Tuesday, November 19, 2013

Silent Running

The above screencast, by David Koski, was meant to have sound.

He narrated over the phone what was going on.

I thought I could keep it in my head, but the zig-zag pattern of three tetrahedrons in the frustum is frustrating to memorize.

Start with ye regular old tetrahedron then move a face outward from its opposite vertex to make the edges phi (1.618...) times what they were.

The three zig zag tetrahedrons inside are now 1/phi, 1, phi in ratio, where 1 = the volume of the original tetrahedron.

You may generalize this result to non-regular tetrahedrons.

Related reading:
Constructing the Desert Tetrahedron (Dec, 2013)
Multiplying Desert Tetrahedron by PHI (Dec, 2013)