This is part of my history and guide to my adopted home - Terre Haute, Indiana.
Introduction
A long time ago, which could be anywhere in the 1960s to 1990s, I read a science fiction short story about what happened when a government tried to legislate away the Law of Gravity. I cannot remember the name of the story or even the author, but it was similar to A Politician Who Campaigned on a Platform of Repealing the Law of Gravity.
When I moved to Indiana in 2001, I heard the strange story of a man who thought Pi (Π) should be 3.2, and tried to convince the Indiana state legislature to proclaim it as such. He almost succeeded!
Pi and Geometric Problems
Pi
Pi is the ratio of a circle's circumference to its diameter. It is usually represented to two or more decimal places such as 3.14 or 3.14159. A rough approximation of Pi is given as 22/7 but the truth is that it is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers. It is also a transcendental number, which means it cannot be calculated using an algebraic equation involving only finite sums, products, powers, and integers.
Mathematicians have long sought to provide an exact value of Pi but it is an irrational number, so its decimal representation never ends, nor enters a permanently repeating pattern. A clay tablet dated 1900 - 1600 BC and found in Babylon (in modern day Iraq) calculated Pi as 3.125. A papyrus found in Egypt from 1850 BC calculated Pi as 3.16. In April 2025, the first 300,000,000,000,000 (300 trillion) digits of Pi were calculated.
Geometric Problems
The ancient Greek mathematicians had three problems they wanted to solve using only a compass and straight edge; these were, doubling the cube, squaring the circle, and trisecting the angle. All are now proved to be impossible except for a few angles in the trisecting the angle problem.
Doubling the Cube
The problem is to create a cube which is exactly double in volume to another. A solution is impossible because although you can create circles centred on one previously defined point and passing through another, and you can create lines passing through two previously defined points. Any added circles and lines do not intersect properly.
Squaring the Circle
The ancient Greeks thought it might be possible to draw a square with the eaxact same area as a circle using only a compass and a straight edge. This was known as Squaring the Circle or Quadrature of the Circle. This goal is an impossibility because Pi is a transcendental number. This had long been thought to be true and was proved once and for all to be so by the Lindemann-Weierstrass theorem developed by Ferdinand von Lindemann and Karl Weierstrass in 1882.
Using just a compass and straight edge you can get some very close apporximations, but not an exact match for the area. Adam Adamandy Kochański came close in 1685 but his value of Pi was only correct to 4 decimal places. Jacob de Gelder published a method in 1849; he got to 5 decimal places for Pi. In 1914, Ramanujan did it with Pi correct to 8 decimal places. This level of precision gave the area of a square very nearly equal to the area of the starting circle; the error being less than a twelfth of an inch when the diameter is 8,000 miles long. Close but not exactly the same.
Trisecting the Angle
The problem is the construction of an angle equal to one third of a given arbitrary angle. The solution is an impossibility as proved by Pierre Wantzel in 1837. However, certain angles such as a right angle, but not all, can be trisected using only a compass and a straight edge.
Dr. Edward Johnston Goodwin
Dr. Edward Johnston Goodwin, whose first name is sometimes given as Edwin, was a medical doctor practising in Solitude, Posey County, in the south west corner of Indiana.
Dr. Goodwin was born near Lynchburg, Amherst County, Virginia on December 30. The year is uncertain, but best believed to be 1828. He obtained his medical degree from the Philadelphia College of Medicine, Philadelphia, Pennsylvania in March 1855. He moved to Solitude in the spring of 1878.
He was also a mathematician, over the years, Dr. Goodwin claimed to have solved all three of the Greek classical geometric problems.
He later explained the true value of Pi was revealed to him by God in March 1888. In July 1894, he published a paper in the American Mathematical Monthly in their Queries and Information section entitled Quadrature of the Circle. The paper was not peer reviewed, but to be fair to the publication, they did say it was "published by request of the author."
Dr. Goodwin's Squaring the Circle
Dr. Goodwin was so sure of his "truth" he copyrighted the method in the United States, as well as England, Germany, Belgium, France, Austria, Italy, and Spain.
Even before Bill 246 reached the Indiana state legislature he had tried to publisize his theories. He apllied for and got space to hold demonstrations of his method at the 1893 Columbian Exposition in Chicago. This was cencelled when Selim H. Peabody, chief of the department, after granting the space, revoked his permit and advised the author to present his solution to the mathematical journals. This Dr. Goodwin did, which is why it appeared in the July 1994 edition of the American Mathematical Monthly.
