Discovery Project: The Geometry of a Tetrahedron
In this video I go over the Discovery Project titled The Geometry of a Tetrahedron. Discovery Projects are advanced math problems in each chapter of my calculus book, and this one is part of the Vectors and Geometry of Space chapter. This project involves 3 Questions regarding the tetrahedron, which is a triangular pyramid. The first question involves finding the areas of each triangular face using the Cross Product. The second question involves finding the volume of a tetrahedron when written in coordinate vector form. And the third question involves deriving the 3D version of the Pythagorean Theorem, which is: the 3 triangular areas squared at a vertex sum up to equal the square of the opposite triangular area!
The topics covered as well as their timestamps are listed below.
- Introduction: 0:00
- Calculus Book Reference: 0:56
- Sections in Calculus Book Chapter: 1:12
- Topics to Cover: 2:03
- Discovery Project: The Geometry of a Tetrahedron: 2:25
- 3 Questions: 3:05
- Question 1: 5:00
- Question 2: 34:59
- Solution to Part (a): 36:10
- The Equation of a Plane: 41:20
- The Distance from a Point to a Plane: 45:31
- Solution to Part (b): 52:43
- Solution to Part (a): 36:10
- Question 3: 1:05:35
Download video notes: https://1drv.ms/b/s!As32ynv0LoaIicNsAiLSiBI1ivS39w?e=V33CkF
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
View video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T
View the full Vectors and the Geometry of Space series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ
Related Videos:
The Cross Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
The Dot Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product
Complex Numbers as Rotation Matrices: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices
Vectors: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
3D Coordinate Systems: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems .
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In this video I go over the Discovery Project: The Geometry of a Tetrahedron, which is a triangular pyramid. I also derive its surface area, volume, and the 3D Pythagorean theorem in vector and coordinate form.
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
View video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T
View the full Vectors and the Geometry of Space series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