INTRODUCTION
Pi—the mathematical constant commonly approximated as 3.14159—is an irrational number; it cannot be expressed by any simple fraction of two integers and, consequently, its decimal representation is infinite. Pi is also a transcendental number, a number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Because of this, attempts at “squaring the circle” have proven impossible using a compass and straightedge. By the late eighteenth century, professional mathematicians had recognized this fact. In 1775, for example, the French Academy resolved that they would no longer examine proposed solutions to the ancient geometric challenge.
Yet despite acceptance of these truths among the international community of mathematicians, one Hoosier sought to prove otherwise. And in 1897, the Indiana State Legislature came dangerously close to falsely redefining the value of Pi "as a contribution to education."
dr. edwin j. goodwin
Dr. Edwin J. Goodwin, a physician and amateur mathematician from Posey County, convinced himself that he had succeeded in squaring the circle. He had apparently discovered a new formula in 1888 and spent several years publicizing his claims. In 1893, he secured exhibit space at the World’s Fair in Chicago “to give scientific lectures.” However, authorities subsequently rescinded their offer upon discovering the substance of Goodwin’s claims. Undeterred, the Indiana physician sent his finding to the American Mathematical Monthly. In 1894, the journal published, “by request of the author,” an article entitled “Quadrature of the Circle.” Here, for the first time, Goodwin explains his theories to the mathematical world:
A circular area is equal to the square on a line equal to the quadrant of the circumference; and the area of a square is equal to the area of the circle whose circumference is equal to the perimeter of the square.
To quadrate the circle is to find the side of a square whose perimeter equals that of the given circle; rectification of the circle requires to find a right line equal to the circumference of the given circle. The square of a line equal to the arc of 90 fulfills both of the said requirements.
LEGISLATIVE HISTORY
Having decided that Indiana should be the first to benefit from this “new mathematical truth,” Goodwin drafted a bill incorporating his new theory. On January 18, 1897, Representative Taylor I. Record—during his first and only term with the Indiana General Assembly—introduced the unfortunate piece of legislation at Goodwin’s request, despite "know[ing] nothing of the bill." As summarized in the preamble, House Bill 246 was "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 the official action of the Legislature of 1897."
“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 the official action of the Legislature of 1897. ”
The full text of the bill incorporated consisted of several pseudo-mathematical claims followed by an account of Goodwin's previous accomplishments as "proof of the value of the author's proposed contribution to education."
Section 1
Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle's area is entirely wrong, as it represents the circle's area one and one-fifth times the area of a square whose perimeter is equal to the circumference of the circle. This is because one fifth of the diameter fails to be represented four times in the circle's circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can in like manner make the square's area to appear one-fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle's circumference.
Section 2
It is impossible to compute the area of a circle on the diameter as the linear unit without trespassing upon the area outside of the circle to the extent of including one-fifth more area than is contained within the circle's circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight. By taking the quadrant of the circle's circumference for the linear unit, we fulfill the requirements of both quadrature and rectification of the circle's circumference. Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four; and because of these facts and the further fact that the rule in present use fails to work both ways mathematically, it should be discarded as wholly wanting and misleading in its practical applications.
Section 3
In further proof of the value of the author's proposed contribution to education and offered as a gift to the State of Indiana, is the fact of his solutions of the trisection of the angle, duplication of the cube and quadrature of the circle having been already accepted as contributions to science 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 insolvable mysteries and above man's ability to comprehend.
Goodwin's model circle as described in section 2 of the bill. It has a diameter of 10 and a stated circumference of "32" (not 31.4159~); the chord of 90° has length stated as "7" (not 7.0710~). Via Wikimedia.
After the bill’s first reading, it was referred to the House Committee on Canals (also known as the Committee on Swamp Lands), an indication perhaps of the bill’s potential application to surveying. On January 19, Representative M. B. Butler, chairman of the Canals Committee, recommended that it be referred to the Committee on Education.
On February 2, Representative S. E. Nicholson of Howard County, Chairman of the Committee on Education, reported favorably on the bill, recommending its passage. Upon concurrence, the bill was read a second time and ordered engrossed. Representative Nicholson “moved that the constitutional rule requiring bills to be read on three days be suspended, [so] that the bill may be read a third time now.” The constitutional rule was suspended by a majority vote and, upon third reading, the bill passed unanimously by a vote of 67 to 0.
