Sources page biographical material

6. GEOMETRIC RECREATIONS
6.A. PI
This is too big a topic to cover completely. The first items should be consulted for older material and the general history. Then I include material of particular interest. See also 6.BL which has some formulae which are used to compute π. I have compiled a separate file on the history of π.
Augustus De Morgan. A Budget of Paradoxes. (1872); 2nd ed., edited by D. E. Smith, (1915), Books for Libraries Press, Freeport, NY, 1967.

J. W. Wrench Jr. The evolution of extended decimal approximations to π. MTr 53 (Dec 1960) 644 650. Good survey with 55 references, including original sources.

Petr Beckmann. A History of π. The Golem Press, Boulder, Colorado, (1970); 2nd ed., 1971.

Lam Lay-Yong & Ang Tian-Se. Circle measurements in ancient China. HM 13 (1986) 325 340. Good survey of the calculation of π in China.

Dario Castellanos. The ubiquitous π. MM 61 (1988) 67-98 & 148-163. Good survey of methods of computing π.

Joel Chan. As easy as pi. Math Horizons 1 (Winter 1993) 18-19. Outlines some recent work on calculating π and gives several of the formulae used.

David Singmaster. A history of π. M500 168 (Jun 1999) 1-16. A chronology. (Thanks to Tony Forbes and Eddie Kent for carefully proofreading and amending my file.)
Aristophanes. The Birds.  414. Lines 1001 1005. In: SIHGM I 308 309. Refers to 'circle-squarers', possibly referring to the geometer/astronomer Meton.
E. J. Goodwin. Quadrature of the circle. AMM 1 (1894) 246 247.

House Bill No. 246, Indiana Legislature, 1897. "A bill for an act introducing a new mathematical truth ..." In Edington's paper (below), p. 207, and in several of the newspaper reports.

(Indianapolis) Journal (19 Jan 1897) 3. Mentions the Bill in the list of bills introduced.

Die Quadratur des Zirkels. Täglicher Telegraph (Indianapolis) (20 Jan 1897) ??. Surveys attempts since -2000 and notes that Lindemann and Weierstrass have shown that the problem is impossible, like perpetual motion.

A man of 'genius'. (Indianapolis) Sun (6 Feb 1897) ??. An interview with Goodwin, who says: "The astronomers have all been wrong. There's about 40,000,000 square miles on the surface of this earth that isn't here." He says his results are revelations and gives several rules for the circle and the sphere.

Mathematical Bill passed. (Indianapolis) Journal (6 Feb 1897) 5. "This is the strangest bill that has ever passed an Indiana Assembly." Gives whole text of the Bill.

Dr. Goodwin's theaorem (sic) Resolution adopted by the House of Representatives. (Indianapolis) News (6 Feb 1897) 4. Gives whole text of the Bill.

The Mathematical Bill Fun-making in the Senate yesterday afternoon -- other action. (Indianapolis) News (13 Feb 1897) 11. "The Senators made bad puns about it, ...." The Bill was indefinitely postponed.

House Bills in the Senate. (Indianapolis) Sentinel (13 Feb 1897) 2. Reports the Bill was killed.

(No heading??) (Indianapolis) Journal (13 Feb 1897) 3, col. 4. "... indefinitely postponed, as not being a subject fit for legislation."

Squaring the circle. (Indianapolis) Sunday Journal (21 Feb 1897) 9. Says Goodwin has solved all three classical impossible problems. Says π = 3.2, using the fact that 2 = 10/7, giving diagrams and a number of rules.

My thanks to Underwood Dudley for locating and copying the above newspaper items.

C. A. Waldo. What might have been. Proc. Indiana Acad. Science 26 (1916) 445 446.

W. E. Edington. House Bill No. 246, Indiana State Legislature, 1897. Ibid. 45 (1935) 206 210.

A. T. Hallerberg. House Bill No. 246 revisited. Ibid. 84 (1975) 374 399.

Manuel H. Greenblatt. The 'legal' value of pi, and some related mathematical anomalies. American Scientist 53 (Dec 1965) 427A 434A. On p. 427A he tries to interpret the bill and obtains three different values for π.

David Singmaster. The legal values of pi. Math. Intell. 7:2 (1985) 69 72. Analyses Goodwin's article, Bill and other assertions to find 23 interpretable statements giving 9 different values of π !

Underwood Dudley. Mathematical Cranks. MAA, 1992. Legislating pi, pp. 192-197.

C. T. Heisel. The Circle Squared Beyond Refutation. Published by the author, 657 Bolivar Rd., Cleveland, Ohio, 1st ed., 1931, printed by S. J. Monck, Cleveland; 2nd ed., 1934, printed by Lezius Hiles Co., Cleveland, ??NX + Supplement: "Fundamental Truth", 1936, ??NX, distributed by the author from 2142 Euclid Ave., Cleveland. This is probably the most ambitious publication of a circle-squarer -- Heisel distributed copies all around the world.
Underwood Dudley. π_t: 1832-1879. MM 35 (1962) 153-154. He plots 45 values of π as a function of time over the period 1832-1879 and finds the least-squares straight line which fits the data, finding that π_t = 3.14281 + .0000056060 t, for t measured in years AD. Deduces that the Biblical value of 3 was a good approximation for the time and that Creation must have occurred when π_t = 0, which was in -560,615.

Underwood Dudley. π_t. JRM 9 (1976-77) 178 & 180. Extends his previous work to 50 values of π over 1826-1885, obtaining π_t = 4.59183 - .000773 t. The fact that π_t is decreasing is worrying -- when π_t = 1, all circles will collapse into straight lines and this will certainly be the end of the world, which is expected in 4646 on 9 Aug at 20:55:33 -- though this is only the expected time and there is considerable variation in this prediction. [Actually, I get that this should be on 11 Aug. However, it seems to me that circles will collapse once π_t = 2, as then the circumference corresponds to going back and forth along the diameter. This will occur when t = 3352.949547, i.e. in 3352, on 13 Dec at 14:01:54 -- much earlier than Dudley's prediction, so start getting ready now!]