The Indiana Pi Bill

Today’s unusual wikipedia article is a complex tale – and as a commited arithmophobe, this is all greek to me…

The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most famous attempts to establish mathematical truth by legislative fiat. Despite that name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π (pi), the ratio of the circumference of a circle to its diameter. However, the bill does contain text that appears to dictate various incorrect values of π, such as 3.2 (π = 3.14159265…).

The bill never became law, due to the intervention of a mathematics professor who happened to be present in the legislature.

The impossibility of squaring the circle using only compass and straightedge, suspected since ancient times, was rigorously proven in 1882 by Ferdinand von Lindemann. Better approximations of π than those inferred from the bill have been known since ancient times.

In 1894, Indiana physician and amateur mathematician Edwin J. Goodwin (ca. 1825–1902) believed that he had discovered a correct way of squaring the circle. He proposed a bill to Indiana Representative Taylor I. Record, which Record introduced in the House under the long title “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”.

The text of the bill consists of a series of mathematical claims, followed by a recitation of Goodwin’s previous accomplishments:

“… his solutions of the trisection of the angle, doubling the cube and quadrature of the circle having been already accepted as contributions to science by the American Mathematical Monthly … 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.”

Upon its introduction in the Indiana House of Representatives, the bill’s language and topic occasioned confusion among the membership; a member from Bloomington proposed that it be referred to the Finance Committee, but the Speaker accepted another member’s recommendation to refer the bill to the Committee on Swamplands, where the bill could “find a deserved grave”. It was transferred to the Committee on Education, which reported favorably; following a motion to suspend the rules, the bill passed on February 6, without a dissenting vote. The news of the bill occasioned an alarmed response from Der Tägliche Telegraph, a German-language newspaper in Indianapolis, which viewed the event with significantly less favor than its English-speaking competitors. As this debate concluded, Purdue University Professor C. A. Waldo arrived in Indianapolis to secure the annual appropriation for the Indiana Academy of Science. An assemblyman handed him the bill, offering to introduce him to the genius who wrote it. He declined, saying that he already met as many crazy people as he cared to.

Although the bill has become known as the “pi bill”, its text does not mention the name “pi” at all, and Goodwin appears to have thought of the ratio between the circumference and diameter of a circle as distinctly secondary to his main aim of squaring the circle.

It is unknown what made Goodwin believe that his rule could be correct. In general, figures with identical perimeters do not have identical area; the typical demonstration of this fact is to compare a long thin shape with small enclosed area (approaching zero as the width decreases) to one of the same perimeter that is approximately as tall as it is wide, obviously of much greater area.

The day after New Zealand legalised same-sex marriage, a Catholic priest appeared on a television news show and drew parallels between legalising same-sex marriage and the 1897 attempt to regulate pi, saying pi – and heterosexual marriage – were both “pre-existing” realities that couldn’t be changed. 


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About Author Profile: Worm

In between dealing with all things technological in the Dabbler engine room, Worm writes the weekly Wikiworm column every Saturday and our monthly Book Club newsletters.

15 thoughts on “The Indiana Pi Bill

    October 19, 2013 at 13:32

    Using the good old tried and trusted British method for relating circumference to diameter we utilise the fraction three and one seventh. Ergo any circumference you care to throw into the arena will be three and one seventh times greater than it’s diameter. Not for nothing is our standing in the world of the built environment where it is today, so what that the Comet fell out of the sky, Cockerell’s hovercraft died the death, Clive’s C5 deep sixed, Concorde cost-a-fortune, the Mini lost-a-fortune, Jaguars fell-apart, the Chinkies are about to own our power generation and Dave needs a wooly pully. What was good enough for our fore-bearers is good enough for us chickens as we calculate government IT system costs, GPs remuneration, vet’s and lawyer’s bills etc.

    It’s all in the sevenths dear Dabblers, the sevenths, seals and fractions.

    The seals of course leaked oil; the fractions are enough, near enough.

