With March upon us, here are some ideas for activities and investigations on Pi Day (3/14):
1. Read The Greedy Triangle by Marilyn Burns. This is the story of a triangle who so loved his sides and angles that he asked a shape-shifter to give him more and more and more…until he found himself rolling down hills and crashing into everything. The book includes notes for teachers about the mathematics and discussion topics about polygons and circles.
2. What is a circle? Challenge your students to provide a definition of a circle. Chances are they will say things like “a shape with no sides”, “a round shape”, “a shape with infinite lines of symmetry” but not be able to describe exactly what defines a circle. Guide them to a definition with the following activity: Draw a point on the board. Using a 12-inch ruler, have students come up to the board one by one and each draw one or several points that are exactly 12 inches away from the original point. Have the last student at the board connect the points. Then ask the students again, what is a circle? Guide them towards precise language in saying, from what they observed and discovered, that a circle is a set of points in a plane that are all the same distance away from a given point, which is its center. Then introduce the radius as the line connecting the center to any point on the circle, as well as the distance of each point from the center, and diameter as the distance from one point on the circle to another going through the center.
3. Read Sir Cumference and the Dragon of Pi by Cindy Neuschwander. In this story, the author uses character names and settings (baking pies, a carpentry shop) to teach us about the way in which pi might have been discovered. Then have your students write their own story about how pi, the ratio of the distance around a circle to the distance across, or how many times the diameter of a circle fits around its circumference, might have been discovered.
4. Investigate the relationship between area, perimeter of rectangles, and circumference with the following problem: Tex wants to build a corral for his horses. He has only 170 feet of fencing. He wants the horses to have the maximum amount of space to run around. If he wants the corral to be either rectangular or circular, what are the dimensions and the areas of some different shapes he could build? Which gives his horses the most room to run?
5. The ancient Egyptians calculated the area of a circle by squaring 8/9 of the diameter. Compare to the formula we use for area of a circle (pi x radius squared). What is the “Egyptian” value of pi?
6. The Babylonians determined that the area of a circle is equal to 1/12 the square of the circumference. How does the area they calculated compare with the area formula as we know it?
7. Archimedes, who lived around 300 BC, wrote “The area of a circle is to the square on its diameter as 11 is to 14.” What value of pi does this yield?
8. Aryabhata, a sixth-century Hindu mathematician, used this procedure for finding the area of a circle: “Half the circumference multiplied by half the diameter is the area of a circle.” How accurate is his rule?
9. Aryabhata also wrote: “Add 4 to 100, multiply by 8, and then add 62,000; the result is approximately the circumference of a circle of 20,000. By this rule, the relation of the circumference to diameter is given.” What value of pi do you derive from this rule?
10. Nehemiah, a Hebrew rabbi and scholar who lived around 150 AD, wrote: “If one wants to measure the area of a circle, let him multiply the thread (diameter) into itself and throw away the 1/7 and the half of 1/7; the rest is the area.” Find the value of pi that this procedure yields.