Kneading Maths?

(Also, sorry for yesterday's accidental reblog…)

One of those occurrences where mathematics makes use of a German word!

Your Cartesian coordinates won't be able to describe the world well when you'll be a bird, flying through the morning breeze

There are quite a few fractals that are shaped like snowflakes; here are three of them.

How do you reliably convey information when your pathway has noise in it (be it electrical... or acoustic)? Error-correcting codes provide an answer. (Sidenote: this illustrates a linear error-correcting code in particular.)

Happy new year! Hypergraphs are a generalization of graphs; trying to count hyperforests without seeds (i.e. without isolated nodes) leads to this integer sequence, containing 2026...

How do you construct a pentagon? There are some well-known constructions. But what we're illustrating here, is how we can use algebra to figure out a (non-optimal) construction!

A very standard combinatorics problem about counting paths. Well then, how many?

Happy new square! This year, don't forget to end your proofs with not just a simple square, but with this elusive square year.

Last one for this year. Fermat strikes again! A new statement without proof; lucky for us, many proofs have been found, including a version "Proved on a Chessboard".

Heavily based on this article by Bill Casselman, and its follow-up. Of course, the recent Veritasium video is a great introduction to rainbows (and a good way to uncover the simplifications made here).

Nowadays, both Fermat's little theorem and Wilson's theorem are proved using group theory. It doesn't have to be that way!

Do you know why you might find the word witch in maths dictionaries?

When planning a (long) flight, maps may deceive you!