Indiana’s House of Representatives once voted unanimously to change the value of pi (π)

How an incorrect value of pi almost got codified into law

||| FROM SCIENTIFIC AMERICAN |||

An ancient problem known as “squaring the circle” stumped mathematicians for more than 2,000 years. During that time, professionals and amateurs alike unknowingly published thousands of false proofs claiming to resolve it. False proof attempts are natural stumbling blocks on the road to mathematical progress. They tend to fall by the wayside, either when peers uncover flaws in expert research or when crank arguments fail basic smell tests for legitimacy. But one didn’t fade quietly. Instead it forced a volunteer mathematician to tutor state senators, sparked media ridicule and nearly got an incorrect value of pi (π) codified into law.

Here’s the problem that consumed ancient Greek mathematicians and countless others since: given a circle, construct a square with the same area as it using only a compass and straightedge. You may remember compasses from school. They can take any two points and draw a circle centered at one of them while passing through the other. A straightedge helps you draw straight lines; it’s like a ruler without measurement markings. As the founders of the geometric proof, the Greeks placed special emphasis on the ability to draw, or construct, their objects of study with these simplest possible tools.

The task seems straightforward, but a solution remained surprisingly elusive. In 1894 physician and mathematical dabbler Edward J. Goodwin believed he had found one. He felt so proud of his discovery that, in 1897, he drew up a bill for his home state of Indiana to enshrine what he thought was a mathematical proof into law. In exchange, he would allow the state to use his proof without paying royalties. At least three major red flags should have prompted lawmakers to regard Goodwin with skepticism. Math research has no norm around charging royalties or precedent for legally ratifying theorems, and the supposed proof was nonsense. Among other errors, it claimed that pi, the ratio of a circle’s circumference to its diameter, is 3.2 rather than the well-established 3.14159…. Yet, in a bizarre legislative oversight, the Indiana House of Representatives passed the bill in a unanimous vote.

Why would politicians enact hogwash and sully their sterling reputation of passing fact-based policy? In their defense, they seemed confused about the bill’s contents and played hot potato with it, first tossing it to the Committee on Canals, which flung it over to the Committee on Education. They held three formal readings of the bill before voting. Goodwin had also managed to publish his work in theAmerican Mathematical Monthly, a highly reputable journal to this day. This probably lent him credibility to outside eyes, even though the journal had a policy back then of uncritically publishing all submissions with a “by request of the author” tag. Perhaps Indiana’s house wanted to punt the problem to the state senate to determine the fate of the imperiled constant.

As if this story wasn’t outlandish enough, Goodwin’s endeavor to square the circle was actually doomed from the start: mathematician Ferdinand von Lindemann had proven the task impossible in 1882. Furthermore, Lindemann’s argument explains why so many false proofs of squaring the circle hinge on erroneous values of pi.

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