A Slice of Pi

You may recall from high school or college math that pi, π, is the ratio of the circumference of a circle (called C) to its diameter (called D).

π = C / D

This value is roughly 3.14159, though in today’s computer age it’s been calculated to over a trillion digits. For my high school and college math and physics I memorized it to five places, 3.14159, though in a feat of geekdom I memorized it out to twenty decimal places last pi day (March 14 of every year). But its value was estimated pretty accurately by the ancients. Archimedes (third century BC) showed it to lay between 223/71 and 22/7. Egyptians even further back (c. 1650 BC) used 256/81, or 3.16049, for π.

The amazing thing about π, to me, is that it creeps up just about everywhere you look in mathematics and physics. You use it to calculate the areas of circles and spheres and the volumes of spheres, in trigonometry and in surveying. In physics you see it in the equations of electricity and magnetism to cosmology and quantum mechanics. It got to the point where one day a few years ago I wondered almost out loud (I try not to talk math out loud when my wife is present) how this simple ratio of a circle found its way into just about all the hard sciences. Then, shortly thereafter, I read that π is not the ratio of C / D. Well, yeah, that’s one of its properties, but only one. Our friend π is a component of this physical universe that manifests itself (its properties) in hundreds of ways in various disciplines of thought.

Wow. That blew my mind.

But I just happened across a story about π that I remember reading a couple years back. I think you’ll like it.

It seems that sometime around the end of the 19th century, 1897, I think, an amateur mathematician by the name of Dr. E. J. Goodwin in Indiana believed he had discovered a unique property about π. But instead of contacting famous mathematicians or mathematical journals or even his local math club, he decided to take it to his state senator and persuaded him to introduce the following bill: Be it enacted by the General Assembly of the state of Indiana, that it has been found that a circular area is equal to the square on a line equal to the quadrant of the circumference. Long story short, this produces a value of π to be exactly … 4.

The bill was never enacted, thanks in part to press attention after some non-partisan mathematicians discovered the flawed formulations.