Did’ja hear the one about Pi=3?
(WHTM) — It’s one of those urban legends that pops up again and again, that somewhere, sometime, in some governing body in the United States (usually a state legislature, though the U.S. Congress figured in at least one telling) an attempt is made to pass a law stating that the numerical value of Pi should be 3.0. The underlying aim of these stories is usually to poke fun at the scientific ignorance of members of one or both political parties, but every one of these stories is either a hoax or a myth!
Except for that one time…
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In 1897 an Indiana physician who dabbled in mathematics, Edward (or Edwin) Goodwin, was convinced he had found a solution to a problem that had challenged and frustrated mathematicians since Anaxagoras of Clazomenae first proposed it around 450 BCE. The problem, called Squaring the Circle, asks whether you can produce a square of equal area to a given circle using just a compass and a straightedge.
In 1882 German mathematician Ferdinand von Lindemann published a rigorous mathematical proof that squaring the circle is impossible. But either Goodwin never learned of the proof, or decided to ignore it and press on. He actually managed to get his theory published in the prestigious American Mathematical Monthly. (It should be noted it appeared in the “Notes and Queries” section where the general public could send submissions, and that it was listed with the disclaimer “Published by the request of the author.”)
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Goodwin persuaded his local state representative, Taylor I. Record, to introduce “A bill for an act introducing a new mathematical truth” on January 18, 1897, which would make Goodwin’s method for squaring a circle part of Indiana law. (The bill also did a little name-dropping, mentioning the proof “having been already accepted as contributions to science by the American Mathematical Monthly, the leading exponent of mathematical thought in this country.”
Not knowing what to do with it, the legislature referred the bill to the House Committee on Canals. By 1897 the canal era was pretty much at its end, and the Committee on Canals was often called the Committee on Swamplands. Perhaps the bill was referred to the Committee to give them something to do. What they did was kick the can over to the Committee on Education. That committee, for reasons unknown, reported favorably on the bill, and on February 6. 1897 it passed the House 67-0.
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The bill was on its way to the Indiana Senate. But as it happened, the day the House voted on it, they had a visitor-Clarence Abiathar Waldo, head professor of Mathematics at Perdue University, and president of the Indiana Academy of Science, who had come to lobby for University Funding. He was given a copy of the bill and asked if he wanted to meet the author. Waldo, as he later wrote, replied that “he was acquainted with as many crazy people as he cared to know.”
The Senate prepared to vote for the bill, by sending it to the Committee on Temperance. One wonders if they thought the bill would strike a blow for or against the temperance movement. Waldo, meanwhile, was meeting with senators, explaining what was wrong with the bill, and urging them to vote against it.
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At this point, you may be wondering where the value of Pi enters into this legislation. Pi is the ratio of the circumference of a circle to its diameter, and is 3.141592 out to-who knows? It’s an infinite or irrational number; you can keep dividing and dividing, and never reach its end. (The current record, set in 2022, is 100 trillion digits. It took some of Google’s most powerful computers 157 days to work that out.)
In an article posted on the website of the University of Waterloo (Ontario) in 1998, Alex Lopez-Ortiz worked through the mathematics cited in the bill and found it produces different values for Pi, ranging from 3.2 to 9.24.
By now word of Bill 246 was getting around, and had been dubbed the Indiana Pi Bill. Legislators were catching on to the fact they were making fools of themselves in the public eye by pushing this bill forward.
So, when the bill finally went before the Senate, there was a great deal of merriment at its expense, coupled with a realization that it’s just not a good idea to rewrite science by legislation. It was moved that the bill should be “postponed indefinitely,” a procedural move to kill a motion without taking a direct vote on it.
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So the Indiana Pi Bill went down in defeat, science and mathematics were saved, and a template was created for hoaxes and spoofs in the future.
To read Prof. Waldo’s account of the bill, click here.
To read the University of Waterloo article explaining the math errors, click here.
To read about computing Pi to 100 trillion digits, click here.
To read some of the “Pi=3” spoofs, click here and here.
Here’s the Indiana Pi Bill in its entirety, whether you want it or not:
HOUSE BILL NO. 246
“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.”
“Section 1. Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle’s area is entirely wrong, as it represents the circles area one and one-fifths times the area of a square whose perimeter is equal to the circumference of the circle. This is because one-fifth of the diameter fils to be represented four times in the circle’s circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can, in like manner make the square’s area to appear one fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle’s circumference.”
“Section 2. It is impossible to compute the area of a circle on the diameter as the linear unit without trespassing upon the area outside the circle to the extent of including one-fifth more area than is contained within the circle’s circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight. By taking the quadrant of the circle’s circumference for the linear unit, we fulfill the requirements of both quadrature and rectification of the circle’s circumference. Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four; and because of these facts and the further fact that the rule in present use fails to work both ways mathematically, it should be discarded as wholly wanting and misleading in its practical applications.
“Section 3. In further proof of the value of the author’s proposed contribution to education, and offered as a gift to the State of Indiana, is the fact of his solutions of the trisection of the angle, duplication of the cube and quadrature having been already accepted as contributions to science by the American Mathematical Monthly, the leading exponent of mathematical thought in this country. And be it remembered that these noted problems had been long since given up by scientific bodies as unsolvable mysteries and above man’s ability to comprehend.”
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