User:2^67-1/New Hemipyth Nonsense

NO I AM NOT STARTING A CULT

Not coincidences

The 24-cell with side length 1: it only has lengths of sqrt(1), sqrt(2), sqrt(3), and sqrt(4) between any two distinct vertices.
- 96 sqrt(1) lengths, 72 sqrt(2) lengths, 96 sqrt(3) lengths, 12 sqrt(4) lengths (all 3-smooth numbers!)
- Total edge lengths are 96, total area is 24*sqrt(3), total cell volume is 8*sqrt(2), total volume is 2.
- Radius of sphere touching the middles of all the cells is sqrt(2)/2 or sqrt(1/2)
- Radius of sphere touching the middles of all the faces is sqrt(6)/3 or sqrt(2/3)
- Radius of sphere touching the middles of all the edges is sqrt(3)/2 or sqrt(3/4)
- Radius of sphere touching the vertices is 1 or sqrt(1)
Matt Parker calling 2 and 3 subprimes and 2 and 3 literally forming the bedrock of almost every 'natural' JI system (I agree with him)
The truncated Spiral of Theodorus up to the 1-sqrt(3)-2 triangle
Trigonometric ratios (Note the denominators of the sine and cosine fractions are all 3-smooth!):
- sin(pi/6) = cos(pi/3) = sqrt(1)/2 = 1/2
- sin(pi/4) = cos(pi/4) = sqrt(2)/2
- sin(pi/3) = cos(pi/6) = sqrt(3)/2