/sci/ - Science & Math

>>7502959

This is very good, and far more elegant than what I spent a long essay on. I started to have the idea that my proof was unnecessarily long once I caught wind of the idea that an Euler brick must have an odd edge length (which I don't know yet).

I'm with you up until the point where your a and c must both be even. What am I missing? I understand that your language is in terms of the exposition at

https://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple

I've already confused (Eu)ler and (Eu)clid myself at least once on this thought process. Apart from Eugene and Europe, "Eu" doesn't crop up in proper nouns too much in America. :^)

I have to internalize pic related, because along with babby-stuff (and "Ramiel" on the cover, referencing my octahedron thing), Sierpinski also leaves the work about showing the wiki Euler Brick properties to the reader (once context is built up). Having known this ahead of time might have rendered the above onerous process unnecessary, but I'm still pleased about the relationships in my result.