As I write this, Pi Day is just around the corner, and the typical fare includes π art projects and memorization challenges. But π is such a fascinating topic that it can inspire curiosity and wonder on its own. Presented correctly, students’ mouths should drop open as they ask, “Why is it like that?”
Here’s a video I put together to illustrate how strange π is with regard to area and circumference.
Area
- Square the radius of a circle. This makes a square with sides r and area r2.
- Try to fit as many of these squares as you can into a circle. You’ll find that four is too
- You need exactly π of these squares to fill the circle.
- This is why the area of a circle is equal to π times r2
Circumference
- Now, imagine walking across a circle. It takes two radii or one diameter to get across.
- The distance around the circle is certainly longer than the distance across, but how much?
- Hmm… it’s not two diameters. It’s not three diameters. It’s exactly π diameters to get around a circle.
- This is why the circumference of a circle is 2πr or πd
For some other ways to explore π in your class:
- Circumference and famous circles
- The relationships between area and perimeter
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