Today is my birthday! Please tell me fun maths facts
@christianp Can’t really think of a *fun* maths fact off the top of my head, but happy birthday to you!!
@christianp Happy Birthday.. My current favourite is the Banach Fixed point theorem.. Which (i think!) says if you lay a map of your home on the floor of your home, one point of the map is exactly above the same point in your home.
Also the Curry-Howard correspondence.
@kat ahh, I set a puzzle for New Scientist using that theorem, but it was a bit too wordy so I think it's being saved for a Christmas issue or omnibus book or something
@christianp Students learning their multiplication tables often use the consecutive digits in the products \(12=3\times4\) and \(56=7\times 8\) as a memory aid. Base 10 is the only base that has any "multiplication facts" of the form \(d_1d_2 = d_3\times d_4\) with the d's consecutive digits.
Base 16 does admit a cute additive identity, \(12 = 3+4+5+6\).
@christianp happy birthday!
I read that:
2021 is the smallest natural number that can be expressed as the product of two consecutive primes.
2021 produces a palindrome when multiplied by its reverse, 1202
The 2021th digit of π, e and φ all equal 3.
@christianp Consider the following sequence of rational numbers: 7/3, 99/98, 13/49, 39/35, 36/91, 10/143, 49/13, 7/11, 1/2, 91/1.
Starting with n_0=10 let nᵢ₊₁=nᵢ*p/q, with p/q being the first fraction in above sequence, such that nᵢ*p/q is an integer. Then the exponents of the powers of 10 generated by this are successive primes.
(taken from https://esolangs.org/wiki/Fractran)
@christianp The attached figure shows two pentagons inscribed in each other: each vertex of one pentagon lies on a line through a side of the other pentagon. You can't do this with quadrilaterals in the Euclidean plane, but you can in the complex projective plane: see https://en.wikipedia.org/wiki/M%C3%B6bius%E2%80%93Kantor_configuration
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