Indiana Pi Bill

Today is Pi Day! The date is April 26, the day when Earth has made 2 radians of its orbit around the sun since the New Year. The time when Earth completed \frac1\pi of its orbit was at 4:23:41AM this morning, when I was asleep. Though I missed the precise time (and also failed to eat pie today), I’d still like to recognize this glorious holiday. So today, we’ll honor this holiday by recalling some history.

In 1897, the human named Edwin J. Goodwin believed that he had found a way to square the circle, and he proposed to allow the state of Indiana to use this result for free, provided that they passed a bill accepting his results and defining the \pi = 3.2. The gullible representative Taylor I. Record introduced this bill (number 246) to the Indiana House for approval. After some deliberation, the bill was endorsed by the Committee on Education and subsequently passed unanimously by the House. Luckily, just as this bill was being endorsed by the Senate, the mathematician C. A. Waldo visited the Senate and persuaded the senators to suspend a decision on the bill indefinitely. This is one of the most famous attempts to legislate mathematics.

The consideration of this bill is ridiculous in several ways. First of all, the mathematics in the bill is incorrect, demonstrating that the Indiana representatives at the time had no mathematical knowledge and no proper fact checking. Even worse, Goodwin stated that passage of the bill was a prerequisite for using his proof free of charge, despite the fact that royalties cannot be requested for mathematical results.

Thus, we see that by voting on this bill, the Indiana General Assembly showed that they are not qualified to make any decision on mathematical results, and the Committee on Education showed that they are incompetent. Though such a bill is unlikely to be considered today, the general trend still holds. Legislators in America (as well as the general public) are not well-informed about basic facts, but they still believe that they have the right to legislate on matters that they do not fully understand. Furthermore, the modern equivalent of the Committee on Education is still highly under-qualified to make decisions on mathematical education, and I still wouldn’t trust them with properly treating the value of pi. As an over-generalization, we see that many of our elected officials should never have been elected at all. Those who elected them — the general public — should be banned from voting. Dictatorship is certainly a much more efficient system than democracy.

The full text of the Indiana Pi Bill (Bill 246 of the 1897 Indiana General Assembly):

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.

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.

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