    • Worm
      October 19, 2013 at 14:56

      Excellent rhetoric Malty!

    October 19, 2013 at 13:56

    There is a book called The History of Pi, by Petr Beckmann that touches on this incident. The legislators were apparently dazzled by the promise that the state’s schools would not have to pay copyright on the new text this revolution would bring in. Are you sure that it isn’t trisecting the angle that can’t be done with just compass and straightedge? Squaring the circle in the sense of providing a square with equal area to a given circle, just can’t be done with rational numbers, though of course a square of pi units to the side will be equal in area to a circle with radius unit 1.

    There was a far more recent prank by Alan Sokal, who a dozen or 20 years ago induced an academic journal to publish his paper “The Social Determination of Pi”, which (as far as I know) without reference to Indiana purported to prove that pi is as socially determined as gender, patriarchy, what have you.

    October 19, 2013 at 13:58

    Oops-the square must have sides the square root of pi on each side. And of course square roots have been causing anxiety, dread, what have you, for a very long time. The Pythagoreans are said to have done away with the fellow who proved that the square root of two is irrational.

      October 19, 2013 at 17:14

      Constructing a regular septagon (seven sides), squaring the circle, cubing the sphere and trisecting an angle are all impossible with compass and straight edge. Poor old Galois proved all that and more, so the story goes, the night before getting a bullet in the stomach. Although that’s not quite true, it does improve the telling of it.

      On the other hand, constructing square roots is easy.

      Michael Smith
      October 20, 2013 at 02:16

      George, if the sides of the square are the square root of pi can they really be equal to each other? Can indeterminate quantities be equal, short of infinity?

  4. Worm
    October 19, 2013 at 14:58

    All numbers are irrational in my book. Horrible, nasty non-wordy things

      October 19, 2013 at 15:20

      Tut, tut. What would Georg Cantor say?

      And it has been established that pi is not merely irrational, it is transcendental.

      • Worm
        October 19, 2013 at 15:47

        I was a little harsh in my dismissal of all numbers, I am interested in the idea of Pi in the philosophical, chaos theory sense. Incidentally, the film of the same name is pretty good

          October 19, 2013 at 17:24

          Somewhere, deep inside the decimal expansion of Pi, you will find the complete works of Dosdoyevsky encoded in Ascii; further along, you will find the same, translated into Aramaic in the most ingenious manner; some time later, far beyond the reach of the most powerful brain ever imagined or yet to be imagined, lurks the Bible with an accurate pronunciation guide; and were you granted eternity, long after the sun had boiled-off to oblivion, you would finally discover what were first words ever uttered by man. Really, you just have to know where to look.

          October 19, 2013 at 17:25

          I might add, there’s actually a mathematical proof for that.

          • Worm
            October 19, 2013 at 17:34

            But (and excuse my total ignorance on this) is it not a case of pi being infinite and ‘a million monkeys and a million typewriters’ and all that?

            October 19, 2013 at 17:43

            Basically, but there are lots of ways you can be infinite. At one end, you can be infinitely repetitive, like 0.1212121212…, and so on, but Pi sits at the other: every combination imaginable appears in the decimal expansion of Pi, essentially with equal frequency. The general rule is that if there is any exotic property to be had, Pi probably has it.

            October 19, 2013 at 17:56

            Or put in slightly different terms: Pi is of the purest simplicity, expressing merely the relationship between a circle and its radius, but yet Pi contains within itself the most complete chaos – that cacophony of a million monkeys at their million typewritters, chattering away to eternity – and then deep inside that chaos, order spontaneously appears, and wonder with it.

            I could wax lyrical on this stuff forever, you know.

          • Gaw
            October 20, 2013 at 21:22

            ‘…and then deep inside that chaos, order spontaneously appears’

            Thanks Graham. This is all new to me and very interesting. I’m wondering whether the order you refer to is a chaotic generation of something that merely looks like order?

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