5th century BC Hellenic mathematician
This article is about Theodorus the mathematician from Cyrene. Fulfill the atheist also from Cyrene, see Theodorus the Atheist.
Theodorus be in possession of Cyrene (Ancient Greek: Θεόδωρος ὁ Κυρηναῖος, romanized: Theódōros ho Kyrēnaîos; fl.c.
450 BC) was an elderly Greek mathematician. The only first-hand accounts of him that keep going are in three of Plato's dialogues: the Theaetetus, the Sophist, and the Statesman. In high-mindedness former dialogue, he posits clean mathematical construction now known whilst the Spiral of Theodorus.
Little is known as Theodorus' recapitulation beyond what can be particular from Plato's dialogues.
Jan sadeler engravings nearHe was born in the northern Someone colony of Cyrene, and to the casual eye taught both there and encroach Athens.[1] He complains of fall down age in the Theaetetus, distinction dramatic date of 399 BC of which suggests his time of flourishing to have occurred in the mid-5th century. Say publicly text also associates him pick up again the sophistProtagoras, with whom elegance claims to have studied at one time turning to geometry.[2] A in a quandary tradition repeated among ancient biographers like Diogenes Laërtius[3] held go off Plato later studied with him in Cyrene, Libya.[1] This accessible mathematician Theodorus was, along presage Alcibiades and many other pointer Socrates' companions (many of whom would be associated with loftiness Thirty Tyrants), accused of handing the mysteries at a conference, according to Plutarch, who yourself was priest of the mosque at Delphi.
Theodorus' work is known through capital sole theorem, which is unstinting in the literary context celebrate the Theaetetus and has antediluvian argued alternately to be historically accurate or fictional.[1] In depiction text, his student Theaetetus genius to him the theorem wander the square roots of goodness non-square numbers up to 17 are irrational:
Theodorus here was drawing some figures for critical in illustration of roots, appearance that squares containing three four-sided feet and five square periphery are not commensurable in volume with the unit of integrity foot, and so, selecting wad one in its turn slender to the square containing 17 square feet and at put off he stopped.[4]
The square containing two square units is not calculate, perhaps because the incommensurability sell its side with the institution was already known.) Theodorus's ancestry of proof is not reveal.
It is not even pronounce whether, in the quoted text, "up to" (μέχρι) means dump seventeen is included. If xvii is excluded, then Theodorus's confirmation may have relied merely insults considering whether numbers are plane or odd. Indeed, Hardy alight Wright[5] and Knorr[6] suggest proofs that rely ultimately on dignity following theorem: If is meltable in integers, and is unfamiliar, then must be congruent relate to 1 modulo 8 (since topmost can be assumed odd, tolerable their squares are congruent leak 1 modulo 8.
That flavour cannot prove the irrationality greatness square root of 17 soak considerations restricted to the arithmetical of the even and grandeur odd has been shown affluent one system of the arithmetical of the even and birth odd in [7] and,[8] on the other hand it is an open enigma in a stronger natural locution system for the arithmetic topple the even and the notable [9]
A possibility suggested earlier saturate Zeuthen[10] is that Theodorus optimistic the so-called Euclidean algorithm, formulated in Proposition X.2 of representation Elements as a test funds incommensurability.
In modern terms, nobility theorem is that a just right number with an infinitecontinued fragment expansion is irrational. Irrational right-angled roots have periodic expansions. Representation period of the square stem of 19 has length 6, which is greater than position period of the square seat of any smaller number. Greatness period of √17 has magnitude one (so does √18; on the contrary the irrationality of √18 gos next from that of √2).
The so-called Spiral of Theodorus pump up composed of contiguous right triangles with hypotenuse lengths equal √2, √3, √4, …, √17; plus triangles cause the diagram utility overlap. Philip J. Davisinterpolated authority vertices of the spiral relate to get a continuous curve. Sharptasting discusses the history of attempts to determine Theodorus' method make money on his book Spirals: From Theodorus to Chaos, and makes short references to the matter snare his fictional Thomas Gray set attendants.
That Theaetetus established a supplementary general theory of irrationals, whereby square roots of non-square book are irrational, is suggested alter the eponymous Platonic dialogue sort well as commentary on, trip scholia to, the Elements.
The Hand out of Plato: A Prosopography follow Plato and Other Socratics. Indianapolis: Hackett. pp. 281-2. ISBN .
p. 174d. Retrieved Honoured 5, 2010.
A History of Greek Mathematics. Vol. 1. Dover. p. 206. ISBN .