The Indiana Pi Bill and the Attempt to Redefine Mathematics Through Legislative Fiat

Indiana Pi Bill attempt to change value of pi

Do you remember when you first learned of the concept of π? Have mathematics always been at least a little bit difficult for you? Haven’t you wished you could just pass a law to make it all a lot easier to understand? When some elected legislators attempted to use their political power to change some basic mathematical truths, the result was the infamous “Indiana Pi Bill” It stands as a lasting legacy to the political conceit that believes politicians are qualified to legislate on any subject they choose.

Edwin J. Goodwin was a physician, but he fancied himself to be an amateur mathematician. In his spare time, he liked to tackle problems that had vexed the experts for centuries. When he set his mind to the problem of “squaring the circle,” he was sure he had just earned his place among the greatest thinkers of history. He was correct in his assessment that he would be remembered. It turned out that history remembers him for all the wrong reasons.

From ancient times, mathematicians had grappled with the puzzle of how to “square the circle.” It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with a compass and straightedge. It ultimately was proven to be impossible in 1882 by Ferdinand von Lindemann. Goodwin vehemently disagreed with von Lindemann, however. He believed he had solved the problem. In 1897, he drafted House Bill 246 and presented it to some representatives for passage.

Goodwin announced that he had figured out how to “square the circle” and wanted to immortalize his findings in the legislative record and make sure Indiana’s students got the primary benefit of his discovery. The bill would allow Indiana schools to use Goodwin’s discovery free of charge. Other states would have to pay royalties for the privilege.

The text of House Bill 246 was as follows. (Don’t worry; we’ll try to explain what it all means before this is all over):

“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 circle’s area one and one-fifth times the area of a square whose perimeter is equal to the circumference of the circle. This is because one-fifth of the diameter fails 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.”

The day after the bill was introduced, the following article appeared in the Indianapolis Sentinel:

“Claims Made That This Old Problem Has Been Solved. “The bill telling how to square a circle, introduced in the House by Mr. Record, is not intended to be a hoax. Mr. Record knows nothing of the bill with the exception that he introduced it by request of Dr.Edwin Goodwin of Posey County, who is the author of the demonstration. The latter and State Superintendent of Public Instruction Geeting believe that it is the long-sought solution of the problem, and they are seeking to have it adopted by the legislature. Dr. Goodwin, the author, is a mathematician of note. He has it copyrighted and his proposition is that if the legislature will indorse the solution, he will allow the state to use the demonstration in its textbooks free of charge. The author is lobbying for the bill.”

Bill 246 was, curiously enough, referred to the House Committee on Swamp Lands. Perhaps this was an early indication of the muck and mire this ill-fated expedition was bound to encounter.

The chairman of the committee, Representative M. B. Butler, of Steuben County, submitted a report upon receipt of the bill, stating that the committee “begs leave to report the same back to the House with the recommendation that said bill be referred to the Committee on Education.”

Inasmuch as the proposed legislation dealt with scholarly things, as well as how these matters would affect Indiana’s schoolchildren, that seemed to be a prudent measure. Here is where things become particularly alarming. Those who serve on a committee dealing with education presumably have some kind of educational background that would qualify them for the position. At the very least, it seems reasonable that they would consult with those who have demonstrated aptitude in the matters under consideration. Whatever their background, and whomever they consulted, the committee failed to grasp the central problem with the legislation. If you follow the mathematical concepts annunciated in the bill, you basically had your choice of the value of pi:

(1) The ratio of the diameter of a circle to its circumference is 5/4 to 4. In other words, pi equals 16/5 or 3.2

(2) The area of a circle equals the area of a square whose side is 1/4 the circumference of the circle. Working this out algebraically, we see that pi must be equal to 4.

(3) The ratio of the length of a 90-degree arc to the length of a segment connecting the arc’s two endpoints is 8 to 7. This gives us pi equal to the square root of 2 x 16/7, or about 3.23.

