Juan Antonio
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nokyotsu.me
Juan Antonio
@nokyotsu.me
140 followers 430 following 39 posts
Geek de las matemáticas convertido en científico de cómputo—un entusiasta por la divulgación de la ciencia, la filosofía, el humanismo, y cosas … sobre todo cosas.

https://nokyotsu.com/me/es/
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nokyotsu.me
Turns out magic squares of squares are actually *easy* to find in most finite rings (called non-Parker). And the Parker rings (which do *not* work) are the harder ones to find!

Anyway, fun nice weekend project! Here is my code in case anyone cares: colab.research.google.com/drive/1luEjB...
Google Colab
colab.research.google.com
February 16, 2025 at 2:40 PM
nokyotsu.me
It was _only_ after writing my code that I bothered to look up "magic squares of squares in finite fields" and found a paper from 2019 (arxiv.org/abs/1908.03236 - with a much better algorithm!) and Matt Parker's video from 2021 (youtu.be/FCczHiXPVcA) discussing the idea of finite fields and rings.
Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares
We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular ...
arxiv.org
February 16, 2025 at 2:40 PM
nokyotsu.me
Lately I just scroll past posts on /the state of things/ ... it just keeps feeding the outrage and nothing comes out of it.

More cats and fun things is definitely why I'm here on Bluesky!
January 25, 2025 at 2:03 PM
nokyotsu.me
Indeed! Found about it from your interview on @andrewcopson.bsky.social 's "What I Believe". After reading the story about the Forelius pusillus ants, I just knew I had to know more!
January 23, 2025 at 6:52 PM
nokyotsu.me
By working together, the earliest humans were increasingly able to overcome the challenges that nature threw at them: food scarcity, water shortages, dangerous predators. But as a consequence, other humans became our primary threat. We were no longer battling against nature, but against each other. Cooperation is, at heart, a means by which entities improve their own position in the world. In other words, cooperation is favoured if and when it offers a better way to compete. A corollary of this is that cooperation frequently has victims.
January 20, 2025 at 7:41 PM
nokyotsu.me
Sometimes a male orb-weaving spider manages to force a copulation with a juvenile female, inserting both of his palps into the female's separate sperm- storage organs. If the male succeeds, something strange happens to him: his heart spontaneously stops beating and he dies in flagrante. Ancestral Homo may have looked much like you or I, but to the sabre-toothed cats and gigantic lions that prowled the savannah, I suspect that our human relatives probably looked a lot like lunch. A dominant male chimp rules by force. Dominance is taken and imposed upon others, against their will. But ancestral humans did things differently. In a world where anyone could hurl a stone or strike a spear from afar, brawn was no longer a viable means to wield authority. The mutiny had begun.
January 20, 2025 at 7:41 PM
nokyotsu.me
Interesante!
January 18, 2025 at 7:29 PM
nokyotsu.me
... and rearranged as a sum of cubes!
A sum of cubes 1^3 + 2^3 + ... + 9^3 = (1 + 2 + ... + 9)^2 = 45^2 = 2025.
January 6, 2025 at 10:45 AM
nokyotsu.me
Most interestingly, the square of a triangle number can always be broken up groups, ...
A square where each side is made of (1 + 2 + ... + 9) units. Therefore, the square has 45^2 = 2025 units total.
January 6, 2025 at 10:45 AM
nokyotsu.me
Calculating the sum of numbers from 1 to 9 is easy. If you duplicate the triangle, you obtain a 9 x 10 rectangle. So the sum must be (9 x 10) / 2 = 45.
A (9 + 8 + ... + 1) triangle on top of a (1 + 2 + ... + 9) triangle, forming a 9 x 10 rectangle.
January 6, 2025 at 10:45 AM
nokyotsu.me
Moreover, 45 is a triangle number. This means it can be arranged as a sum of consecutive numbers, looking like a triangle.
The sequence 1 + 2 + ... + 9 = 45 which looks like a triangle.
January 6, 2025 at 10:45 AM
nokyotsu.me
😧 I'm old! (1980)
December 31, 2024 at 2:32 PM
nokyotsu.me
Rolled the entire sequence of 419 digits! 🤣 Ha, no chance!

Good work by the way!
December 30, 2024 at 3:19 PM
nokyotsu.me
(And she's deputy editor at @ourworldindata.org, so she knows what she's talking about!)
December 24, 2024 at 8:57 PM
nokyotsu.me
Anyway, can't recommend enough @hannahritchie.bsky.social ”Not the End of the World”. For all of us dreading what the future may bring due to climate change; she brings some (data based!) rays of hope and focus on actions that can actually have an impact.
December 24, 2024 at 8:57 PM