Rules for Making Pi Digestible
To those readers sufficiently philosophic to survey the imaginative vagaries of our legislatures, we commend a characteristic example borrowed from the storehouse of American political thought and submitted to us by the reader whose letter is printed below. The ratio of the circumference of a circle to its diameter (pi) is expressed by the inordinately inconvenient figure of 3.14159265. Democratically speaking, this is an outrage perpetrated by Nature, which deserves disciplinary measures. The legislature of Indiana attempted to correct this ancient ill. We hope our readers will point out the historic incident to the legislators who misrepresent them, as the story is not without its lesson.
EVANSTON, ILLINOIS
DEAR ATLANTIC, —
In the Atlantic for April inquiry is made by Mr. It. W. Mattoon concerning the proposal of a state legislature to fix by law the value of the mathematical symbol TT (pi). He suggests that the proposal was made by the legislature of Kansas. In this he is in error. The honor belongs to Indiana.
I chance to have a copy of this proposed law, treasured for more than thirty-five years. It was introduced by a Mr. Record in the session of 1897, listed as House Bill No. 246, was referred to the Committee on Canals, by this Committee was considered and sent back to the House with a recommendation that it be sent to the Committee on Education, which in turn recommended that the bill ‘do pass.’ I was told at the time that the bill actually passed the House but was lost in the Senate.
Ridiculous as this legislation is, some recent attempts to fix by law matters which cannot be so regulated appear almost as absurd. But there is no telling what a legislature may attempt to do. A copy of the Indiana proposal is enclosed. What it is all about or what it says, no mathematical student can understand.
Yours sincerely,
THOMAS F. HOLGATE
HOUSE BILL NO. 246
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, That 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 scpiare 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 unsolvable mysteries and above man’s ability to comprehend.
MR. SPEAKER:
Your Committee on Canals, to which was referred House Bill No. 246, introduced by Mr. Record, has had the same under consideration, and begs leave to report the same back to the House with the recommendation that said bill be referred to the Committee on Education.
M. B. BUTLER
MR. SPEAKER:
Your Committee on Education, to which was referred House Bill No. 246, introduced by Mr. Record, has had the same under consideration, and begs leave to report the same back to the House, with the recommendation that said bill do pass.
NICHOLSON, Chairman