Friday, 18 January 2013

How Pi Was Almost Equal to Three in Indiana

So what about the state that passed a law that set Pi = 3? Well, it was in the paper, and on the internet, but it never happened, although it did get close once. A hoax article was printed and widely circulated (on April 1, 1998) that said that NASA engineers in Huntsville, Alabama were upset about the discovery that the Alabama legislature had just passed a law making Pi=3. When the perpetrators of the hoax realized that the article was being paraphrased (without all the hints that it was a joke, such as the authors name, April Holiday) and circulating as truth, they tried to circulate a notice of the hoax, but found the truth spread much more slowly than the sensational story.

But it was on this day in 1897 that an actual bill was introduced into the state House of Indiana to pass a law which would have, in effect, make pi equal to ... well several numbers it seems. And I should point out that the proposed bill was the idea idea of a fellow who had already proved many of the impossible constructions of geometry, such as squaring the circle. Here is a another description of the bizarre incident by Cecil Adams from his web column, "Straight Dope":
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It happened in Indiana. Although the attempt to legislate pi was ultimately unsuccessful, it did come pretty close. In 1897 Representative T.I. Record of Posen county introduced House Bill #246 in the Indiana House of Representatives. The bill, based on the work of a physician and amateur mathematician named Edward J. Goodwin (Edwin in some accounts), suggests not one but three numbers for pi, among them 3.2, as we shall see. The punishment for unbelievers I have not been able to learn, but I place no credence in the rumor that you had to spend the rest of your natural life in Indiana. [ Although it is often called the Pi Bill, 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). In fact pi is not mentioned in the text of the bill.]

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."
Goodwin's "solutions" were indeed published in the AMM, though with a disclaimer of 'published by request of the author'.

If you feel up to the task, the bill can be found here.

Just as people today have a hard time accepting the idea that the speed of light is the speed limit of the universe, Goodwin and Record apparently couldn't handle the fact that pi was not a rational number. "Since the rule in present use [presumably pi equals 3.14159...] fails to work ..., it should be discarded as wholly wanting and misleading in the practical applications," the bill declared. Instead, mathematically inclined Hoosiers could take their pick among the following formulae:
(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.

There may have been other values for pi as well; the bill was so confusingly written that it's impossible to tell exactly what Goodwin was getting at. Mathematician David Singmaster says he found six different values in the bill, plus three more in Goodwin's other writings and comments, for a total of nine.

Lord knows how all this was supposedly to clarify pi or anything else, but as we shall see, they do things a little differently in Indiana. Bill #246 was initially sent to the Committee on Swamp Lands. The committee deliberated gravely on the question, decided it was not the appropriate body to consider such a measure and turned it over to the Committee on Education. The latter committee gave the bill a "pass" recommendation and sent it on to the full House, which approved it unanimously, 67 to 0.

In the state Senate, the bill was referred to the Committee on Temperance. (One begins to suspect it was silly season in the Indiana legislature at the time.) It passed first reading, but that's as far as it got. According to The Penguin Dictionary of Curious and Interesting Numbers, the bill "was held up before a second reading due to the intervention of C.A. Waldo, a professor of mathematics [at Purdue] who happened to be passing through." Waldo, describing the experience later, wrote, "A member [of the legislature] 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."

The bill was postponed indefinitely and died a quiet death. According to a local newspaper, however, "Although the bill was not acted on favorably no one who spoke against it intimated that there was anything wrong with the theories it advances. All of the Senators who spoke on the bill admitted that they were ignorant of the merits of the proposition. It was simply regarded as not being a subject for legislation."

Tennessee is also frequently mentioned as a state that "passed a pi=3 bill" but that seems to come from a small reference by Robert Heinlein in Stranger in a Strange Land. "In the Tennessee legislature a bill was again introduced to make the ratio pi exactly equal to three"."

* Much of the text was taken from http://www.straightdope.com. and Wikipedia