Cutting π  
Materials To Do and Notice What’s Going On? 



Wearing π  
Materials To Do and Notice What’s Going On? 



Searching π  
Materials To Do and Notice Go to the PiSearch Page and type your sequence in the search box at the top of the page. This web site will search the first 200 million digits of pi in a fraction of a second. (See “How it works” on the PiSearch Page to find out how this is accomplished.) 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. What’s Going On? 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. 



Tossing π  
Materials To Do and Notice It’s time to count. First, remove any toothpicks that missed the paper or poke out beyond the paper’s edge. Then count up the total number of remaining toothpicks. Also count the number of toothpicks that cross one of your lines. Now use this formula to calculate an approximation of pi: What’s Going On? The proof of why this works involves a bit of meaty math and makes a delightful diversion for those so inclined. (See links at bottom of page.) Increasing the number of tosses improves the approximation, but only to a point. This experimental approach to geometric probability is an example of a Monte Carlo method, in which random sampling of a system yields an approximate solution. 



Seeing π  
Materials To Do and Notice What’s Going On? You can see that the height of the can is approximately 3 tennisball diameters, or h = 3d. But the circumference is pi times the tennisball diameter, or c = πd. Pi—3.14—is a little greater than 3, so the circumference of the container is slightly greater than the height 