Why pi?

Vid Stanford hålls en årlig föreläsning av Donald Knuth. I år är det en 16e och den handlar om pi. Professor Knuth beskriver själv föreläsningen:

"Mathematicians have known for almost 300 years that the value of 'n factorial' (the product of the first n positive integers) is approximately equal to n/e to the nth power times the square root of 2(Pi)n, where Pi is the ratio of the circumference of a circle to its diameter. That's 'Stirling's approximation'. But it hasn't been clear why there is any connection whatever between circles and factorials;the appearance of Pi has seemed to be purely coincidental, one of the amazing accidents of nature. Recently however Johan Wästlund has found a nice explanation of this phenomenon, and the reason turns out to be connected with the theory of trees."

Läs mer, [Stanford university] ...

Se föreläsningen, [Stanford university] ...

Johan Wästlund, [Chalmers] ...