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

Graphing a Hyperboloid of Two Sheets in 3D https://youtu.be/MCSeF52Kn20

In this video I sketch a hyperboloid of two sheets, which is a quadric surface with horizontal traces being hyperbolas while vertical traces are comprised of both hyperbolas and ellipses.

#math #geometry #science #GeoGebra #STEM

Graphing a Shifted Elliptic Paraboloid in 3D https://youtu.be/d5FrR07zAHQ

In this video I graph a shifted and horizontal elliptic paraboloid, which is a quadric surface that opens up along parabolic traces while the cross-section has elliptical traces.

#math #GeoGebra #science #Geometry #STEM

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.

#math #geometry #GeoGebra #STEM #education

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

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

Scalar and Vector Projections: Formulas and Diagrams https://youtu.be/A_cwD8ck2ps

In this video I go over a quick review of the formulas for the scalar and vector projections of one vector onto another, as well as showing their visual representations.

#math #science #geometry #education #STEM

The Cross Product and its Useful Properties https://youtu.be/8GgG-1O_WvU

In this video I go over a review of the cross product, its definition and formulas, as well its many useful applications in mathematics and physics.

#math #science #education #geometry #STEM

Calculating Area of a Parallelogram and Volume of Parallelepiped with the Cross Product https://youtu.be/6wuT6abp-vo

In this video I show how the cross product can be used to determine the area of a parallelogram and the volume of a parallelepiped.

#math #science #education #geometry #STEM

Finding the Normal or Perpendicular Vector of a Plane https://youtu.be/As_Z3nqWk4Y

In this video I show that the cross product of two non-parallel vectors on a plane obtains a vector perpendicular to that plane, and is called the normal vector.

#math #science #education #STEM #geometry