The State that Attempted to Legislate Pi

There is a rumor that Indiana once passed a law that specified a rational value for pi and a process for solving for it. Of course this is false; it only got passed the Indiana State House. How could this have happened? A doctor named E. J Goodwin submitted the proposal to Indiana House Representative Taylor I. Record who, knowing nothing about the validity of bill, submitted it to the Indiana State House. In 1897, the apparently equally unknowledgeable House passed the bill unanimously before the required third reading of the law (maybe they just wanted to stop hearing the confusing nonsensical mathematics of the bill). What may be even more surprising is this happened with the full support of the State Superintendent of Public Instruction. The Senate suspended action on the bill indefinitely (which is the current state of the bill) but only after significant controversy.

The bill was actually based on an accepted submission
by Goodwin to the *American Mathematical
Monthly* titled “Quadrature of the Circle” in which no rebuttal
or criticism ever appeared, even though a translation of a Felix Klein work
that included Lindemann’s proof of the
transcendence of pi appeared in the *Monthly
*about a year and a half after Goodwin’s publication in the July 1894
issue. There are two reasons given for this massive failure of oversight.
First, the *Monthly* was in its first
year of publication and was trying to find material and promote itself. Second,
the authors of the *Monthly* admitted
to a Non-Euclidian school of thought, so they welcomed the challenge to
tradition that Goodwin presented.

At first, the only dissent from the bill was an
article including the history of pi that appeared in the Indianapolis newspaper
*Der Tägliche
Telegraph*, but it was completely in German. This lack of dissent is amazing
considering the lack of reason present in Goodwin’s so-called discovery.
The bill actually gives two processes that are logically inconsistent (but
Goodwin wasn’t using logic). The bill arbitrarily states that the ratio
of a 90° chord in a circle to 90° of the circumference is 7 to 8, and
the ratio of the chord to the diameter is 7 to 10 (which gives a value of pi of
3.2). In another section of the bill, Goodwin attempts to give the area of a
circle as ¼ of the circumference squared, which is even more inaccurate,
because it treats the circumference of a circle the same as the perimeter of a
square (and thus gives a value of pi of 4), whereas in the other process, the
two are at least considered different. Including his work outside the bill,
Goodwin gave processes that implied values of pi anywhere between 2.56 and 4.

Goodwin’s publication in the *American Mathematical Monthly*, claim of
support from the National Observatory in Washington D.C., public challenge to
the Smithsonian Institute to award $10,000 prizes to anyone able to find an
exception to (not even a falsehood in) his proposal or explain why his
arbitrary relationships worked, and copyright in England and the United States
convinced many of the legitimacy of the bill. Ridicule eventually occurred in
local and out-of-state newspapers, and Purdue mathematician C.A. Waldo went in
to “coach” the legislature. However, the ultimate failure of the
bill is pinned on the inappropriateness of attempting to legislate
pi rather than the inaccuracy of the bill itself.

Works Cited

Hallerberg, Arthur E.. “Indiana’s Squared Circle.” Is Mathematics Inevitable?: A

Miscellany. Ed. Underwood Dudley. United States of America: The Mathematical Association of America, 2008. 261-270.

©2009 Jorge Eduardo Fernandez