Power Plants https://youtu.be/ceWkMHHr5gw

In this video I go over a quick overview of some of the many applications of quadric surfaces.

Graphing a Hyperboloid of One Sheet in 3D https://youtu.be/a5SxZACKsoM

In this video I graph a Hyperboloid of One Sheet, which has horizontal traces being ellipses and vertical traces being hyperbolas. 

#math #geometry #GeoGebra #STEM #science