another christmas cracker

Definitions that give the value of PI

pie is always valuable

One fun way to express Pi is in terms of the success probability of certain geometric experiments.  The classic one is tossing a needle onto the floor “at random” and asking, what's the probability it crosses between two floorboards?

https://en.wikipedia.org/wiki/Buffon%27s_needle_problem

People love asking “What is Pi?“, but has anyone ever asked “How is Pi?”

Pi is half of the whole it should be.

The strangest way I know to get decimals of Pi, through counting collisions of blocks: https://www.youtube.com/watch?v=jsYwFizhncE 3Blue1Brown video.

Another strange fact that maybe aliens would not discover is the BBP formula allowing to compute the hexadecimal digits of Pi, one by one:  https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula

to calculate the area of a pie, remember pie are square

Carroll, so for n digits of accuracy using a base B numbering system, the ratio of masses must be B^{n and the total number of adiabatic collisions is always floor(pi*(B}n)). Of course B is usually 10.

@David there is a sqrt in the mass ratio: sqrt(m2/m1) so if m2 is B^{n and m1 is 1 we get B}(n/2) hence floor(pi*(B^(n/2)).