Sources page biographical material

6.BF. PYTHAGOREAN RECREATIONS
6.L might be considered as part of this section. There are some examples of problems with ladders which look like crossed ladders, but are simple Pythagorean problems.

See also 6.AS.2 for dissection proofs of the theorem of Pythagoras. I will include here only some interesting ancient examples. See Elisha Scott Loomis; The Pythagorean Proposition; 2nd ed., NCTM, 1940, for many proofs.

Aryabhata I, v. 17, states the Theorem of Pythagoras and the related theorem that if ABC is a diameter of a circle and LBM is a chord perpendicular to it, then LB² = AB x BC; Bhaskara I's commentary applies the latter in several forms where modern algebra would make it more natural to use the former. Brahmagupta, v. 41, states LM² = AB x BC.

I had overlooked the examples in Mahavira -- thanks to Yvonne Dold for pointing them out.

Fibonacci. 1202. Pp. 397 398 (S: 543-544) looks like a crossed ladders problem but is a simple right triangle problem.

Vyse. Tutor's Guide. 1771?

Prob. 9, 1793: p. 178, 1799: p. 189 & Key p. 224. A ladder 40 long in a roadway can reach 33 up one side and, from the same point, can reach 21 up the other side. This is actually a simple right triangle problem. There is a misprint of 9 for 6 in the answer.

Prob. 17 (in verse), 1793: 179, 1799: p. 190 & Key p. 228. A variation of the Broken Bamboo problem, cf below, with D = 30, H - X = 63, which is a simple right triangle problem.

Hutton. A Course of Mathematics. 1798?

Prob. VIII, 1833: 430; 1857: 508. = Vyse, prob. 19.

Prob. IX, 1833: 430; 1857: 508. = Vyse, prob. 17 with D = 15, H - X = 39.