------------------------------ Date: Sat, 20 Aug 1994 21:32:45 +0200 --- Date: Wed, 24 Aug 94 20:52:40 EST From: james@cssnps.com (James Dudley) Subject: pi = 3 (Re: Wayner, RISKS-16.34) Actually, my home state of Indiana did try to legislate that the value of pi should be 3. Here is some information from the alt.folklore.urban archives from an article written by Mark Bader (msb@sq.com) (Further information can be found in "Mathematical Cranks", Underwood Dudley, The Mathematical Association of America, Washington D.C.). James Dudley THE STORY The author of the bill was Dr. Edwin J. Goodwin, an M.D., of Solitude, Indiana. It seems that he was a crank mathematician. He contacted his Representative, one Taylor I. Record, with his epoch-making suggestion: if the State would pass an Act recognizing his discovery, he would allow all Indiana textbooks to use it without paying him a royalty. Nobody in the Indiana Legislature knew enough mathematics to know that the "discovery" was nonsense. In due course the bill had its third House reading, and passed 67-0. At this point the text of the bill was published "and, of course, became the target for ridicule", "in this and other states". By this time a real mathematician, Prof. C. A. Waldo, had learned what was going on. In fact, he was present when the bill was read on February 5, 1897. ("...imagine [the author's] surprise when he discovered that he was in the midst of a debate upon a piece of mathematical legislation. An ex-teacher was saying ... 'The case is perfectly simple. If we pass this bill which establishes a new and correct value for Pi, the author offers ... its free publication in our school text books, while everyone else must pay him a royalty'", Waldo wrote in a 1916 article.) But the House had passed the bill. Fortunately, Indiana has a bicameral legislature. The bill came up for first reading in the Senate on Thursday, February 11. Apparently in fun, they referred it to the Committee on Temperance. The Committee reported back on Friday, February 12, approving the bill, which then had its second reading. The Indianapolis Journal reported what happened: "The Senators made bad puns about it, ridiculed it, and laughed over it. The fun lasted half an hour. Senator Hubbell said that it was not meet for the Senate, which was costing the State $250 a day [!], to waste its time in such frivolity ... He moved the indefinite postponement of the bill, and the motion carried. ... All of the senators who spoke on the bill admitted that they were ignorant of the merits of the proposition. [In the end,] it was simply regarded as not being a subject for legislation." ANNOTATED TEXT OF THE BILL /* Following is the text of Indiana House Bill #246 of 1897, with my * own annotations (in comment signs and exdented, like this text). * In my annotations, A, r, d, c, and s are respectively the circle's * area, radius, diameter, circumference, and the side of the inscribed * square. */ 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 ac- cepted and adopted by the official action of the leg- islature of 1897. /* You normally have to pay royalties on mathematical truths? * The Pythagoras estate must be doing well by now... */ 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 cir- cumference, as the area of an equilateral rectangle is to the square on one side. /* The part after the last comma is a remarkable way of saying * "as 1 is to 1". In other words, this says A = (c/4)^2, which * is the same as A = (pi*r/2)^2 = (pi^2/4)*r^2 instead of the * actual A = pi*r^2. */ 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. /* The formula A = pi*r^2 is interpreted as A = d*(c/4), which is correct. * The author claims that the d factor should be c/4, so the ratio of * the area by the author's formula to the area by the real formula * is c/(4*d), that is, pi/4. Since he believes pi = 3.2, this ratio * is 3.2/4, which is 4/5. Therefore the area by the author's rule * is 1/5 smaller than the actual area. Now he apparently thinks that * the reciprocal of 1-1/5 is 1+1/5, and thus that the other area is * 1/5 larger than his area, which of course would actually require * the ratio to be 5/6. */ This is because one-fifth of the di- ameter fails to be represented four times in the circle's circumference. /* In other words, c = (1-1/5) * (4*d); consistent with pi = 3.2. */ For example: if we multiply the per- imeter 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. /* He says that if we consider the area of a square of side x to be * (4*x)*(x/4) and we replace the second x by (1+1/5)*x, we get an * area 1/5 too large, and this is analogous to using d in place of * c/4 with the circle. */ 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 the circle to the extent of in- cluding one-fifth more area than is contained within the circle's circumference, because the square on the diame- ter produces the side of a square which equals nine when the arc of ninety degrees equals eight. /* I can only assume that "nine" is a mistake for "ten". See also * the annotation after the next one. */ 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. /* Getting repetitive here... */ Furthermore, it has revealed the ra- tio 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, disclos- ing the fourth important fact, that the ratio of the di- ameter 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. /* The meat of the bill. He says that s/(c/4) = 7/8, and d/s = 10/7, * therefore d/c = (10/7)*(7/8)/4, which he reduces only as far as * (5/4)/4. Of course this is 5/16, and gives pi = c/d = 16/5 = 3.2. * It also implies that the square root of 2 is 10/7. */ SECTION 3. In further proof of the value of the author's pro- posed 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. /* When I first posted this I assumed that the A.M.M. must have had a * policy of politely acknowledging crankish submissions, but apparently * at one time they simply printed whatever they were sent. I haven't * checked this out. */ And be it remembered that these not- ed problems had been long since given up by scientific bodies as unsolvable mysteries and above man's ability to comprehend. /* "Given up" is not the same as "proved insoluble"! */ [Also noted by pcw@access.digex.net (Peter Wayner), "Tom Zmudzinski" , who suggests using 355/113, mhaynes@bgsu.edu (Michael F. Haynes), clark@cpd125.cpd.ford.com (Andrew Clark), nhy@panix.com (Nina H. Yuan), George Jansen , dalamb@qucis.queensu.ca (David Lamb), and cc32859@vantage.fmrco.com (Donald Sharp), who wonders ``how many other technically flawed ideas have actually been codified into law because not enough people in the legislature understood flaw? And what is the risk involved in trying to implement laws that contradict the fundamental truths of nature?''. (However, two of those remembered the state incorrectly.) I am delighted to have this urban nonlegend put to rest. Thanks. PGN] ------------------------------ Date: Thu, 25 Aug 1994 06:56:54 -0500 (CDT) From: "Prof. L. P. Levine" Subject: PI = 3 There are two biblical verses that show PI to have a value of three. They seem to be the same information repeated, but from the King James version as reported in the Library of the Future CDROM, which seems to be filled with texts from the past: Kings-1 verse 7:23 And he made a molten sea, ten cubits from the one brim to he other: [it was] round all about, and his height [was] five cubits and a line of thirty cubits did compass it round about. Chronicles-2 verse 4:2 Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about. Leonard P. Levine, Professor, Computer Science, Univ. of Wisconsin-Milwaukee Box 784, Milwaukee, WI 53201 levine@cs.uwm.edu 1-414-229-5170 ------------------------------ Added by FNC in Jan 2012: http://en.wikipedia.org/wiki/Indiana_Pi_Bill