Theodoros of Cyrene (mathematician)

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Theodoros of Cyrene ( Greek Θεόδωρος Theódōros ; * around 475/460 BC; † after 399 BC) was an ancient Greek mathematician .

Life

Theodoros came from Cyrene , a Greek city in what is now Libya . According to Plato's account, he belonged to the generation of Socrates . This agrees with the information given by Eudemos of Rhodes in his "History of Geometry". This results in a date of his birth around 475/460 BC. Since he survived Socrates, he is after 399 BC. Died.

Theodoros was a pupil and friend of the famous sophist Protagoras , but he turned away from sophistics early on and turned to geometry. He was not only a mathematician, but was also considered an excellent expert in astronomy and music. In these subjects he taught. The mathematician Theaetetus was one of his students . Perhaps Plato was also taught by him. It is unclear whether he was in Athens, where Plato lived, or whether Plato visited him in Cyrene, as the historian of philosophy Diogenes Laertios claims. His stay in Athens, about which Plato reports, is possibly a literary invention. The late antique philosopher Iamblichus counted Theodoros among the Pythagoreans , but the credibility of this message is doubted in research. Apparently Theodoros was not a philosopher; According to Plato's account, he did not want to take part in philosophical investigations because he did not consider himself competent in this area.

Root snail

According to Plato, Theodoros showed that not only - as the Pythagoreans had already recognized - the square root of 2, but also the square roots of the non-square natural numbers from 3 to 17 are irrational . He proceeded geometrically by showing that the side length of a square with an area of 3 square feet with the unit of length 1 foot is incommensurable and therefore an irrational number. He did the same for the square roots of 5, 6, 7, etc. until he broke off at 17. It is not known how Theodoros demonstrated it; Research even doubts that it is actually a mathematical proof . Holger Thesleff , who took up an idea put forward by Jakob Heinrich Anderhub as early as 1941, says that Theodoros did not prove his assumption, but only demonstrated it in a drawing using a construction, and that he had to stop at 17 because the spiral drawing only offers space for 17 triangles . It is the " root snail " used to construct roots , which is called "Theodorus wheel" or "Theodorus spiral".

Theodoros also dealt with curves. The late antique philosopher Proklos reports that Theodoros described the helix as a “fusion” (krásis) of a straight and a round line. Proclus protested against this, who said that the mixture of the straight and the round line in the helical line does not come about either through composition or fusion. The identity of Theodorus mentioned by Proklos with Theodoros of Cyrene is, however, controversial in research.

Literary reception

Theodoros is a participant in Plato's fictional literary dialogue Theaitetos . The dialogue takes place in the year 399 BC. BC, Theodoros is already an old man. Theodoros is also among those present in Plato's dialogues Sophistes and Politikos , but he only plays a minor role in the conversation.

Source collections

literature

Web links

Individual evidence

  1. ↑ Eudemos of Rhodes, fragment DK 43 A 2.
  2. ↑ See Kurt von Fritz: Theodoros (31) . In: Pauly-Wissowa RE, Volume 5 A / 2, Stuttgart 1934, Sp. 1811-1825, here: 1811; Leonid Zhmud: Theodoros from Cyrene . In: Hellmut Flashar et al. (Ed.): Frühgriechische Philosophie , Basel 2013, pp. 420f., Here: 420; Leonid Zhmud: Pythagoras and the Early Pythagoreans , Oxford 2012, p. 128.
  3. ^ To the friendship of Plato, Theaetetus 161b. On the relationship between Theodoros and Protagoras, see Kurt von Fritz: Theodoros (31) . In: Pauly-Wissowa RE, Volume 5 A / 2, Stuttgart 1934, Sp. 1811-1825, here: 1812.
  4. ↑ Plato, Theaetetus 165a.
  5. ↑ Plato, Theaetetos 145a and 169a.
  6. ^ Plato, Theaetetos 145c – d.
  7. ↑ Diogenes Laertios 2,103 and 3,6.
  8. ↑ Diogenes Laertios 3.6.
  9. ^ Kurt von Fritz: Theodoros (31) . In: Pauly-Wissowa RE, Volume 5 A / 2, Stuttgart 1934, Sp. 1811-1825, here: 1811; Leonid Zhmud: Theodoros from Cyrene . In: Hellmut Flashar et al. (Ed.): Frühgriechische Philosophie , Basel 2013, pp. 420f., Here: 420.
  10. ^ Iamblichos, De vita Pythagorica 267.
  11. ^ Kurt von Fritz: Theodoros (31) . In: Pauly-Wissowa RE, Volume 5 A / 2, Stuttgart 1934, Sp. 1811-1825, here: 1811f .; Bartel Leendert van der Waerden : Awakening Science , 2nd, supplemented edition, Basel 1966, pp. 233–240, here: 233; Leonid Zhmud arrives at a different assessment: Theodoros from Cyrene . In: Hellmut Flashar et al. (Ed.): Frühgriechische Philosophie , Basel 2013, pp. 420f.
  12. ↑ Plato, Theaitetos 146b; see. 165a.
  13. ↑ Plato, Theaetetus 147d.
  14. ↑ For a discussion of this question, see Debra Nails: The People of Plato , Indianapolis 2002, p. 282; Ludger Hellweg: Mathematical irrationality in Theodoros and Theaetetos. An attempt to regain their theories , Frankfurt am Main 1994, pp. 5-87; Bartel Leendert van der Waerden: Awakening Science , 2nd, supplemented edition, Basel 1966, pp. 233–240; Walter Burkert : Wisdom and Science , Nuremberg 1962, p. 439, note 105.
  15. ↑ Holger Thesleff: Theaitetos and Theodoros . In: Arctos 24, 1990, pp. 147-159, here: 151-153.
  16. ^ Proklos, In primum Euclidis elementorum librum commentarii , ed. Gottfried Friedlein, Leipzig 1873, p. 118; Translation by Leander Schönberger, Max Steck : Proclus Diadochus 410–485: Commentary on the first book of Euclid's "Elements" , Halle (Saale) 1945, p. 248.
  17. ^ Ivor Bulmer-Thomas: Theodorus of Cyrene . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography , Vol. 13, New York 1981, pp. 314-319, here: pp. 318f. Note 25.
personal data
SURNAME Theodorus of Cyrene
BRIEF DESCRIPTION Greek mathematician
DATE OF BIRTH around 475-460 BC Chr.
DATE OF DEATH after 399 BC Chr.