User:2^67-1/New Hemipyth Nonsense - Revision history

2^67-1 at 01:45, 26 April 2025

2025-04-26T01:45:10Z

← Older revision		Revision as of 01:45, 26 April 2025
Line 9:		Line 9:
	** Radius of sphere touching the vertices is 1 or sqrt(1)		** Radius of sphere touching the vertices is 1 or sqrt(1)
	* [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 up to the 1-sqrt(3)-2 triangle
	* Trigonometric ratios (Note the denominators of the sine and cosine fractions are all 3-smooth!):		* 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/6) = cos(pi/3) = sqrt(1)/2 = 1/2

2^67-1 at 01:40, 25 April 2025

2025-04-25T01:40:07Z

← Older revision		Revision as of 01:40, 25 April 2025
Line 4:		Line 4:
	** 96 sqrt(1) lengths, 72 sqrt(2) lengths, 96 sqrt(3) lengths, 12 sqrt(4) lengths (all 3-smooth numbers!)		** 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 24sqrt(3), total cell volume is 8sqrt(2), total volume is 2.		** Total edge lengths are 96, total area is 24sqrt(3), total cell volume is 8sqrt(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)
	* [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
	* Trigonometric ratios (Note the denominators of the sine and cosine fractions are all 3-smooth!):		* Trigonometric ratios (Note the denominators of the sine and cosine fractions are all 3-smooth!):
	** sin(pi/6) = cos(pi/3) = 1/2		** sin(pi/6) = cos(pi/3) = sqrt(1)/2 = 1/2
	** sin(pi/4) = cos(pi/4) = sqrt(2)/2		** sin(pi/4) = cos(pi/4) = sqrt(2)/2
	** sin(pi/3) = cos(pi/6) = sqrt(3)/2		** sin(pi/3) = cos(pi/6) = sqrt(3)/2

2^67-1 at 01:38, 25 April 2025

2025-04-25T01:38:08Z

← Older revision		Revision as of 01:38, 25 April 2025
Line 6:		Line 6:
	* [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
			* Trigonometric ratios (Note the denominators of the sine and cosine fractions are all 3-smooth!):
			** sin(pi/6) = cos(pi/3) = 1/2
			** sin(pi/4) = cos(pi/4) = sqrt(2)/2
			** sin(pi/3) = cos(pi/6) = sqrt(3)/2
	==Coincidences==		==Coincidences==
	* EulerGamma ≈ 1/sqrt(3)		* EulerGamma ≈ 1/sqrt(3)
	* QPochhammer[1/2] ≈ 1/sqrt(12)		* QPochhammer[1/2] ≈ 1/sqrt(12)

2^67-1 at 01:36, 25 April 2025

2025-04-25T01:36:38Z

← Older revision		Revision as of 01:36, 25 April 2025
Line 2:		Line 2:
	==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!)
	** ~~This implies the same property for the 16-cells with side~~ lengths ~~1 and~~ sqrt(2) ~~and~~ 8~~-cell~~ (~~tesseract~~) ~~with side length 1 as well~~,~~a s ewll as every other subset~~		** Total edge lengths are 96, total area is 24sqrt(3), total cell volume is 8sqrt(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

2^67-1 at 03:08, 7 April 2025

2025-04-07T03:08:27Z

← Older revision		Revision as of 03:08, 7 April 2025
Line 1:		Line 1:
	NO I AM NOT STARTING A CULT		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.		* 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
Line 6:		Line 6:
	* [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
			==Coincidences==
			* EulerGamma ≈ 1/sqrt(3)
			* QPochhammer[1/2] ≈ 1/sqrt(12)

2^67-1 at 02:10, 4 April 2025

2025-04-04T02:10:23Z

← Older revision		Revision as of 02:10, 4 April 2025
Line 3:		Line 3:
	* 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
	** This implies the same property for the 16-cells with side lengths 1 and sqrt(2) and 8-cell (tesseract) with side length 1 as well		** This implies the same property for the 16-cells with side lengths 1 and sqrt(2) and 8-cell (tesseract) with side length 1 as well,a s ewll as every other subset
	* [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

2^67-1 at 21:36, 2 April 2025

2025-04-02T21:36:56Z

← Older revision		Revision as of 21:36, 2 April 2025
Line 3:		Line 3:
	* 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
			** This implies the same property for the 16-cells with side lengths 1 and sqrt(2) and 8-cell (tesseract) with side length 1 as well
	* [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)

2^67-1 at 07:31, 6 February 2025

2025-02-06T07:31:27Z

← Older revision		Revision as of 07:31, 6 February 2025
Line 3:		Line 3:
	* 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
	* [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 ~~syatem~~		* [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)

2^67-1 at 07:28, 6 February 2025

2025-02-06T07:28:38Z

← Older revision		Revision as of 07:28, 6 February 2025
Line 1:		Line 1:
	I ~~challenge all of you XENners to find mathematical objects that bear some relation to hemipyth's ratios.~~		NO I AM NOT STARTING A CULT

	~~I'm going to start.~~
	* 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
			* [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 syatem

2^67-1: Created page with "I challenge all of you XENners to find mathematical objects that bear some relation to hemipyth's ratios. I'm going to start. * The 24-cell with side length 1: it only has le..."

2024-12-17T12:51:45Z

Created page with "I challenge all of you XENners to find mathematical objects that bear some relation to hemipyth's ratios. I'm going to start. * The 24-cell with side length 1: it only has le..."

New page

I challenge all of you XENners to find mathematical objects that bear some relation to hemipyth's ratios.

I'm going to start.
* 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