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Take the strip of paper and wrap it around the can. Using the strip, measure the distance around the can and cut off any excess paper that goes beyond the distance. This length is called the circumference. |
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Now, with the ruler, measure the length of the strip using centimeters. Write C = and the measurement in centimeters onto the paper strip. Cut off the excess (extra paper). Circumference is the distance around a circle. It is a linear measure. For demo purposes, let's say our can here has a C of approximately 26 cm. |
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Take your Circumference strip, the same one, and measure across the TOP of the can. This time you are going to measure the diameter of the can. The diameter is the distance across the circle, through the center. |
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Where the strip hits the edge of the can, where you actually have the diameter, FOLD the strip. Make a mark with your pencil along the fold. Measure the the diameter using your ruler and write it down onto the strip as d = . For our demo purposes, I've measured the can and the diameter is approximately 8.25 cm. Estimate, how many times do you think you can actually fold the strip along your Circumference? Try it and see. I bet you folded the diameter a total of three times, right? And, was there a little bitty bit of paper strip leftover? Well, guess what! You have demonstrated Pi! |
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Pi is the ratio of the Circumference measure to the diameter measure. Get your calculator. Enter the Circumference measure. Press the division button. Now press your diameter measure. Hit equals. What did you get? Something around 3.14159… right? Or, at least it was 3 with a fractional remainder (or decimal remainder). Woo-hoo! |
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P.S. π is NOT 22/7 and it is also NOT 3.14. These are both approximations. If you want to use a 'good' and accepted approximation in your calculations, use the first five decimal places, i.e., 3.14159 |
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Ooooh! Circles! Yeah, I know, some of you are saying, "Yuck! Circles! They're SOOO hard!" Nah, you have NOOOO idea how easy it is to learn how to work around circles. tee-hee! So, let's get started with the vocabulary because that's key to working with circles.
circle: a set of points in a plane equidistant from a given point. The center of the circle is called the origin.
radius: the distance from the origin (center) O to any point on the circle
diameter: twice the radius or the longest distance through the center point or origin O from one side of the circle to the other
Pi: an irrational number (non-repeating, non-terminating decimal) represented by the Greek letter, calculated as the ratio of the circumference/diameter
No, we're really not talking about PIE but pi as in the Greek letter π. tee-hee! This important symbol is key when working with circles so let's explore what it is before we do anything else, 'kay?
Go get yourself the following supplies: (the green thing is a strip of paper)
• soup can
• strip of paper
• scissors
• calculator
• pencil
• ruler
circumference: the linear distance around the circle