Reals: a Python library for real-number arithmetic
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'.
Lang's paper pentasia: https://langorigami.com/publication/paper-pentasia-an-aperiodic-surface-in-modular-origami/
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 https://link.springer.com/article/10.1007/s00283-021-10088-4 (Barry Cipra on the 1993 discovery of this surface with Conway) and https://langorigami.com/wp-content/uploads/2015/09/paper-pentasia.pdf (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 https://en.wikipedia.org/wiki/Poisson_point_process
The traditional images aren't of the Hilbert curve, but of one of the approximations that tend to it in the limit.
Even if you evenly space the points you don't get the traditional image.
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