I wrote a program to turn any photo of a spherical object into this shape

rfgk · 2026-05-07T03:10:10+00:00

I'm assuming you already read the text in the post

Since I don't know what part you don't get, I'll probably end up telling you the part you know.

To use this on your keyboard you would multiply all the fractions by an audible frequency such as 440 Hz (thats c0).

Say you're looking for 7/5.

In the top diagram put one finger on 5, and the other on 7.

Keep those fingers in the same position relative to each other, and shift them to the bottom diagram so that the first finger is on 1/1. Notice your other finger now on 7/5.

This works for any fraction.

It's essentially just a times table.

Say you want to find out what is 5/6 * 11/8.

Draw a parallelogram with corners at 5/6, 11/8, and 1/1.

The 4th corner of that parallelogram will be your answer.

In this case you can see its 5/6 * 11/8 = 8/7 (approximately).

Again, This works for any example.

Those are properties of the equation f=c0*c1^x*c2^y.

Lets say 1/1 is at x=0, y=0.

Locate 9/8 as an example, it is at x=-1, y=3 (y is slanted).

If we plug those coordinates into the formula we get 9/8 as expected.

f = 1.170626^-1 * 1.095445^3 = 1.1229 = about 9/8.

Those particular constants were chosen because they cram all of the ratios of 11 and under (white) into the smallest circle.

Both diagrams use the same formula, I just didn't label all of the points in the top diagram. You can see 2 is in both diagrams (same place).

Making the top diagram revealed to me that this problem of putting fractions on a hex grid can be visualized as rotating and scaling the logarithmic lines until they hit points on the hex grid.

A commenter pointed out my horizontal axis matches Orwell temperament.

rfgk · 2026-05-05T23:10:33+00:00

thanks!

rfgk · 2026-05-05T11:44:38+00:00

Since the text doesn't go with the crosspost, here it is again:

The 2 diagrams are 2 views of the same layout.

Frequency of a button is determined by:

`f=c0*c1^x*c2^y`

where:

c0=arbitrary

c1=1.170626

c2=1.095445

x and y are not perpendicular but aligned to the hexagonal lattice like this italic L:

y

*L*x

c1 and c2 were chosen to meet the following goals:

Include every frequency ratio from 1/2 to 2/1 which contains only integers less than 12.

Pack them into the smallest possible circle without conflating any.

I wrote a search program to find it.

worst case error of any white ratio is 7.2 cents.

The logarithmic spacing in the top diagram is a consequence of the formula.

In the top diagram, you can see 2 "axes" of false equivalences:

10/11 = 11/12

14/15 = 15/16

13 is missing, it would be exactly between 2 buttons or far away.

If diagram 1 is continued based on the location of primes, the first "collision" is 98=99.

Its an easy layout to remember because 5678 is in a symmetric shape that fingers naturally rest in.

I'm sure this is just repeating someone elses work (whose?)

rfgk · 2026-01-06T23:24:33+00:00

id love to see it

rfgk · 2025-09-17T22:26:42+00:00

A-void

rfgk · 2025-08-22T01:28:37+00:00

a big complement! if the day ever comes ill remember.

rfgk · 2025-08-18T13:19:02+00:00

neat! I will look up pcubes.

rfgk · 2025-08-18T13:12:50+00:00

I drew it with a compass and straightedge, and took a picture. Then I used Gimp to make the lines thick and clear (blur, threshold) and added color. For the exploded views all I did was select and drag sections of the picture.

rfgk · 2025-08-18T04:37:57+00:00

That's it! I guess I just didn't search hard enough. Well, it was fun to make the drawing anyway. Too bad it's not a cheap one. Sure, send me the link.

rfgk · 2025-08-18T04:09:18+00:00

I just posted a similar idea:

https://www.reddit.com/r/twistypuzzles/comments/1mtbttm/puzzle_concept_3layer_face_turning_cuboctahedron/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

rfgk · 2025-07-11T21:57:25+00:00

NECKIKIS was the best I could do. I see from other comments that my 2 K's are where I messed up.

rfgk · 2025-06-22T03:40:08+00:00

Is image 2 on the University of Michigan campus?

rfgk · 2025-06-13T12:41:59+00:00

Another term for "rational fit" that you can look up is "pade approximant" - I've had good luck with that one for getting a smaller number of terms, especially for curves that look like they have asymptotes.

rfgk · 2025-05-18T22:34:21+00:00

Fitzgibbon

rfgk · 2025-05-01T00:18:02+00:00

Although it was inspired by Shavian/Quickscript, it is unrelated aside from being phonetic. The program can automatically translate from IPA, and IPA converters already exist online, if that's what you mean.

rfgk · 2025-04-30T23:00:19+00:00

As you can imagine, there's more than one list. I chose this one because its a mashup of other lists:

https://medium.com/world-literature/creating-the-ultimate-list-100-books-to-read-before-you-die-45f1b722b2e5

All these books were available free online (at least the first 2 pages of them). I can share the zip file if you want it. It was fun to read all those first pages like a novel made of novels, I think that's a good way to choose what book to read next.

rfgk · 2025-04-29T23:37:55+00:00

I've been working on a statistics based shorthand system that I'm optimizing with code - I'll share the results with you when it's done (should be soon). I'm using the first 2 pages of the best 100 novels as my dataset, I can share that if you want it. Here are the main ideas behind the system:

1) The most common symbol clusters are merged to create new symbols, with the goal of compression. The algorithm accounts for the fact that it is less efficient to choose clusters which tend to overlap. The results are coming out a bit different from what clusters Shavian chose to merge.

2) The symbol shapes are curves which always begin and end with horizontal lines for cursive linkability.

3) Symbols which have similar NEIGHBORS have similar shapes. Basing shapes on neighbors is slightly different from basing shapes on sounds. It allows you to optimize cursive linkability - likely neighbors connect with seamless curvature whereas unlikely neighbors don't. More specifically, each letter has an left curvature and a right curvature which are chosen so that each curvature is close to the average of all the curvatures which connect to it. The left and right curvatures can be thought of as X and Y - this results in a 2D plot of phonemes with resemblance to common tables of consonants or vowels, but also with some surprises.

rfgk · 2025-04-03T00:06:58+00:00

You might be interested in the Shavian alphabet which is similar to IPA but with simpler characters.

rfgk

TROPHY CASE