Theodorus of Cyrene
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Theodorus of Cyrene was a Greek mathematician of the 5th century BC who was admired by Plato (who mentions him in several of his works, most notably the Theatetus) . Little is known about him; however, Plato attributes to him the first proof of the irrationality of the square roots of 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 and 17. The method he used is not stated, but since he stopped at 17, it seems that he used the traditional Pythagorean method of odds and evens, since 17 is the first number this method breaks down[1]. One conjecture involves a spiral comprised of contiguous right triangles with hypotenuse lengths equal to the square root of 2, square root of 3, square root of 4,..., up to the square root of 17 (where he stopped - possibly because additional triangles would cause the diagram to overlap, although one mathematician humorously suggested that "the bell rang"). There is no historical evidence for this, however.
Philip J. Davis interpolated the vertices of the spiral to get a continuous curve that he named the Spiral of Theodorus. He discusses the history of attempts to determine Theodorus' method in his book Spirals: From Theodorus to Chaos, and makes brief references to the matter in his fictional Thomas Gray series.
[edit] References
- ^ James R. Choike (1980). "Theodorus' Irrationality Proofs". The Two-Year College Mathematics Journal.
