Geometry of a Tetrahedron: Question 1: Calculating Area with Cross Products
In this video I go over Question 1 of the Discovery Project: Geometry of a Tetrahedron. In this question, we are asked to show that the 4 vectors pointing away from the tetrahedron and with lengths equal to the area of the opposite facing triangles all sum up to equal the 0 vector. In solving this question, I calculate the vectors as cross products, and their lengths as half the length of the cross products. However, for the direction of the resulting cross product vectors, I ensure they are indeed in the direction opposite of the triangular face, so I make the vector components positive or negative accordingly.
This video was taken from my earlier video listed below:
- Discovery Project: The Geometry of a Tetrahedron: https://youtu.be/yRws7Jk2iHU
- Video notes: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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This video was taken from my earlier video listed below:
Hi friend, thanks for educating us and teaching us the interaction of the vectors involved in the geometry of a tetrahedron.
Regards
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Hi Mathew, let me thank you for the support you have shown on my post featuring a video on about how to store NFTs as pixel art that scales a thousands years, this document explain what it can avoid facing AI threaths of details recognition and profile assessment and also why it features yet a high quality visual potential yet even if it stays low-weight images, it explains everything and it might well be made especially for your interest and curiosity you've shown to pixa's system. https://github.com/pixa-pics/pixa-pics.github.io/blob/main/1000%20Years%20ready%20NFTs%20-%20Handbook.pdf
Hi Mathew, let me thank you for the support you have shown on my post featuring a video on about how to store NFTs as pixel art that scales a thousands years, this document explain what it can avoid facing AI threaths of details recognition and profile assessment and also why it features yet a high quality visual potential yet even if it stays low-weight images, it explains everything and it might well be made especially for your interest and curiosity you've shown to pixa's system. https://github.com/pixa-pics/pixa-pics.github.io/blob/main/1000%20Years%20ready%20NFTs%20-%20Handbook.pdf
EDIT:
data:image/png;base64,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
Wow that is interesting! Sounds like a great idea to store images for the long term and still be upscaled without quality loss! wow!