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It is the 120th anniversary of the passing of a bill by the House of Congress of Indiana to change the value of pi to 3.2! [Errors in the original are copied here verbatim. -Ed]
Weird as it sounds, in effect the House voted 67-0 on H.B. 246 "Introducing a new mathematical truth" on February 5th, 1897 and referred to the Senate of Indiana.
On February 2, 1897 Representative S. E. Nicholson, of Howard County, chairman of the Committee on Education, reported to the House:
"Your Committee on Education, to which was referred House Bill No. 246, entitled a bill for an act entitled an act introducing a new mathematical truth, has had same under consideration, and begs leave to report the same back to the House with the recommendation that said bill do pass."
The bill was duly passed to the Senate on February 10th and read on the 11th, then referred to the Temperance Committee. On February 12 Senator Harry S. New, of Marion County, Chairman of the Committee on Temperance made the following report to the Senate:
"Your Committee on Temperance, 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 Senate with the recommendation that said bill do pass."
On the afternoon of February 12 "Senator Bozeman called up House Bill No. 246. The bill was read a second time by title. Senator Hogate moved to amend the bill by striking out the enacting clause. The motion was lost. Senator Hubbell moved to postpone the further consideration of this bill indefinitely. Which motion prevailed."
The bill was never voted on, it was simply postponed following ridicule from the press. "Senator Hubbell characterized the bill as utter folly. The Senate might as well try to legislate water to run up hill as to establish mathematical truth by law. Leading papers all over the country, he said, were ridiculing the Indiana Legislature. It was outrageous that the State of Indiana should pay $250 a day to have time wasted on such frivolous matters."
A very interesting story by Will E. Edington then at DePauw University, published by the Proceedings of the Indiana Academy of Science. Sorry PDF only.
(Score: 3, Interesting) by AthanasiusKircher on Tuesday February 14 2017, @06:56PM
There's nothing in this bill that actually SETS a value for Pi by legislative fiat. In fact, I'm pretty sure the author of this BS wasn't even trying to propose a new value for Pi in general. The closest it comes is stating a finding:
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 if you sort out what that means, it does have an implication that Pi=3.2. But that's not the point of the bill at all, which is actually to square the circle [wikipedia.org] with compass and straightedge. This is made clear in Section 2:
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.
In other words, some moron (Edward Goodwin, M.D.) was adjusting the size of the circle he was supposed to be squaring in order to make the math work out. This was a classic geometrical problem known since antiquity, and he decided that he could pass off an approximation of it as a "solution" which he seemed to want to copyright/patent whatever. The true purpose of the bill is made abundantly clear in the final section:
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.
Squaring the circle (or quadrature), the doubling of the cube, and trisection of the angle, are basically THE THREE ancient problems which were known not to be solved by using only compass and straightedge. These are things that any educated man in the 19th century would know from studying Euclidean geometry at school. What this dude was trying to do was pass off his "solutions" to such standard problems as if they were fact.
Bizarrely, in the process of solving this ancient problem of squaring the circle, he claimed the value of Pi necessary to make his "proof" work was actually a better value. Here's a link [purdue.edu] to his publication in the American Mathematical Monthly that explains the proof in more detail. Basically, he directly acknowledges that his ratio for Pi (5/4:4, or 3.2) "represents the area of the circle to be more than the orthodox ratio, yet the ratio (3.1416) represents the area of the circle whose circumference equals 4 [as] 2% greater than the finite ratio (5/4:4)..."
He then goes on to compare ratios using his computational method (i.e., 1:3.2, and 1.25:4) with ratios using the traditional value of Pi (1:3.1416, and 1.2732:4), and he concludes through cross-multiplication in these proportions that 3.2*1.25 does indeed equal 4, but 3.1416*1.2732 does not precisely equal 4. (It actually equals 3.99988...) Basically, his "proof" amounts to "I'm using a defined rational number," whereas his approximate values for the real value of Pi don't seem to match up perfectly. Or, to put it another way, he assumed he had actually "squared the circle" using his proportion, and then decided it must be a better value for Pi, since his proportions look nicer.
