Popular Science

When is π = 3.2? How senators in the United States almost fell in line with crazy Dr. Goodwin

Legislative initiatives, especially in the United States, have often become the subject of irrepressible controversy and sincere misunderstanding. So today I want to tell you about bill 246 - a legal act that was considered in the Senate of Indiana in 1897.

imageThree years earlier, rural physician Edward Goodwin (1825-1902), who considered himself a good mathematician, published an article in the American Mathematical Months in which he claimed to have solved the problem of squaring the circle.

To solve the problem of squaring a circle means to construct a square equal to the area with a circle with a compass and a ruler. In the 19th century, it was proved that construction with a compass and a ruler is possible if it is reduced to an algebraic equation, the roots of which are expressed at most in terms of square radicals. To square the circle, it was necessary to find an equation, the root of which would be the number π or any combination of it with square roots, multiplication, etc. In 1882, the German mathematician Ferdinand von Lindemann proved that π cannot be the root of any algebraic equation (trivial options do not count) and is transcendental number , which means that the solution of the problem of squaring the circle is theoretically impossible.


imageDrawing by Goodwin's article , published in the "Notes and Questions" section, which assumed a disclaimer on the part of the editorial board of the journal. This is the first justification for publishing such blatant nonsense. The second is that in modern language, the magazine tried to "hyip". By the way, Edward himself was sure that he had also solved two other great problems of antiquity - trisection of an angle and doubling a cube. Well what can I say, the main thing is to believe in yourself.

The main mistake is right at the beginning of the article: Edward claims that the area of a circle is equal to the area of a square with the same perimeter, which is incorrect.

For example, if we take the number π as the side of a square, its perimeter is P = 4π, S = π ^ 2, which gives S = 4π for a circle of the same length! What a coincidence! Our hero clings to it.

The article claims that the ratio of the length of the arc and the chord that contracts the angle is proved as 8/7 and (attention!) The ratio of the diagonal of the square and its side as 10/7. In this regard, the question arises: was the author familiar with the Pythagorean theorem? But the most amazing thing is that in the drawing given by Goodwin as a proof, the value π = 3.2 appears (four chords of 8 inches divided by a diameter of 10 inches).

Interestingly, other works by Goodwin have even more surprising values of the fundamental constant, including 4, 3.2325 ... and even 9.2376, which is probably "the largest overestimation of π in the history of mathematics."

To understand how this undoubtedly creative stream flowed, contemporaries did not have the desire, and indeed the meaning, because Edward himself claimed that he had divine providence in this regard.

And it would be okay that it all ended, because as long as mathematics lives, there are so many people with "revolutionary" ideas. However, Edward went further. On January 18, 1897, Goodwin persuaded a member of the State House of Representatives to introduce a bill that would make his method of squaring the circle part of the Indiana code of law.

Bill 246 provided, in particular, royalties for "new mathematical truth and contributions to education" in the case of using the new value of π in other states. For his native Indiana, however, the generous genius did not provide for a tax.

imageOriginal text of bill 246. The third section uses the classic "Argumentum ad verecundiam" - appeal to authority. The point is that "do the sovereigns dare to contradict the reviewers of the American Mathematical Monthly?"

And the ice broke. State newspapers began to publish materials about the bill and its author, calling him an outstanding mathematician and comparing it with Newton, then with Galileo. The only newspaper that tried to convey to readers that the problem of squaring the circle was unsolvable was Der Tagliche Telegraph, but it was only published in German, so its publications in Indiana went unnoticed.

With support from the press, Bill 246 was successfully selected by the State Education Committee, receiving 67 votes out of 67 possible. The next step was consideration in the Senate. It would seem that Dr. Goodwin's victory is close.

Everything changed when the president of the Indiana Academy of Sciences and at the same time the leading professor of mathematics at Purdue University Clarence Abiathar Waldo learned about Bill 246.

imageIn his memoirs, Waldo said that he was present at the reading of the bill. They even tried to introduce him to Goodwin, to which the mathematician replied that "he is already familiar with so many crazy people that he does not need new ones."

The reading ended with the Senators sending Bill 246 for another hearing to the Committee on Temperance, from where it returned with a final recommendation for adoption. By then, Indianapolis lawmakers had been laughed at both inside and outside the state.

imageFor example, local Senator Orrin Hubbell declared the bill "sheer stupidity" and suggested that the Senate "might as well try to legislate to allow water to run up the hill."

In the end, under pressure from the public and the efforts of Professor Waldo, the House of Representatives overturned the bill. It is noteworthy that, although the majority of the senators voted "against", no one had any doubts that there might be something wrong with the proposed theory, no one ever thought about the obvious delusionalism of the crazy doctor's theory, because everyone knew him very well and could the reviewers of a serious journal be wrong? Bill 246 was simply declared unregulated.

Dr. Goodwin died in 1902, but he never gave up hope that his theory would be accepted. You know, he's even a little sorry. But this does not change the fact that the number π = 3.14159 ...
Papay 2 april 2021, 17:08
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