The American Mathematical Monthly became a very respected publication but in 1894, the publisher, Benjamin F. Finkel, would print whatever he could get.
The Indianapolis Journal of February 21, 1897, said that "He [Dr. Goodwin] is six feet tall and his frame is strong and elastic and his massive,angular head correctly suggests his rugged mathematical brain." The article was published nine days after Bill 246 was put to rest which was on February 12, 1897. The Indianapolis Journal article did not refer to this at all.
Dr. Goodwin remained adamant he was right and everyone else was wrong. In the February 28, 1897, edition of the Indianapolis Journal he wrote:
Of course they know it is impossible, and particularly this Mr. Heal [William Ephraim Heal], whom I do not know. It must be impossible to square the circle, for Mr. Heal says so. Now isn't that a brightargument? Drop out the middle initial of W. E. Heal's name, and it is W-h-e-a-1, or wheel, and if a man has wheels in his name he may also have them in his head, and a man with wheels in his head always thinks he is the only man on earth whose trolley is not misplaced.
He continues:
What if Professor Beman, of Ann Arbor, is writing a book to demonstrate the impossibility of the quadrature of the circle. My demonstration is already out. Professor Beman should have written his book a century ago to have been original.
Dr. Goodwin gave an interview to the Indianapolis Sun which appeared in their February 6, 1897 issue:
If I live ten years, and I hope I shall, you watch out for Goodwin. My discovery will revolutionize mathematics. The astronomers have all been wrong. There's about 40,000 square miles on the surface of this earth that isn't here. Watch out for Goodwin if you live ten years,
Dr. Goodwin died in Solitude on June 23, 1902. He was buried in Moore Cemetery, near Farmersville,Indiana, on the New Harmony-Mt. Vernon road.
House Bill No. 246
House Bill 246 did not specify what Pi should be, it was concerned wtih Goodwin's method of Squaring the Circle. Several mathematicians tried using Goodwin's method and Pi variously worked out to be 3.2, 3.23, 4, 9.2376, or practcally any number you can think of except for the correct number of 3.14159.
The Bill was introduced to the House by Mr. Taylor I. Record, who lived in New Harmony, and who was Representative from Posey County, on January 18, 1897.
Opening page of House Bill 246
The opening page of House Bill 246 reads:
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.
Part of House Bill 246 read "Since the rule (Pi) in present use fails to work, it should be discarded as wholly wanting and misleading in the practical applications."
One member of the legislature suggested the Bill be passed to the Finance Committee, but it was passed to the Committee on Canals which was often referred to as the Committee on Swamplands. They considered it and then decided it was not appropriate body to consider such a Bill and passed it to the Committee on Education. One reason it might have been passed to the Committee on Canals in the first place was perhaps to find "a deserved grave" for it. The Committee on Education gave the bill a "pass" recommendation and sent it on to the full House, which approved it unanimously, 67 to 0 on February 6, 1897.
The Bill then passed to the Senate and was looked at by the Committee on Temperance. The Bill passed its first reading but luckily Clarence Abiathar Waldo, Head Professor of Mathematics at Purdue University was attending the Senate to secure the annual appropriation for the Indiana Academy of Science. He was asked if he would like to be introduced to Goodwin. He declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know.
Clarence Abiathar Waldo, Head Professor of Mathematics at Purdue University
Image: Wikimedia Commons
Waldo did speak to several members of the Senate and when the Bill reached them on February 12, 1897, they postponed the Bill indefinitely. Apart from Waldo, there were other reasons. One Senator said that the General Assembly lacked the power to define mathematical truth, and some Senators noted that some newspapers were making fun of them.
Problems
One of the first newspapers to criticize the Bill was the Indianapolis, German-language newspaper Der Tägliche Telegraph. On January 19, 1897, the day after its introduction to the House, it wrote:
The clerk of the House, O. P. Iles, succeeded in reading the Greek words with which the bill superabounded only with the greatest effort. The members could hardly believe their ears, as they were compelled to listen to the new way to accomplish this squaring, and how it should b etaught in the schools.
After the bill was read and the representatives had enough time to recover from their amazement and dread, the Speaker posed the humble question as to which committee the Squaring of the Circle should be referred. Gast of Bloomington, a Democrat, moved, amid great laughter, that the bill bereferred to the Finance Committee as it has made itself responsible for the solving of great problems, and since it has the time to do the job.
Another representative arose and said that he believed the Committee on Swamplands was the appropriate place for successful wrestling with the problems.
Midst general cheerfulness the Speaker then referred the "Squaring of the Circle" to the Committee on Swamplands where, in the swamp, the bill will find a deserved grave.