Admittedly, the bill is so confusing that there may be other interpretations as well. Mathematician David Singmaster claims to have found six different values in the bill, plus three more in Goodwin’s other writings and comments, for a total of nine.

All of this escaped the notice of the Education Committee. On February 2, 1897, the Committee on Education unanimously recommended that the bill be adopted. It was forwarded to the full House.

Clarence A. Waldo, a professor of mathematics from Perdue University, just happened to be visiting the Indiana Capitol on February 8, the day Bill 246 came up for consideration. He was there for the purpose of lobbying for funding for the Indiana Academy of Science. He entered the visitors’ gallery of the House and discovered that he was in the midst of a debate upon a piece of mathematical legislation. He later wrote of the experience:

“An ex-teacher from the eastern part of the state was saying: ‘The case is perfectly simple. If we pass this bill which establishes a new and correct value for pi, the author offers to our state without cost the use of his discovery and its free publication in our school textbooks, while everyone else must pay him a royalty.'”

The House voted 72 to 0 to waive the constitutional requirement that the bill be read on three consecutive days before voting. When the bill itself came up for a vote, it passed by 67 to 0 and was referred to the Senate for consideration. It was then that Waldo had an opportunity to look at the bill. Someone asked him if he would like an introduction to Dr. Goodwin, the bill’s author. Waldo declined, saying he was acquainted with as many crazy people as he cared to know.

Waldo seemed to be alone in recognizing the absurdity of the situation. The newspapers reported the suspension of the constitutional rules and the unanimous passage of the bill without much comment at all, except for one line in the Indianapolis Journal that “this is the strangest bill that has ever passed an Indiana Assembly.”

The Senate received the bill from the House on February 10. It was read for the first time on February 11 and sent, curiously, to the Committee on Temperance. Just as the House’s Committee on Swamp Lands may have been a foreshadowing of where it was heading, perhaps those who referred Bill 246 to the Committee on Temperance believed that only those who were under the influence of alcohol would seriously entertain adopting such a measure.

If that was the plan, it failed. On February 12, Senator Harry S. New, of Marion County, Chairman of the Committee on Temperance, made the following report to the Senate: “Your committee on Temperance, to which was referred House Bill No.246, introduced by Mr. Record, has had the same under consideration and begs leave to report the same back to the Senate with the recommendation that said bill do pass.”

Incredibly, a law to decree that which mathematical axioms prevents now found itself before the Senate, ready to be adopted.

By this point, Professor Waldo was sufficiently alarmed that briefly abandoned his attempts to lobby for funding, and instead devoted his energies to trying to educate some senators about mathematics. He told as many senators as he could that “the Senate might as well try to legislate water to run uphill as to establish mathematical truth by law.”

The Senate Journal mentions only that the bill was read a second time on Feb.12, 1897, that there was an unsuccessful attempt to amend the bill by strike out the enacting clause. After that, further consideration of the measure was postponed indefinitely.

And so it happened that the Indiana Pi Bill narrowly avoided becoming the law of the state of Indiana. It happened not because any legislators looked at the concept and declared, “This is just plain silly.” It didn’t happen because they brought in learned experts on the matter. It failed to pass primarily out of dumb luck when a real mathematician just happened to overhear what was going on.

Goodwin, for his part, continued to swear by his extraordinary mathematical discovery. Sadly, five years after his signature legislation died, Goodwin did too. According to an obituary, he lived out the remainder of his years, “doomed to disappointment, the child of his genius still unreceived by the scientific world.”

This entire bit of legislative tomfoolery would all be somewhat hilarious, but for one fact. The only thing that distinguishes this piece of legislation from countless other situations where legislators vote on things they know nothing about is that fate intervened to prevent Bill 246 from being enacted. It should also be noted that technically, the Indiana Pi Bill was not defeated; it was merely tabled indefinitely. There is nothing that prevents the Indiana legislature from taking it up again for further consideration.

Read about more stupid laws.

Read more fun facts about mathematics.

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