Sources page biographical material

6.AD. ISOPERIMETRIC PROBLEMS
There is quite a bit of classical history which I have not yet entered. Magician's Own Book notes there is a connection between the Dido version of the problem and Cutting a card so one can pass through it, Section 6.BA. There are several relatively modern surveys of the subject from a mathematical viewpoint -- I will cite a few of them.
Virgil. Aeneid.  19. Book 1, lines 360 370. (p. 38 of the Penguin edition, translated by W. F. Jackson Knight, 1956.) Dido came to a spot in Tunisia and the local chiefs promised her as much land as she could enclose in the hide of a bull. She cut it into a long strip and used it to cut off a peninsula and founded Carthage. This story was later adapted to other city foundations. John Timbs; Curiosities of History; With New Lights; David Bogue, London, 1857, devotes a section to Artifice of the thong in founding cities, pp. 49-50, relating that in 1100, Hengist, the first Saxon King of Kent, similarly purchased a site called Castle of the Thong and gives references to Indian, Persian and American versions of the story as well as several other English versions.

Pappus. c290. Synagoge [Collection]. Book V, Preface, para. 1 3, on the sagacity of bees. Greek and English in SIHGM II 588 593. A different, abridged, English version is in HGM II 389 390.

The Friday Night Book (A Jewish Miscellany). Soncino Press, London, 1933. Mathematical Problems in the Talmud: Arithmetical Problems, no. 2, pp. 135-136. A Roman Emperor demanded the Jews pay him a tax of as much wheat as would cover a space 40 x 40 cubits. Rabbi Huna suggested that they request to pay in two instalments of 20 x 20 and the Emperor granted this. [The Talmud was compiled in the period -300 to 500. This source says he is one of the few mathematicians mentioned in the Talmud, but gives no dates and he is not mentioned in the EB. From the text, the problem would seem to be sometime in the 1-5 C.]

The 5C Saxon mercenary, Hengist or Hengest, is said to have requested from Vortigern: "as much land as can be encircled by a thong". He "then took the hide of a bull and cut it into a single leather thong. With this thong he marked out a certain precipitous site, which he had chosen with the greatest possible cunning." This is reported by Geoffrey of Monmouth in the 12C and this is quoted by the editor in: The Exeter Book Riddles; 8-10C (the book was owned by Leofric, first Bishop of Exeter, who mentioned it in his will of 1072); Translated and edited by Kevin Crossley-Holland; (As: The Exeter Riddle Book, Folio Society, 1978, Penguin, 1979); Revised ed., Penguin, 1993; pp. 101-102.

Lucca 1754. c1330. Ff. 8r 8v, pp. 31 33. Several problems, e.g. a city 1 by 24 has perimeter 50 while a city 8 by 8 has perimeter 32 but is 8/3 as large; stitching two sacks together gives a sack 4 times as big.

Calandri. Arimethrica. 1491. F. 97v. Joining sacks which hold 9 and 16 yields a sack which holds 49!!

Pacioli. Summa. 1494. Part II, ff. 55r-55v. Several problems, e.g. a cord of length 4 encloses 100 ducats worth, how much does a cord of length 10 enclose? Also stitching bags together.

Buteo. Logistica. 1559. Prob. 86, pp. 298-299. If 9 pieces of wood are bundled up by 5½ feet of cord, how much cord is needed to bundle up 4 pieces? 5 pieces?

Pitiscus. Trigonometria. Revised ed., 1600, p. 223. ??NYS -- described in: Nobuo Miura; The applications of trigonometry in Pitiscus: a preliminary essay; Historia Scientarum 30 (1986) 63-78. A square of side 4 and triangle of sides 5, 5, 3 have the same perimeter but different areas. Presumably he was warning people not to be cheated in this way.

J. Kepler. The Six Cornered Snowflake, op. cit. in 6.AT.3. 1611. Pp. 6 11 (8 19). Discusses hexagons and rhombic interfaces, but only says "the hexagon is the roomiest" (p. 11 (18 19)).

van Etten. 1624. Prob. 90 (87). Pp. 136 138 (214 218). Compares fields 6 x 6 and 9 x 3. Compares 4 sacks of diameter 1 with 1 sack of diameter 4. Compares 2 water pipes of diameter 1 with 1 water pipe of diameter 2.

Ozanam. 1725.

Question 1, 1725: 327. Question 3, 1778: 328; 1803: 325; 1814: 276; 1840: 141. String twice as long contains four times as much asparagus.

Question 2, 1725: 328. If a cord of length 10 encloses 200, how much does a cord of length 8 enclose?

Question 3, 1725: 328. Sack 5 high by 4 across versus 4 sacks 5 high by 1 across. c=  Q. 2, 1778: 328; 1803: 324; 1814: 276; 1840: 140-141, which has sack 4 high by 6 around versus two sacks 4 high by 3 around.

Question 4, 1725: 328 329. How much water does a pipe of twice the diameter deliver?

Les Amusemens. 1749.

Prob. 211, p. 376. String twice as long contains four times as much asparagus.

Prob. 212, p. 377. Determine length of string which contains twice as much asparagus.

Prob. 223-226, pp. 386-389. Various problems involving changing shape with the same perimeter. Notes the area can be infinitely small.

Ozanam Montucla. 1778.

Question 1, 1778: 327; 1803: 323-324; 1814: 275-276; 1840: 140. Square versus oblong field of the same circumference.

Prob. 35, 1778: 329-333; 1803: 326-330; 1814: 277-280; 1840: 141-143. Les alvéoles des abeilles (On the form in which bees construct their combs).

Jackson. Rational Amusement. 1821. Geometrical Puzzles.

No. 30, pp. 30 & 90. Square field versus oblong (rectangular?) field of the same perimeter.

No. 31, pp. 30 & 90-91. String twice as long contains four times as much asparagus.

Magician's Own Book (UK version). 1871. To cut a card for one to jump through, p. 124, says: "The adventurer of old, who, inducing the aborigines to give him as much land as a bull's hide would cover, and made it into one strip by which acres were enclosed, had probably played at this game in his youth." See 6.BA.

M. Zacharias. Elementargeometrie und elementare nicht-Euklidische Geometrie in synthetischer Behandlung. Encyklopädie der Mathematischen Wissenschaften. Band III, Teil 1, 2te Hälfte. Teubner, Leipzig, 1914-1931. Abt. 28: Maxima und Minima. Die isoperimetrische Aufgabe. Pp. 1118-1128. General survey, from Zenodorus (-1C) and Pappus onward.