User:2^67-1/New Hemipyth Nonsense: Difference between revisions
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==Not coincidences== | ==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. | * 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 | ** 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. | ||
* [https://www.youtube.com/watch?v=ZMkIiFs35HQ 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) | * [https://www.youtube.com/watch?v=ZMkIiFs35HQ 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 | * The truncated Spiral of Theodorus | ||
Revision as of 01:36, 25 April 2025
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.
- 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
Coincidences
- EulerGamma ≈ 1/sqrt(3)
- QPochhammer[1/2] ≈ 1/sqrt(12)