Teachers and other math nerds are preparing to celebrate an epic Pi Day on 3/14/15. Unfortunately, the activities I see on teacher blogs and Pinterest don’t include much actual math. They stress the pi/pie wordplay or memorizing the digits.
With a bit of digging, however, I found a couple of projects that let you sink your metaphorical teeth into real mathematical meat. So I put those in the March “Let’s Play Math” newsletter, which went out this morning to everyone who signed up for Tabletop Academy Press math updates.
If you’re not on the mailing list, you can still join in the fun:
Math Snack: Why Pi?
In math, symmetry is beautiful, and the most completely symmetric object in the (Euclidean) mathematical plane is the circle. No matter how you turn it, expand it, or shrink it, the circle remains essentially the same. Every circle you can imagine is the exact image of every other circle there is.
This is not true of other shapes. A rectangle may be short or tall. An ellipse may be fat or slim. A triangle may be squat, or stand up right, or lean off at a drunken angle. But circles are all the same, except for magnification. A circle three inches across is a perfect, point-for-point copy of a circle three miles across, or three millimeters…
2 thoughts on “Playful Math Snacks: Why Pi?”
Wouldn’t all squares and equilateral triangles share the self-similarity property?
Yes, all regular polygons are self-similar, as far as angles and proportional distance is concerned — that is, by the standard definition of similarity. Circles are the only ones that include the ultimate degree of rotational self-similarity, though. No matter how you turn them, they are still the same.
And this is why it makes sense to define something like pi for a circle, but not for any other shape. The circle is the only shape for which “distance across” is not ambiguous, because it’s the same no matter where on the circle you start walking.