Fun reddit thread about 'Junk Theorems'; mathematical statements that are only true because of the way we encode them in terms of set theory.

For example, 'An element of an integer is a topolgical space if and only if that integer is the graph of the successor function'.

reddit.com/r/math/comments/xki

Lang's paper pentasia: langorigami.com/publication/pa

The kite and dart Penrose tiling lifts to a surface in 3d with two equilateral triangles per tile, overhanging for the darts. Robert Lang made these nice physical models. Explanations at link.springer.com/article/10.1 (Barry Cipra on the 1993 discovery of this surface with Conway) and langorigami.com/wp-content/upl (Lang and Barry Hayes, also on a related 3d surface for the rhombic Penrose tiling).

Me: Can I have a random point, uniformly distributed over the plane?
Probablility theory: Sorry, there's no such thing.
Me: Can I have infinitely many of them?
Probability theory: Oh yah, no problem en.wikipedia.org/wiki/Poisson_

The traditional images aren't of the Hilbert curve, but of one of the approximations that tend to it in the limit.

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Hilbert's space filling curve evaluated at 2048 uniformly random points.

Mathstodon

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