The ratio of the circumference of a circle to its diameter is always the same number. This number is Pi=3.141592... . The "..." stands for the fact that the decimal expansion of Pi does not end. Lists of the digits of the decimal expansion of Pi are available on the internet to thousands of places (one example). Looking at this list, no clear, long-term pattern jumps out. Is there any pattern in the digits of Pi?

  Getting Started

Look at a list of the digits of Pi. Are there more "1"'s than "4"'s. The list 1234567890123456789... has equal numbers of each digit, but it is very predictable. Does the fact that there are only eight "1"'s in the first 100 digits surprise you? Do repeated digits, "11", "22", and so forth occur more often than you would expect? What other patterns could you look for?

  Going Deeper

What does it mean for a list of digits to have no patterns? Does this mean it is "random". Are there ways to generate lists of digits without patterns? Does the list of letters on this web page have patterns?

Communicated by G. Hall.