One of our activities in the L & LC on Tuesday March 14, 2023, is Making Pi with paper strips representing the digits of pi. Each digit, 0 through 9, is represented by a color. Select a colored strip of paper that matches the next digit of pi on the chain--write your name on it!--then loop it, staple it on, and cross off that digit from the decimal expansion of pi.
0 = blue
1 = green
2 = red
3 = yellow
4 = orange
5 = lime green
6 = hot pink
7 = light pink
8 = light green
9 = salmon
Type in YOUR BIRTHDAY at The Pi Search Page to find out where your birthday is within the digits of pi. This website will search the first 200 million digits of pi in a fraction of a second. If it finds your sequence, it will tell you at what position in pi your sequence begins and will display your sequence along with surrounding digits. No result? Try another sequence. The shorter the sequence, the better the odds of finding it. Pi is an irrational number, which means that its digits never end and that it doesn’t contain repeating sequences of any length. If Pi-Search didn’t find your sequence of numbers, that’s probably because the sequence occurs somewhere past the first 200 million digits. Note the qualification “probably”: Mathematicians can’t say with absolute certainty that pi contains every possible finite number sequence—but they strongly suspect that this is the case.
Strings of digits of pi are sometimes used to generate sequences of random numbers, but are the digits of pi truly random? To explore this question research what it means for a number to be a “normal number” – a concept introduced in 1909 by mathematician E. Borel. As of 2011, pi has been calculated to 10 trillion decimal places. When mathematicians study any sample of this huge number, they find that each digit, 0–9, occurs as often as any other, and that the occurrence of any digit seems unrelated to the preceding digit. This makes pi appear to be statistically random. If this statistical randomness is unending, then pi must contain all finite sequences of digits, including the birth dates of everyone ever born and yet to be born. It would also contain every winning lottery number—too bad we don’t know how to identify them.