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Laboratory Project: Putting 3D in Perspective https://youtu.be/3txedAqdtkQ In this video I go over the math involved in computer graphics programming to project 3D images onto 2D screens while maintaining 3D perspective. - HIVE video notes - Video sections…
Vectors and the Geometry of Space: Cylinders and Quadric Surfaces https://youtu.be/k4EyLr4uOUA

In this video I explore the wonderful world of cylinders and quadric surfaces. Cylinders are defined as a 3D surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given plane curve. Quadric surfaces are the graphs of a second-degree equation in three variables x, y, and z.

Video notes - Video sections playlist - Vectors and the Geometry of Space playlist

#math #calculus #science #STEM #geometry
MES Links
Graphing an Ellipsoid in 3D https://youtu.be/30yEp-lSwM0 In this video I graph the Ellipsoid quadric surface, whose vertical and horizontal traces are all ellipses. #math #STEM #Geometry #science #GeoGebra
Graphing an Elliptic Paraboloid in 3D https://youtu.be/qIsgOTZSwwY

In this video I graph an elliptic paraboloid in 3D both manually as well as using the GeoGebra 3D graphing calculator. An elliptic paraboloid has vertical traces being parabolas and horizontal traces being ellipses.

#math #STEM #Geometry #science #GeoGebra
MES Links
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
Table of Computer Drawn Quadric Surfaces https://youtu.be/IJ0rl3jt_f4

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.

#math #geometry #science #STEM #GeoGebra
MES Links
Modeling Earth as an Ellipsoid https://youtu.be/N2HEZAjE54s In this video I model the Earth as an ellipsoid as used by the World Geodetic System of 1984 (WGS-84) since it is a more accurate model than a sphere. #math #geometry #Earth #science #GeoGebra
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.

#math #geometry #GeoGebra #STEM #education
MES Links
Vectors and the Geometry of Space: Cylinders and Quadric Surfaces https://youtu.be/k4EyLr4uOUA In this video I explore the wonderful world of cylinders and quadric surfaces. Cylinders are defined as a 3D surface that consists of all lines (called rulings)…
Vectors and the Geometry of Space: Review of Chapter https://youtu.be/VMKb69uDVt0

In this video I go over the end of chapter review questions covering the Vectors and the Geometry of Space chapter. There are 19 questions in total and serve as a good review on vectors, dot products, cross products, as well as the equations of lines, planes, and their applications.

#math #science #geometry #calculus #education