Indiana Pi Bill

The Indiana State House in Indianapolis , seat of the House of Representatives and the Senate

Indiana Pi Bill is the unofficial name of a bill that was submitted to the parliament of the American state Indiana for approval in 1897 . With its adoption - technically untenable - statements of the doctor Edward J. Goodwin about the circle calculation and the squaring of the circle should gain legal force, in return Goodwin wanted to allow the state of Indiana the free use of his findings.

The bill was accepted by the House of Representatives without a dissenting vote. After intervention by the mathematics professor Clarence A. Waldo , the Senate postponed the final approval indefinitely.

prehistory

The question from ancient Greek mathematics as to whether a square of the same area can only be constructed for a given circle with the help of a compass and ruler was unanswered for a long time. It was only in 1882 that Ferdinand von Lindemann was able to prove that such an elementary squaring of the circle is in principle not possible. Since modern times, however, the representation and any precise calculation of the circle number have not been a problem . Regardless of the scientific work on squaring the circle and calculating circles, these topics were a popular field of activity for amateur mathematicians, especially in the 18th and 19th centuries. ${\ displaystyle \ pi}$

Edward Johnston Goodwin of Solitude in Posey County published several versions of a work on squaring the circle starting in 1892. He himself wrote about his inspiration that in 1888 he found out "in a supernatural way the exact size of the circle" . One of the versions, entitled Quadrature of the Circle , appeared in the Queries and Information heading in the first volume of the American Mathematical Monthly in 1894 . The remark “ Published by the request of the author ” identifies the article as an advertisement Goodwin, which was presumably included as filler material by the editors of the magazine. This article was the basis for the later draft law.

Some sizes that can be read from Goodwin's work

The article in the American Mathematical Monthly is unclear and contradicting itself. The American mathematician David Singmaster was able to read a total of nine different values for from this and other treatises by Goodwin . In his work, Goodwin initially assumes that square and circle are equal in area if they have the same circumference, i.e. a quarter of the circumference corresponds to the side of the square. The article begins with the statement ${\ displaystyle \ pi}$

“A circular area is equal to the square over a distance equal to the quadrant of the circumference; [...] "

Taking into account the fixed definitions of the number of circles as the ratio of the circumference of a circle to its diameter or (equivalent) the area of a circle with radius 1, this approach yields the equation

{\ displaystyle \ left ({\ frac {2 \ pi r} {4}} \ right) ^ {2} = \ pi r ^ {2},}

which corresponds to the value . However, a later passage suggests that Goodwin favored the value . He determined the ratio of a quarter-circle arc to the corresponding chord as 8: 7, that of the square side to the diagonal as 7:10 and derived 16: 5 as the ratio of the circumference to the diameter. However, Goodwin's other remarks leave room for further interpretations. ${\ displaystyle \ pi = 4}$ ${\ displaystyle \ pi = 3 {,} 2}$

Legislative process

Clarence A. Waldo: His intervention prevented the law from being passed

Indiana's parliament consists - similar to the United States Congress - of two chambers , the House of Representatives and the Senate, both of which have to approve a new law. First chamber is the House of Representatives, the Taylor I. Record, MP from Goodwin's native constituency of Posey County, on January 18, 1897 House Bill No. 246 submitted. Their preamble reads:

“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. ”

"A bill that introduces a new mathematical truth and is offered as a contribution to education for the sole use of the State of Indiana without the expense of any fee whatsoever, provided it is passed and introduced through the official legislative process of 1897."

The draft was by Goodwin, the content largely coincided with the 1894 essay. There is also a note there that Goodwin has placed its findings under copyright law .

After the first reading in the House of Representatives, the submission was first referred to the Committee on Canals , which, however, did not see its responsibility and had it passed on to the Committee on Education the following day . On February 2, the latter recommended that the draft be approved. The second and - with suspension of the regular procedure - also the third reading in plenary followed on February 5. The House Bill No. 246 was passed with 67 votes to 0 and passed on to the Senate. One MP - a former teacher - justified his agreement:

“The case is perfectly simple. If we pass this bill which establishes a new and correct value for , the author offers to our state without cost the use of his discovery and its free publication in our school text books, while everyone else must pay him a royalty. " ${\ displaystyle \ pi}$

“The case is perfectly simple. If we pass this law that introduces a new and correct value for , the author will offer our state the free use of his discovery and its free distribution in our school books, while everyone else has to pay him a fee. " ${\ displaystyle \ pi}$

A casual guest at the meeting was Clarence Abiathar Waldo, a math professor at Purdue University . After the House passed the bill, he contacted the Senate and tried to educate the Senators about the content of Goodwin's work.

