Squaring a circle

Once again, I learned a rather interesting bit of trivia about the number π a few weeks after (not before) International Pi Day (see another post from the past, "Pi and Infinite Monkeys" which I posted on September 3, 2023).  March 14th is always a fun day in our house, because my wife is a middle school math teacher!  She always celebrates International Pi Day by having her students bring in either pizza or pie, and there's always a contest to see which student can recite the highest number of digits in π.  While I am confident that almost everyone can remember that π is roughly equal to 3.14, I suspect that many of us forget that (1) π is what is classified as an irrational number (a real number that cannot be expressed as a fraction), (2) the decimal representation of π never ends and never repeats itself (although there are occasional short repeating elements, such as the six consecutive nines that appear starting at the 762nd decimal place, commonly known as Feynman's Point after the brilliant physicist Richard Feynman, (3) π is the ratio of a circle's circumference to its diameter.

What I didn't know is that my home state of Indiana almost passed a law in 1897 to change the value of π to 3.2.    

Since antiquity, mathematicians have tried to solve a problem known as "squaring a circle".  The problem can be stated as follows: Given a circle, construct a square with the same area as the circle using only a compass and straight edge.  Unfortunately, solving the problem has proven to be impossible, which is why "squaring a circle" is now an idiomatic expression used to describe a problem that is impossible to solve.  Here's where the Indiana law comes in.  Back in 1894, an Indiana physician and math enthusiast named Edward J. Goodwin believed that he had discovered a solution for the "squaring the circle" problem.  He was so proud of his proof that he asked his friend, Taylor I. Record to introduce a bill (Bill 246) in the Indiana House of Representatives under the title, "A Bill for an act introducing a new mathematical truth" in 1897.  Bizarrely, if passed, the law would have allowed the state of Indiana to publish his discovery in its textbooks for free, while everyone else would supposedly have to pay royalties to Goodwin.  I'm not sure that's exactly how copyright laws work, but that didn't seem to bother Goodwin or Record.

Interestingly enough, Goodwin's proof only worked if π was equal to 3.2.  The other state representatives in the Indiana House were confused by the topic and whether it was even appropriate for them to vote on such a bill.  One representative referred the bill to the Finance Committee, presumably because the bill involved numbers.  Another representative joked that the bill should go to the Committee on Swamplands, where it would "find a deserved grave."  The bill eventually made its way in the House Education Committee, which approved it and sent it to the General Assembly for a vote.  The Indiana House of Representatives voted by majority to approve the bill on February 6, 1897.

Before the bill went to the Indiana Senate, however, another mathematician caught wind of the bill.  Purdue University's Clarence Abiathar Waldo had apparently stopped by at the Indiana Statehouse in order to request funding for the Indiana Academy of Science.  Instead, he found himself teaching Indiana Senators on the finer points of geometry.  Waldo later recalled in the Proceedings of the Indiana Academy of Science, "A member then showed the writer a copy of the bill just passed and asked him if he would like an introduction to the learned doctor, its author. He declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know."

Despite Waldo's impromptu geometry lesson, the bill nearly passed the Senate.  However, the Senate agreed to postpone consideration of the bill indefinitely on February 12, 1897, narrowly avoiding what would assuredly result in widespread ridicule.  Waldo later wrote, "My state did not further this monstrosity, and it was probably the Indiana Academy of Science alone which prevented it.  That one act of protection was worth more to Indiana, jealous of her fair fame as she is, than all she ever contributed or can contribute to the publication of the proceedings of her Academy of Science."

It's an interesting footnote in the history of mathematics.  I wonder why I was never heard about this story when we were taught Indiana State History in grade school?  And even though I am posting this on April Fool's Day, as far as I can tell, the story is absolutely true (Goodwin even published his proof in the prestigious journal, The American Mathematical Monthly under the title "Quadrature of the Circle")!