Extracting Pi from Image Data

In 1881, Ernesto Cesàro[1] proved that the probability that two random integers are relatively prime is

6/

2

π

≈0.61

. In this Demonstration, the pairs of random integers are chosen from among the pixel values of selected images.

Using enough random pairs of pixel data from almost any sufficiently complex picture gives an approximation of

π

with between 1 and 4 correct digits.

[1] B. Gourevitch. "The World of Pi: Cesaro." (March 14, 2012) www.pi314.net/eng/cesaro.php.

Erik Mahieu