The Senate dealt with House Bill No. 246 for the first time on February 11th. After the first reading, the draft was referred to the Committee on Temperance , ie the “abstinence committee”; whether on purpose remains speculation. At the next Senate meeting on February 12, the committee recommended that the draft be passed. The second reading followed, at which the success of Waldo's persuasion was evident. According to newspapers, the senators cracked bad jokes about the draft, laughed, and were in a good mood for half an hour. In the official Senate report, however, it was only briefly stated: “Senator Hubbell requested that further deliberations on the bill be postponed indefinitely. The motion was granted. ”The main reason for the stay of the proceedings was not that Goodwin's theories were considered false by the senators, but“ that they were unable to assess the value of the proposal. It was just not considered a matter of legislation. "

reception

The House Bill No. 246 was initially seen by the local press as a serious draft bill. The Indianapolis Sentinel wrote on January 20, “ The bill […] is not intended to be a hoax. [...] Dr. Goodwin, the author, is a mathematician of note. “The mood changed when, after the House of Representatives passed the draft, national newspapers became aware of the strange legislative process. Senator Hubbell justified his motion to postpone the draft by stating, after reading the leading East Coast and Chicago newspapers, that the Indiana state legislature had already ridiculed itself enough with this process.

The Indiana Pi Bill has now become part of scientific entertainment literature. Since 1916, papers on this topic have appeared at irregular intervals.

Remarks

↑ The second solution of the quadratic equation , , is disregarded. ${\ displaystyle \ pi = 0}$

Literature and Sources

The article essentially follows the presentation of

David Singmaster : The Legal Values of Pi. In: The Mathematical Intelligencer , 7, 1985, pp. 69-72.

The following sources are also cited:

Underwood Dudley: A Law About Pi. In: Mathematics Between Madness and Joke. Fallacies, False Evidence, and the Importance of the Number 57 in American History. Birkhäuser, Basel 1995, ISBN 3-7643-5145-4 , pp. 158-166.
Will E. Edington: House Bill No. 246, Indiana State Legislature, 1897. In: Proceedings of the Indiana Academy of Sciences , 45, 1935, pp. 206-210.
Edward J. Goodwin: Quadrature of the circle. In: The American Mathematical Monthly , 1, 1894, pp. 246-247.

The works of Goodwin, Edington, and Singmaster are reprinted in:

Lennart Berggren, Jonathan M. Borwein, Peter Borwein (Eds.): Pi: A Source Book. 3rd edition, Springer, New York 2004, ISBN 0-387-20571-3 , pp. 230-239.

Web links

Text of the draft law (copy in the Internet Archive)

Individual evidence

^ Based on Singmaster and Goodwin's contribution to the American Mathematical Monthly . Edington knows him as Edwin J. Goodwin.
↑ Singmaster, p. 69. German translation after Dudley, p. 161.
↑ Goodwin, p. 246. German translation after Dudley, p. 164.
↑ u. a. at Singmaster, p. 71.
↑ Singmaster, p. 70.
↑ Edington, p. 209.
↑ after Edington, p. 209.
^ Report of the Indianapolis Journal of February 13, 1897. German translation after Dudley, p. 161.
↑ Singmaster, p. 69.
↑ after Edington, p. 209.
↑ s. e.g. the references in Singmaster, p. 72.

[4] The second solution of the quadratic equation , , is disregarded. ${\ displaystyle \ pi = 0}$

[1] Based on Singmaster and Goodwin's contribution to the American Mathematical Monthly . Edington knows him as Edwin J. Goodwin.

[2] Singmaster, p. 69. German translation after Dudley, p. 161.

[3] Goodwin, p. 246. German translation after Dudley, p. 164.

[5] u. a. at Singmaster, p. 71.

[6] Singmaster, p. 70.

[7] Edington, p. 209.

[8] ter Edington, p. 209.

[9] Report of the Indianapolis Journal of February 13, 1897. German translation after Dudley, p. 161.

[10] Singmaster, p. 69.

[11] ter Edington, p. 209.

[12] s. e.g. the references in Singmaster, p. 72.