On February 10, 1897, Engrossed House Bill 246 was referred to the Senate. The following day, the legislation was read for the first time and referred to the Committee on Temperance. And on February 12, Committee Chairman Senator Harry New of Marion County recommended passage. That afternoon, however, following a second reading, the response was less than favorable. Senator Orrin Hubbell moved for the indefinite postponement of the bill, and the motion carried. According to the Indianapolis News:
Representative Record’s mathematical bill legalizing a formula for squaring the circle was brought up and made fun of. The Senators made bad puns about it, ridiculed it and laughed over it. The fun lasted half an hour. Senator Hubbell said that it was not meet [sic] for the Senate, which was costing the State $250 a day, to waste its time in such frivolity.
In admonishing his colleagues, Hubbell proclaimed that “[t]he Senate might as well try to legislate water to run up hill as to establish mathematical truth by law.”
The Intervenor
What happened to House Bill 246? Considering the bill’s initial broad support, including from the Indiana Superintendent of Public Instruction, what explains the abrupt shift in attitude?
On February 5, Professor Clarence Abiathar Waldo, head of the Purdue University Mathematics Department, happened to be at the Statehouse lobbying for the University’s budget appropriation. He was astonished to discover the General Assembly debating mathematical legislation. After reading a copy of the bill, a Representative offered to introduce him to Goodwin. The Professor declined, replying that he was already acquainted with as many crazy people as he cared to know. According to Waldo, he had “properly coached” the senators to reject the bill. In reflecting twenty years later, Professor Waldo claimed that "it was probably the Indiana Academy of Science alone which prevented [this monstrosity]." "[I]f this deduction is correct," he noted, "then that one act of prevention was worth more to Indiana, jealous of her fair fame as she is, than all she ever contributed or can contribute to the publication of the proceedings of her Academy of Science."
Although Waldo certainly influenced the fate of the bill, the media had also played a role. Shortly after its introduction, the bill became the target of ridicule for state and national newspapers. In observing facetiously the “soaring progressiveness” of the legislation, Der Tagliche Telegraph—Indiana’s German-language daily—published a scathing editorial:
Only the great group of the pseudo-educated concerns itself anymore with the squaring of the circle, but this with such eagerness that the famous French academician Arago let it be known that each further solution of this sort sent to him would be tossed aside unread. This class of men is the same as that which continually torments itself with the problem of perpetual motion. Well—such strange fellows there will always be.
LEGACY
Dr. Edwin Goodwin died in 1902, just five years after introducing his infamous piece of legislation. According to his obituary,
[h]e felt that he had a great invention and wished the world to have the benefit of it. In years to come Dr. Goodwin's plan for measuring the heavens may receive the approbation which was untiringly sought by its originator.
As years went on and he saw the child of his genius still unreceived by the scientific world, he became broken with disappointment, although he never lost hope and trusted that before his end came he would see the world awakened to the greatness of his plan and taste for a moment the sweetness of success. He was doomed to disappointment, and in the peaceful confines of village life the tragedy of a fruitless ambition was enacted.
Over a century later, Goodwin's legacy continues to endure in urban legend and popular culture, at least within the mathematical world. Despite his erroneous mathematical conclusions, Goodwin seems to have received an unfair dealing of criticism over the years. The real folly, it seems, lies with state lawmakers in attempting to establish truth by legislative fiat but without considering the broad implications of adopting—uncritically and at face value—a measure based on dubious methods and misguided sources. The comments from Der Telegraph, in an editorial published after the bill had been put to rest, seem fitting:
With regard to the bill introduced by a farmer from New Harmony concerning the squaring of the circle, a leaflet states, among other things: “An inaccuracy of computation cannot be avoided in the irrationality of the number ‘Pi.’ But this apparently does not satisfy those sages. They believe themselves destined to magnify this inaccuracy, and to publicly expose their wholly unclear view of mathematical concepts and values. But the matter also has a serious side. The delusion that everything can be altered through laws must have in such heads climbed to the heights of irreparably muddle-headed thinking.
Sources
Hallerberg, Arthur E. Indiana’s Squared Circle, 50 Mathematics Mag. 136 (1977).
Hallerberg, Arthur E. House Bill No. 246 Revisited, Proc. Ind. Academy Sci. 374 (1974).
Kumar, Mohi. That Time Indiana Almost Made Pi Equal to 3.2 and Other True Stories About Pi, Smithsonian Mag. (Mar. 14, 2013).
Purdue University, Indiana Pi (last visited, Mar. 13, 2015).
Singmaster, David. The Legal Values of Pi, 7 Mathematical Intelligencer 69 (1985).
Wilkins, Alasdair. The Eccentric Crank Who Tried to Legislate the Value of Pi, IO9 (Jan. 31, 2012).