## Pi in Indiana

The story continually surfaces about the Indiana Legislature's attempted or actual redefinition of pi, the ratio of the circumference of a circle to its diameter, to be the value 3. Petr Beckmann relates the history of Indiana House Bill 246 of 18 January 1897, in which Edwin J. Goodman, MD, proposes to give some of his mathematical accomplishments to the people of Indiana, which included squaring the circle, without cost, though inhabitants of other states would have to pay. The Committe on Swamp Lands reported favorably on the bill, and the state was saved the embarrassment of its passage at the last moment by a professor from Purdue.

House Bill 246 does not mention the value 3, and is really not the legislation to which the popular story refers. As much as I would like to laugh at the expense of a Hoosier legislature, they do not deserve the reputation of believing that they could make pi equal to 3, even though many were bible believers, which would make this more likely.

I Kings 7:23 says: "And he (Hiram) made a molten sea, ten cubits from the one brim to the other; it was round all about, and his height was five cubits; and a line of thirty cubits did encompass it round about." So there is biblical authority for π = 3.

The ancient world normally used 22/7 for pi, which is a good approximation, and not hard to do if you can multiply by 22 and divide by 7. However, this was difficult for Indiana farmers, as it probably still was for the graduates of Indiana schools before pocket calculators. The reason a farmer was interested was that one product of an Indiana farm was timber, until the state aquired its present largely timberless aspect. One form of timber that could be sold was telegraph poles, and they were specified as to butt and top diameters, as well as to length, and the dimensions had to be known before cutting the tree to avoid wasting work (wasting trees was hardly a consideration). A farmer could only conveniently measure the circumference, so finding the diameter brought him squarely up against arithmetic, which was probably not his long suit. Farmers complained to the Legislature for relief from this inconvenience.

The legislature concluded that dividing by three was probably within the compass of most Indiana farmers, and so established (at least for government work, but probably generally) that this was close enough to pi, with the difference to the benefit of the farmer, for general use. This was the "pi" bill that was passed, if any was. I do not know the date or the bill number, but I recall that it was mentioned in Taliaferro P. Shaffner's book on telegraphs. Unfortunately, I cannot check the recollection, but it appears somewhere.

### References

Petr Beckmann, A History of Pi (New York: St. Martin's Press, 1971). pp. 174-177.

T. P. Shaffner, The Telegraph Manual, a Complete History and Description of the Semaphoric, Electric and Magnetic Telegraphs of Europe, Asia, Africa and America (New York: Pudney and Russell, 1859). Page reference for Indiana value of pi unknown, and this work currently unavailable to the author to check the reference.

King James Bible, I Kings 7:23.

Skeptical Enquirer, July/August 2003, letter by Mr. D. P. Babcock, p. 68.