Indiana state legislature became a nationwide laughing-stock. The Indianapolis News of February 13, 1897, wrote that:
The bill was brought up and made fun of. The Senators made bad puns about it, ridiculed it and laughed over it. The fun lasted half an hour. Senator Hubbell said that it was not meet for the Senate, which was costing the State $250 a day, to waste its time in such frivolity. He said that in reading the leading newspapers of Chicago and the East, he found that the Indiana State Legislature had laid itself open to ridicule by the action already taken on the bill. He thought consideration of such a proposition was not dignified or worthy of the Senate. He moved the indefinite postponement of the bill, and the motion carried
The same day, the New York Herald wrote:
Let us hope it does not similarly affect the volume of spheres, lest the real capacity of an almost spherical cranium may be much less than its apparent capacity. How seriously that would affect the head of Dr. Goodwin, which seems, by reason of its size, to be in irrepressible conflict with the confines of the universe.
The Chicago Tribune wrote that:
The immediate effect of this change will be to give all circles when they enter Indiana either greater circumferences or less diameters. An Illinois circle or a circle originating in Ohio will find its proportions modified as soon as it lands on Indiana soil.... A Pi that is so simple as 3.2 ought to be free from any entangling features, but if perchance it still proves obdurate no doubt the Legislature will promptly lop off another decimal and call it 3.
The Indianapolis Journal was unimpressed with the critism of the method and on February 21, 1897, wrote, "Dr. Goodwin's discovery is as genuine as that of Newton or Gallileo, and it will endure, whether the Legislature indorses it or not."
On March 6, 1897, the Rock Island Argus of Illinois published this cartoon:
Rock Island Argus of Illinois, March 6, 1897
Image: Wikimedia Commons
Mathematician David Singmaster did an analysis of Goodwin's work and said he found six different values of Pi in House Bill 246 as well as three more in Goodwin's other work.
In 1991, The Straight Dope published an outline of the story and someone wrote to them saying:
Your response to the question about attempts to legislate pi suggests not only that your scholarship is weak but that you are a heathen. When King Solomon constructed the Temple of Jerusalem, the Second Book of Chronicles, chapter 4, verses 2 and 5, tells us:
"Then he made the Sea [a big tub] of cast bronze, ten cubits from one brim to the other; it was completely round. Its height was five cubits and a line of thirty cubits measured its circumference. It was a handbreadth thick; and its brim was shaped like the brim of a cup….. It contained three thousand baths."
The ratio of 30 cubits for the circumference to 10 cubits for the diameter "from one brim to the other" of the "completely round" circle gives the value of pi as being exactly 3. Perhaps reliance on the Word of God motivated the Indiana legislators you trashed. You should have checked with the ultimate reference.
I'm not sure if H.K.S., of Springfield, Virginia, was being serious or not.
Why did it Happen?
I don't think anyone did anything out of malice. There are plenty of people around who once told a task is impossible will attempt to prove everyone else wrong and believe they have found a way to do the impossible. There are plenty of people around trying to create perpetual motion machines, use water as fuel, prove the world is flat, build cold nuclear fusion reactors in their shed and so on.
Local, state and national legislators are not particularly experts on anything, they rely on experts to provide information for them. It may be that Indiana state was influenced by the fact that it was offered something for free that everyone else would have to pay for. It may be that the Bill was given to the Committee on Canals to consider where it could die a quiet death. Unfortunately they passed it which meant it had to go to the Senate, and it was that which got it national attention and ridicule.
As the New York Herald Tribune said their February 24, 1897 issue, "The men who introduce these bills are classed as sane and sensible men, which only goes to show that sane and sensible men can occasionally do very foolish things."
Sources and Resources
Angle trisection, Wikipedia
Chronology of computation of Π, Wikipedia
Did a state legislature once pass a law saying pi equals 3?, The Straight Dope
Doubling the cube, Wikipedia
House Bill No.246 Indiana State Legislature 1897 by Will E. Edington, DePauw University, Indiana Academy of Science, 45 (1935) 206-210.
House Bill No.246 Revisited by Arthur E. Hallerburg, 1966
Indiana's Squared Circle by Arthur E. Hallerburg, Mathematics Magazine, Vol. 50, No. 3 (May, 1977), pp. 136-140
Lindemann-Weierstrass theorem, Wikipedia
Pi, Wikipedia
Pseudomathematics, Wikipedia
Squaring the circle, Wikipedia
The Indiana Pi Bill: The Day Math Got Punk'd by Politics, Abakcus