Any high school geometry student worth his or her protractor knows that pi is an irrational number, but if you’ve got to approximate the famed ratio, 3.14 will work in a pinch. That wasn’t so much the case in late-19th-century Indiana, though. That’s when the state’s legislators tried to pass a bill that legally defined the value of pi as 3.2.
The very notion of legislatively changing a mathematical constant sounds so crazy that it just has to be an urban legend, right? Nope. As unbelievable as it sounds, a bill that would have effectively redefined pi as 3.2 came up before the Indiana legislature in 1897.
The story of the “Indiana pi bill” starts with Edward J. Goodwin, a Solitude, Indiana, physician who spent his free time dabbling in mathematics. Goodwin’s pet obsession was an old problem known as squaring the circle. Since ancient times, mathematicians had theorized that there must be some way to calculate the area of a circle using only a compass and a straightedge. Mathematicians thought that with the help of these tools, they could construct a square that had the exact same area as the circle. Then all one would need to do to find the area of the circle was calculate the area of the square, a simple task.
Sounds like a neat trick. The only problem is that it’s impossible to calculate the area of a circle in this way. It just won’t work. Furthermore, when Goodwin was toying with this problem, mathematicians already knew it was impossible; Ferdinand von Lindemann had proven that the task was a fool’s errand in 1882.
Goodwin wasn’t going to let something trivial like the proven mathematical impossibility of his task deter his efforts, though. He persevered, and in 1894 he even convinced the upstart journal American Mathematical Monthly to print the proof in which he “solved” the squaring-the-circle problem. Goodwin’s proof didn’t explicitly deal with approximating pi, but when you’re quite literally trying to fit a square peg in a round hole, weird things happen. One of the odd side effects of Goodwin’s machinations was that the value of pi morphed into 3.2.
Let's Make a Deal
Although Goodwin’s “proof” was anything but, he was pretty cocky about its infallibility. He didn’t just publish his faulty method in journals; he copyrighted it. Goodwin figured everyone would be lining up to use his revolutionary new trick, and his plan was to collect royalties from businesses and mathematicians who sought to exploit his method.
Goodwin wasn’t totally greedy, though, and that’s where the Indiana legislature entered the picture. Goodwin couldn’t bear the thought of Hoosier schoolchildren being deprived of the fruits of his brilliance just because the state couldn’t foot the bill for his royalties. So he magnanimously offered to let the state use his masterpiece free of charge.
Indiana wasn’t going to get such an awesome deal totally for free, though. The state could avoid paying royalties if and only if the legislature would accept and adopt this “new mathematical truth” as state law. Goodwin convinced Representative Taylor I. Record to introduce House Bill 246, which outlined both this bargain and the basics of his method.
Again, Goodwin’s method and the accompanying bill never mention the word “pi,” but on the topic of circles, it clearly states, “[T]he ratio of the diameter and circumference is as five-fourths to four.” Yup, that ratio is 3.2. Goodwin isn’t afraid to lambaste the old approximation of pi, either. The bill angrily condemns 3.14 as “wholly wanting and misleading in its practical applications.”
Goodwin’s blasting of the old approximation isn’t even the funniest part of the bill’s text. The third and final section extols his other mathematical breakthroughs, including solving the similarly impossible problems of angle trisection and doubling the cube, before reminding any reader who wasn’t sufficiently awestruck at his magnificence, “And be it remembered that these noted problems had been long since given up by scientific bodies as insolvable mysteries and above man's ability to comprehend.“
To anyone who passed the aforementioned high school geometry class, this bill was patently absurd. Apparently Indiana legislators weren’t a pack of math whizzes, though. After the bill bounced around between committees, the Committee on Education finally sent it out for a vote, and the bill passed the House unanimously. No, not a single one of Indiana’s 67 House members raised an eyebrow at a proof that effectively redefined pi as 3.2.
Luckily the state’s senators had a bit more numerical acumen. Well, some of them did. Eventually. After sailing through the House, the bill first went to the Senate’s Committee on Temperance, which also recommended that it pass. By this point, news of Indiana attempting to legislate a new value of pi and endorse an airtight solution to an unsolvable math problem had become national news, and papers all over the country were mocking the legislature’s questionable calculations.
All this attention ended up working in Indiana’s favor. While the state’s lawmakers couldn’t follow Goodwin’s bizarre brand of mathe-magic well enough to refute his proof, there were other smart Hoosiers who could. Professor C.A. Waldo of Purdue University was in Indianapolis while the pi hoopla was unfolding, and after watching part of the debate at the statehouse he was so thoroughly horrified that he decided to intervene.
The legislators may have been nearly bamboozled by Goodwin’s pseudo-math, but Waldo certainly wasn’t. Waldo got the ear of a group of senators after watching the absurd debate and explained why Goodwin’s theory was nonsense. (It seemed that most of the legislators didn’t really understand what was going on in the bill; they just knew that by approving it the state would get to use a new theory for free.)
After receiving Waldo’s coaching, the Senate realized that the new bill was a very, very bad idea. Senator Orrin Hubbel moved that a vote on the bill be postponed indefinitely, and Goodwin’s new math died a quiet legislative death. The Indiana legislature hasn’t tried to rewrite the basic principles of math in all the years since.