Moreover, that's not even the only value he assumes for Pi in the paper. Elsewhere, he states:
These two ratios show the numerical relation of diameter to circumference to be as 1:4.
That is, Pi=4. And later:
We are now able to get the true and finite dimensions of a circle by the exact ratio 5/4: 4, and have simply to divide the circumference by 4 and square the quotient to compute the area.
Here we have a circumference formula that appears to imply Pi=3.2 juxtaposed directly with an area formula that implies Pi=4. Why? Because he wasn't trying to redefine Pi. As is evidence by looking at the way he sets up these formulas: "These properties of the ratio of the square apply to the circle without an exception, as is further sustained by the following formula to express the numerical measure of both circle and square." In other words, we keep adjusting ratios wherever necessary so that the math works out for both the square and the circle... but he ONLY seems to be talking about this specific problem.
These various supposed new values for Pi are merely the consequence of this supposed "solution" of a classic problem from antiquity, and that presumably is what got the attention of lawmakers. If he had just wandered in and said, "I propose we make Pi = 3.2 or maybe 4," he would have been immediately laughed out of the room. Instead, he was proposing a solution method to the quadrature problem, which happened to involve stretching or compressing the Pi ratio in various ways to make a square appear to conform to the measurements of a circle.
(Score: 3, Informative) by AthanasiusKircher on Tuesday February 14 2017, @07:34PM
By the way, the only reference I seem to see to this being about Pi is in Prof. Waldo's account (see the end of the PDF):
An ex-teacher from the eastern part of the state was saying: "The case is perfectly simple. If we pass this bill which establishes a new and correct value for pi, 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.”
Except the bill doesn't clearly define a value for Pi in no uncertain terms. Its title/subject is repeatedly mentioned as "squaring a circle." And newspaper accounts listed in the PDF don't imply anything about Pi... instead:
The bill telling how to square a circle, Introduced in the House by Mr. Record is not intended to be a hoax. Mr. Record knows nothing of the bill with the exception that he introduced it by request of Dr. Edwin Goodwin of Posey County, who is the author of the demonstration. The latter and State Superintendent of Public Instruction Geeting believe that it is the long-sought solution of the problem, and they are seeking to have it adopted by the legislature. Dr. Goodwin, the author, is a mathematician of note. He has it copyrighted and his proposition is that if the legislature will indorse the solution he will allow the state to use the demonstration in its textbooks free of charge.
It doesn't make sense that Dr. Goodwin, no matter how much of a moron he was, believed that he could "copyright" a value of a mathematical constant. He didn't care about Pi. He wanted the credit for "squaring the circle." I suspect what happened here is Prof. Waldo -- who was the mathematician who ultimately debunked the bill -- realized that the "solution" only worked by redefining Pi, and he pointed that out to various Senators, etc. (And perhaps misremembered that as what a teacher told him, or maybe the teacher had realized the implications and said that to him directly.) But I don't see any clear evidence that the bill or its author actually intended to redefine Pi... or how it would even make any sense to license a new mathematical value to schools.
But I do understand how some moron could think that he could copyright the text of a mathematical proof and seek to have it promoted in school textbooks, which appears to be what this bill was actually about.
(Score: 2) by edIII on Tuesday February 14 2017, @11:15PM
So it was patented, and he was giving it as a gift to the legislature and schools?
Sounds like he was trying to create a market for his product, fill it with people trained to use his product, and then a commercial market that has to pay licensing fees to use his product.
Would have been quite a thing to pull off, but this was 1897. Governments giving away vast amounts of wealth to unethical greedy people was standard operating procedure. This just sounded far stupider than giving away vast amounts of the public wealth to create robber barons of rail, coal, etc.
Technically, lunchtime is at any moment. It's just a wave function.