# Pi Day

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Pi Day Cutting
Pi

Materials
circular object
string
scissors
tape

To Do and Notice
Carefully wrap string around the circumference of your circular object. Cut the string when it is exactly the same length as the circumference. Now take your “string circumference” and stretch it across the diameter of your circular object. Cut as many “string diameters” from your “string circumference” as you can. How many diameters could you cut? Compare your data with that of others. What do you notice?

What’s Going On?
This is a hands-on way to divide a circle’s circumference by its diameter. No matter what circle you use, you’ll be able to cut 3 complete diameters and have a small bit of string left over. Estimate what fraction of the diameter this small piece could be (about 1/7). You have “cut pi,” about 3 and 1/7 pieces of string, by determining how many diameters can be cut from the circumference. Tape the 3 + pieces of string onto paper and explain their significance.

Tossing
Pi

 Materialslarge sheet of drawing paper or cardboardmeterstickpentoothpicks (30 or more)calculatorTo Do and NoticeDraw a series of parallel lines on the paper or cardboard, as many as will fit, making sure that the distance between each line is exactly equal to the length of your toothpicks. Now, one by one, randomly toss toothpicks onto the lined paper. Keep tossing until you’re out of toothpicks—or tired of tossing.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:Pi = 2 × (total number of toothpicks) divided by  (number of line-crossing toothpicks)What’s Going On?This surprising method of calculating pi, known as Buffon’s Needles, was first discovered in the late eighteenth century by French naturalist Count Buffon. Buffon was inspired by a then-popular game of chance that involved tossing a coin onto a tiled floor and betting on whether it would land entirely within one of the tiles.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.Serving Pi Materialscan of three tennis ballstape measureTo Do and NoticeWhich do you think is greater, the height or the circumference of the can? Measure to find out.What’s Going On?If you were fooled (and we expect that most people are), blame pi. You can see that the height of the can is approximately 3 tennis-ball diameters, or h = 3d. But the circumference is pi times the tennis-ball diameter, or c = pd. Pi—3.14—is a little greater than 3, so the circumference of the container is slightly greater than the height.                                                                      Make a Pi ChainUse 10 different colors of construction paper, one for each digit 0 – 9.  Give each student 10 digits of pi to make the chain for, using the colored paper to represent the digits.  For example, if 1=red, 2=blue, 3=green, 4=yellow, etc…, 3.141 would be green, then red, then yellow, then red.  Connect the 10 digit chains together to form a long PI CHAIN.     Pi  Day Scavenger HuntMath Glossaries1)  What is the circumference of a circle? 2)  What is the diameter of a circle? The Story of Pi3)  What is PI the ratio of? 4)  What value of PI did the Egyptians obtain 2000 years before Christ? 5)  What value of PI did the Babylonians obtain? 6)  Where in the Bible is there an indication of the value of PI? What was this approximate value? 7) Which fraction is closest to the actual value of PI…..          337/120      or      22/7  or      355/113  ?    What is the decimal equivalent of it (to 8 decimal places)? 8) What does it mean to “square a circle”?  Birthday in Pi9)  Find your birthday in PI using the Pi-Search Page.  Type in your date of birth and record the location. Joy of Pi10) In the year 1997, D. Takahasi and Y. Kanada calculated PI to 51,539,600,000 decimal places.  What type of computer did they use?  Where did they do the calculation? Planet Pi11)  Is PI a rational or irrational number?  Explain why. 12)  What is PI to 30 decimal places? 13) What is the symbol for pi? Who first used it and when?What Swiss mathematician was it popularized by? Web Page Dedicated to Pi14) Who were the first people known to find a value for pi?             When was it? 15) In the first one million digits of pi, how many threes are there?     How many nines? 16) People once thought that trying to square a circle was an illness.  What was the name of the illness? 17) What was the most inaccurate version of PI?  Explain who, when, and what the value was? 18) Who memorized 42,195 digits of PI on Feb. 18, 1995?  Where was the person from? Online Dictionary19) You can memorize PI by using things called “mnemonics”  What is a “mnemonic?                                Easy as Pi Open the file below titled Cartoon Corner: Easy as Pi? Infinitely Not! to complete the first page of worksheet.

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