Kneading Maths?

How 'bout some maths? (Experiments in math pedagogy)

[kneadingmaths]

Just an illustration of the standard analogy of gradient descent as mountain unclimbing.

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

[kneadingmaths]

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

[kneadingmaths]

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

[kneadingmaths]

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

[kneadingmaths]

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

[kneadingmaths]

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.)

[kneadingmaths]

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...

[kneadingmaths]

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!

[kneadingmaths]

There's a nifty trick to solve self-reciprocal polynomials! Did you know it?

[michaelrotonal]

"We can divide by zero"

are you sure about that, pink speech bubble

[kneadingmaths]

That is indeed wrong! A silly mistake on my part. Here's a brand new thing on the same topic (but without the mistake this time).

[kneadingmaths]

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

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

[kneadingmaths]

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".

[kneadingmaths]

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).

[kneadingmaths]

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

[kneadingmaths]

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

[kneadingmaths]

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