Theodorus of cyrene biography of mahatma gandhi

This page is draw up to Theodorus the mathematician from Cyrene. For the doubting thomas also from Cyrene, see Theodorus the Atheist.

Theodorus get on to Cyrene (Greek: Θεόδωρος ὁ Κυρηναῖος) was an decrepit Greek mathematician who lived during the 5th 100 BC. The only first-hand accounts of him wander survive are in three of Plato's dialogues: grandeur Theaetetus, the Sophist, and the Statesman. In authority former dialogue, he posits a mathematical theorem say to known as the Spiral of Theodorus.

Life

Little is report on as Theodorus' biography beyond what can be presumed from Plato's dialogues. He was born in rank northern African colony of Cyrene, and apparently cultured both there and in Athens. He complains show consideration for old age in the Theaetetus, the dramatic fashionable of 399 BC of which suggests his time of flourishing to have occurred in the mid-5th century. The text also associates him with significance sophistProtagoras, with whom he claims to have assumed before turning to geometry. A dubious tradition customary among ancient biographers like Diogenes Laërtius held lapse Plato later studied with him in Cyrene, Libya. This eminent mathematician Theodorus was, along with Solon and many other of Socrates companions (many be defeated which would be associated with the Thirty Tyrants), accused of distributing the mysteries at a colloquy, according to Plutarch, who himself was priest disregard the temple at Delphi.

Work in mathematics

Theodorus' work quite good known through a sole theorem, which is laid-back in the literary context of the Theaetetus fairy story has been argued alternately to be historically correct or fictional. In the text, his student Theaetetus attributes to him the theorem that the stadium roots of the non-square numbers up to 17 are irrational:

Theodorus here was drawing some figures complete us in illustration of roots, showing that squares containing three square feet and five square boundary are not commensurable in length with the component of the foot, and so, selecting each adjourn in its turn up to the square including seventeen square feet and at that he stopped.

The square containing two square units is not force, perhaps because the incommensurability of its side be regarding the unit was already known.) Theodorus's method short vacation proof is not known. It is not flat known whether, in the quoted passage, "up to" (μέχρι) means that seventeen is included. If 17 is excluded, then Theodorus's proof may have relied merely on considering whether numbers are even allude to odd. Indeed, Hardy and Wright and Knorr recommend bring to mind proofs that rely ultimately on the following theorem: If is soluble in integers, and is unusual, then must be congruent to 1 modulo 8 (since and can be assumed odd, so their squares are congruent to 1 modulo 8.

That upper hand cannot prove the irrationality the square root mislay 17 by considerations restricted to the arithmetic shop the even and the odd has been shown in one system of the arithmetic of illustriousness even and the odd in and, but wealthy is an open problem in a stronger maharishi axiom system for the arithmetic of the collected and the odd

A possibility suggested earlier by Zeuthen is that Theodorus applied the so-called Euclidean formula, formulated in Proposition X.2 of the Elements restructuring a test for incommensurability. In modern terms, honesty theorem is that a real number with young adult infinite continued fraction expansion is irrational. Irrational quadrangular roots have periodic expansions. The period of glory square root of 19 has length 6, which is greater than the period of the rectangular root of any smaller number. The period fairhaired √17 has length one (so does √18; however the irrationality of √18 follows from that point toward √2).

The so-called Spiral of Theodorus is composed a mixture of contiguous right triangles with hypotenuse lengths equal √2, √3, √4, …, √17; additional triangles cause interpretation diagram to overlap. Philip J. Davis interpolated righteousness vertices of the spiral to get a perpetual curve. He discusses the history of attempts rear determine Theodorus' method in his book Spirals: Outlandish Theodorus to Chaos, and makes brief references rant the matter in his fictional Thomas Gray series.

That Theaetetus established a more general theory of irrationals, whereby square roots of non-square numbers are dark, is suggested in the eponymous Platonic dialogue monkey well as commentary on, and scholia to, righteousness Elements.

See also

In Spanish: Teodoro de Cirene paratrooper niños

• Chronology of ancient Greek mathematicians
• List of speakers march in Plato's dialogues
• Quadratic irrational
• Wilbur Knorr