Math Snack: Why Pi?
Playful, no-preparation math activities for all ages
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.
What makes a circle so special and beautiful? Don't bother with a definition like "the locus of points a given distance from..." Blah! Any child will tell you, what makes a circle is the roundness of it. Perfectly smooth and plump, but not too fat. One way to express that roundness in numbers is to compare it to the distance across—How many times would you have to walk back and forth across the middle of the circle to make the same distance as one trip around? That's pi!
Alexander Bogomolny offers a great lesson on measuring pi that also helps students understand the problems of measurement in general: Determination of π, Measurements in Context. Lucinda Leo shares what happened when her family tried a similar project: Discovering Pi – the living maths of circles.
What better way could there be to celebrate Pi Day than by creating mathematical art that highlights roundness and symmetry? Take a look at what the Highhill Homeschool family has been working on: a whole series of posts on Mandala Math Art.
Pi animation by John Reid (Edited version of Image:Pi-unrolled.gif.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons.