Ptolemy's value for Pi and Backhouse pancake functions.

Ptolemy's value 377/120 is a wonderful approximation of pi. We prove this using so-called pancake functions and calculus. And we are able to get nice bounds on the error of choosing 377/120 as an approximation for pi. We do all this WITHOUT knowing or assuming any kind of numerical value for pi at all.    • Pi is less than 22/7: the backwards advent...