[-] wafergirl 1 points 1 year ago

Who is the artist that made this?

[-] wafergirl 1 points 1 year ago* (last edited 1 year ago)

I used Amazon basics, but that's because they were the only boyshorts on Amazon with an XXS small size. You may or may not need something that small, so you might want to experiment with sizes.

Edit: I think the size and material is much more important than the brand.

[-] wafergirl 1 points 1 year ago

One of my favorite little math gizmos is Pascal's triangle modulo 2. The most striking fact about it is that if you put each number in a box and color the 0 and 1 boxes two different colors, you'll find that the image converges to the famous fractal Sierpinski's triangle as you zoom out! Try looking up "pascal's triangle mod 2" in Google images or something so you can see for yourself! https://en.m.wikipedia.org/wiki/Sierpi%C5%84ski_triangle

But wait, there's more! If you read each row as a binary number, the rows will enumerate all possible products of Fermat numbers (numbers of the form 2^2^n + 1)! But this isn't restricted to just base 2! If you read the rows on the same triangle in base b, you'll get all possible products of the base b generalized Fermat numbers (which have the form b^2^n + 1)!

You might recognize the Fermat numbers from their role in compass and straightedge constructions, as prime Fermat numbers help describe which regular polygons are possible to construct with a compass and straightedge. Due to a few unrelated coincidences, this means that the first 32 rows of Pascal's triangle mod 2 read as binary numbers list out all currently known regular n-gons with odd n that are possible to construct with a compass and straightedge alone. Whether or not there are more is an open question!

[-] wafergirl 1 points 1 year ago

Math undergrad here. Can I ask what areas of algebra this shows up in?

[-] wafergirl 1 points 1 year ago

That's super interesting! Does this only work with holomorphic functions, or is there a broader class of functions that this works with?

[-] wafergirl 1 points 1 year ago

Yes, all of this is super cool! My favorite part, though, is the continuum hypothesis! A question that went unsolved for a long time is whether or not there exists a set with cardinality in between that of the natural numbers and the real numbers. This problem was eventually solved, and the answer is extremely interesting! The answer is not that the hypothesis is true or false, but that the hypothesis is independent from our currently accepted axioms of math. So, we could have a perfectly valid version of math where the hypothesis is true, as well as a perfectly valid version where it's false. This opens up a whole new world of possibilities for set theory, and there is still active research being done on the consequences that different axioms have on the relative sizes of uncountable cardinals that are less than or equal to the size of the reals.

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wafergirl

joined 1 year ago