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The Time they Tried to Legislate Pi

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This post is by Michael Apfeldorf of the Library of Congress.

March 14 is Pi Day! If you are looking for an interesting piece of history to give your students both some practice with mathematical reasoning and the opportunity to reflect on a unique intersection of mathematical truth and legislative action, introduce them to the Indiana Pi Bill of 1897.

Bill #246 of the 1897 Indiana General Assembly is one of the most notorious attempts to establish a mathematical truth via legislative fiat. As described in the February 21, 1897 Indiana Times, physician and amateur mathematician Edwin J. Godwin successfully lobbied the Indiana General Assembly to introduce legislation recognizing as fact that he had solved “three geometrical problems which [had] puzzled the brains of mathematicians since the erection of the pyramids of Egypt” and which were generally considered to be unsolvable. Foremost among these was “squaring the circle” – constructing a square equal in area to a given circle, using only a ruler and a compass some finite number of times. The article tells us that Goodwin obtained copyrights for his solutions in seven countries and also that his proposed measure successfully passed “one branch of the [Indiana] legislature.” The bill was not ultimately passed, but had Goodwin gotten his way, the Indiana legislature would have officially changed pi to 3.2 instead of the approximation 3.1416+ as commonly thought.

Squaring the Circle. Indianapolis Journal, February 21, 1897

Ask students to analyze the article using two different lenses – a mathematics one and a civics one.

From a mathematics perspective, the article explains that “in his discovery of the new formula for squaring the circle Dr. Goodwin proceeded in a manner that is so simple that the ordinary schoolboy may easily understand the demonstration. He discarded the diameter as a linear unit from which to figure the area of a circle and proceeded to use the perimeter, the same system that is used for a square.”  Knowing now that Goodwin was incorrect in his assertions, see if students can follow Goodwin’s mathematical arguments and identify where he may have gone wrong.

From a civics perspective, ask students to reflect upon the concept of establishing a mathematical or scientific truth via legislative process. What might be pros or cons of such an action?  What do they make of the fact that the bill passed the Indiana House, even though the mathematical solutions were not correct?

As it turns out, a German mathematician named Ferdinand Lindemann had proven that squaring the circle was impossible 15 years earlier, in 1882, as this article from the August 4, 1933, Indianapolis Times reports. Once again, students can analyze the mathematical reasoning in the article. Ultimately, Lindemann’s “proof [was] based upon a demonstration of the fact that pi, the ratio between the circumference and diameter of a circle, is transcendental…incapable of being defined by any combination of a finite number of co-efficients.” Meanwhile, “with ruler and the compass, it is only possible to perform rational operations and the extraction of square roots.”

Let us know what your students think of this unique pi-related event in history!

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