On Feb. 6, 1897, Indiana's state representatives voted to declare 3.2 the legal value of pi. The bill wasn't actually about legislating a rounded value of pi; it was even more ambitious than that. Bill 246 was a bold attempt to attack an ancient mathematical conundrum with the modern blunt force of legislative fiat.
Today, we use "square the circle" as slang for doing the impossible, but the term originated in ancient Greece as a serious challenge in the field of geometry: how to use a compass and a straight-edge to construct a square with the same area as the circle you started with. Squaring the circle was proven impossible in 1882 thanks to the basic mathematical properties of the circle.
Pi is a number that defines what a circle is. It's the ratio of a circle's circumference to its diameter, and it's the same for every circle: 3.141592 followed by a string of over 22 trillion other digits. That unwieldy and enigmatic number is what makes a circle, a circle.
Long decimal numbers whose digits never repeat are called irrational numbers, and pi is a specific kind of irrational number called a transcendental irrational number. The mathematical properties of transcendental irrational numbers like pi mean that it's impossible to square the circle.
But a few years later, undeterred by mathematical proof, doctor and amateur mathematician Edward J. Goodwin thought he had figured out the ancient puzzle after all. He started by trying to throw out Archimedes' formula for the area of a circle and replace it with his own formula. Goodwin's formula was much more complex (and his convoluted writing style didn't do his ideas any favors), and used imprecise versions of the important measurements in his diagram, including pi. As a result, his "area of a circle" ended up about 21% larger than its actual area.
One of those imprecise measurements was pi, which he approximated as a ratio of "five fourths to four," or 3.2. That's not even a correct way to round pi, but that didn't deter Goodwin. He managed to convince Indiana State Representative Taylor I. Record to introduce a bill in the state's General Assembly of 1897 to make Goodwin's method a matter of state law.
Ostentatiously titled "A Bill for an act introducing a new mathematical truth," the proposed legislation promised that Goodwin would allow the state of Indiana to publish his discovery in its textbooks for free, while everyone else would supposedly have to pay royalties to Goodwin. That's not even close to how publishing mathematically discoveries actually works, but it wasn't why lawmakers were so confused by Record's bizarre bill. They simply had no idea what to do with it.
One representative suggested referring to the bill to the Finance Committee, presumably because it contained numbers. Another, obviously either a disgruntled former geometry student or an undercover mathematician, joked that it should go to the Committee on Swamplands to "find a deserved grave." Eventually, Bill 246 found its way to the Committee on Education, which approved it and sent it to the General Assembly for a vote. It passed on February 6, 1897.
Before the bill could befuddle the state's Senate, however, it fell into the hands of Purdue University math professor Clarence Abiathar Waldo, who had stopped by the capital to request funding for the Indiana Academy of Sciences.
"Imagine his surprise when he discovered that he was in the midst of a debate upon a piece of mathetical legislation," Waldo later wrote. He was unimpressed, recalling, "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."
Waldo gave the senators a hasty geometry lesson. Even so, the bill nearly passed, but the senators decided on Feb. 12 to indefinitely postpone the vote.
"My state did not further this monstrosity, and it was probably the Indiana Academy of Science alone which prevented it," Waldo later wrote. "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."
