Why Pi?

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