Discovering Pi

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π, pronounced “pie” is the 16^th letter of the Greek alphabet and was chosen by the mathematician William Jones in 1707 to represent the ratio of the perimeter of a circle (the "circumference") to its diameter.

The ancient Greeks did not use π  to represent this relationship.

For example, a circle with a circumference of 22 inches will have a diameter of approximately 7 inches. In fact, 22/7 (or 3 and 1/7) is often used to estimate this ratio. The number π has now been found to 51 billion digits, the first 20 of which is 3.14159265358979323846…… The "………" on the end means that the decimal digits of π go on forever without repeating or terminating. This is an irrational number.

The ancient Egyptians estimated π to 3.1605 (or 16/9 times 16/9). When the Hebrew Bible was written around 8th to 3rd century BC, they used the number three regarding a cerimonial pool in the Temple of Solomon. Finally, in 250 BC, Archimedes calulated π to between 3.1408 and 3.1429.

The children were not told the value of π. They had to discover it themselves just like the ancient mathematicians. They took a wiki stick that was the size of a circle's diameter, marked a starting point, and stretched it around the circumference of the circle marking each whole diameter. When they got to the 3rd diameter, there was a small portion left over. They bent the wiki stick around 7 times with that portion giving them an approximation of π of 3 1/7. Then I gave them a dozen or so other objects (i.e., CD, frisbee, roll of tape, small wheel, etc.); they used pipe cleaners or wiki sticks to measure the specific circle's diameter and used the same procedure to estimate π. One student proclaimed that π was only 2.5 (this student had used the original circle's diameter to measure the number of diameters that fit around a CD; of course, the CD's diameter was smaller so π could not be measured accurately). This is a common mistake.

I bought two foot square foam from Home Depot and asked them to create a circle. I showed them how to make a compass from a golf tee, string, and a pencil. Then I asked them how I would use this instrument to create my circle. They were able to see that I needed to find the center into which I would place the golf tee. 

I asked them to find the center of the square. They pointed to where they thought it was and I was able to puncture the foam with the golf tee. Over 140 students tried to estimate the center; not one was able to point to the actual center. They were excited to learn how to find the center of any rectangle by finding the intersection of the diagonals.

We traced out the two foot diameter circle and cut it out. 

THIS WEEK there are three challenges:

1. Find several circular objects around the house and estimate πusing our procedure above; record these on the given sheet.

2. Memorize the first 9 digitsof π: 3.141592653. Engineers would only need at most 9 digits of π. Physicists would only need at most 20 digits of π. Realistically, you should only need 3.1415926.

3. Create your own compass (I made compasses for each of the Thursday 4pm K kids) and create a large circle out of cardboard, foam board, or paper.

The attached pdf. has the instructions for each of the three objectives above. Disregard the first page.

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