Sir Cumference and the Dragon of Pi (March 14-17)

Pi day is upon us again as Monday was March 14.  It is called Pi day because the number Pi starts with 3.14. We challenged the Mathletes to think of what 2Pi day would be; calculating 6.28, they say, "June 28." Then 3Pi day is fun; 9.42 gets them thinking about 30 days in September, so some of them go into October 12th.  A silly past-time but fun.

I read the book, Sir Cumference and the Dragon of Pi, to several classes and paraphrased it to others who have heard it before.  It is a great myth about how the number Pi was found.  The students then are challenged to check the conclusions of the book: every circle's diameter can be stretched around its perimeter (or circumference) a little more than 3 times; more precisely, 3 and a 1/7; more precisely 3.141592653589793...........

They do this with string, rulers and several objects that represent circles or spheres.  Miraculously, every circle, or in the case of a sphere, every great circle (the equator), works in the exact same way.  We also observed how surveyors use a meter or yard wheel to measure distance.  They actually rolled the meter wheel along several meter sticks.  Everytime it passed a meter, it clicks.  We investigated how it works and they learned that if you take the 100 cm of a meter stick and divide it by Pi, the exact diameter emerges; in this case 31.83... cm.

To work with Pi, I allowed the Mathletes to use calculators to investigate how multiplying any diameter by Pi would result in circumference.  The attached pdf lists several types of spheres (baseball, basketball, golfball, etc.) with their listed diameters.  The students multiplied the diameter by Pi and recorded the circumference.  When they were done with page one, page two lists the diameter in miles of all of the planets and the sun.  Please disregard references to area of circles, surface area of spheres, and volume of sphere as this is for older classes.  Of course, if you wish to investigate with your children, the formulas are all there.

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Diameter_of_Circles_and_Spheres_chart.doc47.5 KB