How $\pi$ was almost $3.2$

Yes, you read that right. The numerical constant $\pi \approx 3.14$ could have been equal to $3.2$!

In 1894, physician and amateur mathematician Edward J. Goodwin (c.1825-1902) believed that he had found a way to square the circle. It was proven in 1882 that this can't be done by Ferdinand von Lindemann.

How did he do it then? The way he did it implied various wrong values of $\pi$, most commonly $3.2$. Here is an example. He made this diagram, which is a circle with diameter $10$. He then says the circumference is $32$, not $\sim 31.415...$, which means $\pi = 3.2$! However, at the time, $\pi$ was known to 527 correct digits.

He showed this to Indiana state representative Taylor I. Record, so schools could show this as a way to square the circle without royalties. Record then introduced it to the house under the excruciatingly long title "A Bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the Legislature of 1897". It was bill #246 of the 1897 sitting of the Indiana General Assembly.  

The bill somehow passed the Indiana House of Representatives, and was sent to the Indiana Senate. On the day they were going to vote, Professor Clarence Abiathar Waldo happened to be there. He explained to the Senate that the bill redefined $\pi$, and it actually almost passed, but one senator said that they had no power to define mathematical truth. That is why the Indiana Pi Bill did not pass.

No comments:

Post a Comment