Thursday, October 09, 2008

Maths stuff from tweets coagulated

Can't wait for In Our Time's discussion of Gödel's theorem on Radio 4 later. Or maybe I can, can't decide

Appel & Haken's proof of the 4 colour theorem was done on a computer in 1976. In 1976 computer terminals had only two colours. Bollocks then

Prove this: there is (not) a number that contains, as contiguous strings, every number that comes before it (e.g. 126, contains 1,2,6,12,26)

For integers, it's easy

So what's the most a number can contain (as contiguous strings) of its predecessors

123456789101113141516171819202122242526272829303132333536373839404142434446... losing one each placeholder gone

write me an algorithm, I will reply with an aphorism, or an embolism

A number that contains (as contiguous strings) less than 32% of its predecessors, and is odd, is a prime number

Or isn't. Maybe it's 2%.

The sum of two squares is always less than one daddio

answer to previous mathematical question: 91

after 91, it gets weird, and the numbers are solutions to imaginary diophantine equations

this is what investment banking is based on

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