Mathematics saved one hundred years ago today

Ilan Vardi

This Wednesday marks the centennary of an infamous episode in the history of science. On February 12, 1897, the senate of the state of Indiana voted to postpone indefinitely a bill that would decree the number pi to be equal to 3.2. This bill had already passed the house of representatives with a unanimous vote of sixty seven to zero. In fact, it had passed a first reading in the senate, and it was only due to the intervention of C.A. Waldo, a mathematics professor at Purdue University who happened to be visiting the capitol on unrelated business, that the bill did not pass on its second reading.

The author of Bill 246 was Edwin J. Goodwin, M.D., of Solitude Indiana who claimed that is was "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 official action of the legislature in 1897."

The critical passage in the bill is: "...disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four..." This statement claims that pi = 3.2 should be the law of Indiana (there is another passage that can be interpreted as giving a value of pi equal to 16/sqrt(3) which is approximately equal to 9.2).

The House referred the bill to the House Committee on Swamp Lands, which passed it to the Committe of Education, which reported it back to the House "With recommendation that said bill do pass." And so it came to pass unamimously. The Senate gave it to be reviewed by the Committee on Temperance which also recommended it and it passed its first reading. Without the intervention of Professor Waldo, it would surely have become law.

Who was Dr. Goodwin and what were his crendentials? In fact, he gives them in the bill:

"In further proof of the value of the author's proposed contribution to education, and offered as gift to the state of Indiana, is the fact of his solution of the trisection of the angle, duplication of the cube and quadrature of the circle having been already accepted 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 abilities to comprehend."

Note that these "unsolvable mysteries" were all solved in the 19th century when it was rigorously proved that none of Dr. Goodwin's construction were possible (with a ruler and compass).

Remarks on the ridiculous aspect of this incident.

Nowadays this incident is ridiculed as one of those cases where science has been on trial and failed, for example, the trial of Galileo, and the Scopes trial. However, there is a fundamental difference--neither Galileo nor Scopes had strong evidence supporting their beliefs, for example, the first observational confirmation of the Copernican theory that the earth goes around the sun did not occur till one hundred years after Galileo's conviction by the Inquisition. On the other hand, there is a rigorous argument that pi is not equal to 3.2. What I mean by a rigorous proof is not taking a bicycle wheel and rolling it once and checking the distance versus its diameter. I mean taking the mathematical definition of a circle, the points which are a fixed distance from a given point (the distance is defined to be the radius) and comparing the length of this figure to twice its diameter. The exitence of such rigorous arguments explain why the Inquisition didn't imprison anyone for believing that pi = 3, the value given by the Bible in I Kings vii.23 (though this assertion has been challenged). The first rigorous proof was given by Archimedes about 250 B.C., when he proved that pi is less than 3 1/7 but greater than 3 10/71, so that pi is less than 3.1428571... and greater than 3.140845070...

Remarks on the education of mathematicians.

Professor Waldo managed to convince the senate not to pass the bill but would graduates of mathematics programs at modern universities be able to do the same? What is the point of ridiculing the government of the state of Indiana circa 1897 if you yourself have no idea why pi is not in fact 3.2?

As an exercise to mathematics majors who may some day be called upon to save the value of pi. Answers due: Friday, February 21. Return to Professor Vardi.

  1. Prove that pi is greater than 3 and less than 4.
  2. Show that pi exists.
In case you are confused by (1), recall the definition of pi: It's the ratio of the circumference of a circle with its diameter. But which circle? In other words, you have to show that if you take two different circles then the ratio of the circumference to the diameter is the same for both. And for those who have been reading up on fractals, you might also want to prove that pi is not infinity...

The reference for this article is "A History of Pi," by Petr Beckmann, St. Martin's Press 1971. Doron Zeilberger informed me that Beckman had incorrectly refered to "Goodwin" as "Goodman."

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