Legislating the Value of Pi

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The greek letter pi is the mathematical symbol used to represent the number that is the ratio of the circumference of a circle to the length of the circle's diameter. The number is known to be an irrational number[1], approximated by the fraction "22/7", or by the decimal "3.1415926536".

Pi, no doubt because of its fundamental place in geometry and the irritation of its irrationality, has inspired a number of mystics and charlatans throughout history, particularly through vain efforts to "square the circle". Proof in 1882 that the task was impossible[2] apparently did as little to quench interest in the ancient conundrum as thermodynamics did to halt the search for perpetual-motion machines.


Indiana House Bill #246

The most famous -- and only known – case of a state legislature in the US attempting to create by law a new value for pi was that of Indiana in 1897; it has become legendary, and the basis of myth and hoax. Although it has come to represent the occasional ignorance of innumerate legislators, it was not so obviously a bad idea at the time.

The bill was introduced to the house by legislator Mr. Record, but it was reported that "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."[3] The bill began in the Committee on Canals (aka the Committee on Swamp Lands), whose chairman tried unsuccessfully to send it to the Committee on Education.

Redefining the value of pi seems not to have been its principal goal, but a side effect. In fact, the bill seems to have offered four different, new values for pi. Rather, the bill was aimed at benefiting its author, who claimed to have patented a new method for "squaring the circle", which he proposed to let the state of Indiana use free of charge if they would pass his bill! Its opening statement is clear:

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.

To lend credibility to his claim, Dr. Goodwin gave these credentials:

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.

It seems that Dr. Goodwin had already solved two of the great unsolvable problems of ancient geometry and claimed to have solved a third with his method of squaring the circle.

The bill made it through three readings and votes in the House, and its first reading in the Senate. It was evidently seen as of economical benefit, since Indiana would save royalties on the patent, and the legislators proclaimed themselves unfit to comprehend the details of the bill anyway. The finale was dramatic and down to the wire:[4]

That the bill was killed appears to be a matter of dumb luck rather than the superior education or wisdom of the Senate. It is true that the bill was widely ridiculed in Indiana and other states, but what actually brought about the defeat of the bill is recorded by Prof. C.A. Waldo in an article he wrote for the Proceedings of the Indiana Academy of Science in 1916. The reason he knows is that he happened to be at the State Capitol lobbying for the appropriation of the Indiana Academy of Science, on the day the Housed passed House Bill 246. ... The roll was then called and the bill passed its third and final reading in the lower house. A member then showed the writer [i.e. Waldo] 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. That evening the senators were properly coached and shortly thereafter as it came to its final reading in the upper house they threw out with much merriment the epoch making discovery of the Wise Man from the Pocket.


Regardless of its short life and eventual failure to become law, Indiana House Bill #246 has left a legacy.

  • "Like trying to legislate the value of pi" has become a catch phrase used to highlight the patent uselessness of trying to determine mathematical or scientific fact by non-scientific means.[5]
  • It has become an icon, representing misguided attempts on the part of legislative bodies to legislate that which cannot be legislated; moves to legislate the value of pi have, at times, erroneously been ascribed to the state legislatures of Oklahoma, Kansas, Tennessee, Kentucky, and Alabama.
  • In these times of more visible anti-scientific attitudes, the vague memory of the incident in Indiana lent credibility to an April Fool's Day hoax from 1998 claiming that the Alabama state legislature had, indeed, just passed legislation changing the value of pi to equal "3", bringing it into line with the value given in the Bible.[6] The jape has been remarkably persistent[7] and popular.[8]


  1. ^  "Irrational" means that the number cannot be written as a ratio of two integer numbers, as in "1/2" or "7/8". This implies that when irrational numbers are written as decimal numbers, the digits to the right of the decimal point never repeat and never end. In fact, pi is also a transcendental number, meaning that it is not the root of any algebraic equation with rational coefficients; one implication is that age-old efforts to "square the circle" are guaranteed fruitless endeavors.
  2. ^ See, e.g., "Squaring the Circle".
  3. ^ The entire text of the bill, along with contemporary commentary, is in the entry "sci.math FAQ: Indiana Bill sets value of Pi to 3" by Alex Lopez-Ortiz, 17 Feb 2000, which provides most of the historical details given above.
  4. ^ This account is quoted by Lopez-Ortiz, referenced in the previous note.
  5. ^  This Google search for "legislate value pi" returns more than 25,000 examples, most of which use the phrase to ridicule notions that contradict reality.
  6. ^ Barbara Mikkelson, "Alabama's Slice of Pi", snopes.com, 28 October 1998.
  7. ^ Dave Thomas, "Pi are not squared...Pi was a hoax!", NMSR Reports 4, no. 6, June 1998.
  8. ^ The Museum of Hoaxes lists it as #7 on their "Top 100 April Fool's Day Hoaxes of All Time", c. 2003.


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