The man who saved π

I couldn’t call myself a mathematician if I didn’t celebrate Pi Day. Let’s take a moment to appreciate this mathematical constant for… staying constant. Today’s hero came by a hair’s breadth of being changed to 3.2.

Since ancient times mathematicians had been trying to “square the circle”, so given a circle construct a square with the same area, using just a compass and straightedge. Unfortunately for all these fame-seeking mathematicians and amateurs, in 1882 the task was proven impossible. And the culprit was… π.

The circle and square have the same area equal π. In 1882 we learned that constructing such a square isn’t possible. Source: Wikipedia.

To square the circle we’d have to construct a square root of π. However, a German mathematician Carl Louis Ferdinand von Lindemann proved that π is a transcendental number, which means it’s not a root of any polynomial with rational coefficients. Technicalities aside, the important consequence is that we cannot construct pi with a circle compass and straightedge. Not because it requires a genius not yet born, but because maths just doesn’t allow it.

However, this result didn’t discourage Edward J. Goodwin, a physician and amateur mathematician from Indiana. He found the way of squaring the circle and even published his result in the journal American Mathematical Monthly. His “proof” contained the following ground-breaking discovery.

Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four[.] (source: Indiana Pi Bill)

According to Goodwin, the ratio between the diameter (2R) and circumference (2πR) equals 5/16. Hold on, doesn’t this mean that… Yes, he claimed that π=3.2!!!

And he didn’t stop there. In 1987 he convinced the Indiana General Assembly to pass the House Bill 246, today called the Indiana Pi Bill, which contained his “results”. Also in the Senate’s Committee on Temperance nobody raised eyebrows over this mathematical nonsense.

Luckily for Indiana, when the senators were discussing this ingenious idea, professor C.A. Waldo from Purdue University happened to visit Indianapolis. He couldn’t stand observing this pointless debate (as a side note, I’m writing this article while listening to British politicians discussing Brexit, and I can’t decide which of these two sounds more ridiculous), so he gave the legislators a short maths lesson.

Today let’s raise the glass to Prof. Waldo, the man who saved π! Happy Pi Day!

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