The Full Wiki

Archytas: Wikis

Advertisements
  
  

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

Encyclopedia

From Wikipedia, the free encyclopedia

Archytas

Archytas
Full name Archytas
Born 428 BC
Died 347 BC
Era Pre-Socratic philosophy
Region Western Philosophy
School Pythagoreanism
Main interests -
Notable ideas -

Archytas (Greek: Ἀρχύτας; 428–347 BC) was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato.

Contents

Life and work

Archytas was born in Tarentum, Magna Graecia (now Italy) and was the son of Mnesagoras or Histiaeus. For a while, he was taught by Philolaus, and was a teacher of mathematics to Eudoxus of Cnidus. Archytas and Eudoxus' student was Menaechmus.

Archytas

Archytas is believed to be the founder of mathematical mechanics.[1] As only described in the writings of Aulus Gellius five centuries after him, he was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably steam, said to have actually flown some 200 meters.[2][3] This machine, which its inventor called The Pigeon, may have been suspended on a wire or pivot for its flight.[4][5] Archytas also wrote some lost works, as he was included by Vitruvius in the list of the twelve authors of works of mechanics.[6] Thomas Winter has suggested that the pseudo-Aristotelian Mechanical Problems is an important mechanical work by Archytas, not lost after all, but misattributed.[7]

Archytas introduced the concept of a harmonic mean, important much later in projective geometry and number theory. According to Eutocius, Archytas solved the problem of doubling the cube in his manner with a geometric construction.[8] Hippocrates of Chios before, reduced this problem to finding mean proportionals. Archytas' theory of proportions is treated in book VIII of Euclid's Elements, where is the construction for two proportional means, equivalent to the extraction of the cube root. According to Diogenes Laertius, this demonstration, which uses lines generated by moving figures to construct the two proportionals between magnitudes, was the first in which geometry was studied with concepts of mechanics.[9] The Archytas curve, which he used in his solution of the doubling the cube problem, is named after him.

Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a half-century earlier. The Tarentines elected him strategos, 'general', seven years in a row – a step that required them to violate their own rule against successive appointments. He was allegedly undefeated as a general, in Tarentine campaigns against their southern Italian neighbors. The Seventh Letter of Plato asserts that Archytas attempted to rescue Plato during his difficulties with Dionysius II of Syracuse. In his public career, Archytas had a reputation for virtue as well as efficacy. Some scholars have argued that Archytas may have served as one model for Plato's philosopher king, and that he influenced Plato's political philosophy as expressed in The Republic and other works (i.e., how does a society obtain good rulers like Archytas, instead of bad ones like Dionysus II?).

Archytas drowned in a shipwreck in the sea of Mattinata. His body lay unburied on the shore till a sailor humanely cast a handful of sand on it. Otherwise, he would have had to wander on this side the Styx for a hundred years, such the virtue of a little dust, munera pulveris, as Horace calls it.

The crater Archytas on the Moon is named in his honour.

The Archytas Curve

The Archytas Curve is created by placing a semicircle (with a diameter of d) on the diameter of one of the two circles of a cylinder (which also has a diameter of d) such that the plane of the semicircle is at right angles to the plane of the circle and then rotating the semicircle about one of its ends in the plane of the cylinder's diameter. This rotation will cut out a portion of the cylinder forming the Archytas Curve.[1]

Another, less mathematical, way of thinking of this construction is that the Archytas Curve is basically the result of cutting out a torus formed by toating a hemisphere of diameter d out of a cylinder also of diameter d. A cone can go through the same procedures also producing the Archytas Curve. Archytas used his curve to determine the construction of a cube with a volume of half of that of a given cube.

Notes

  1. ^ Diogenes Laertius, Vitae philosophorum, viii.83.
  2. ^ Aulus Gellius, "Attic Nights", Book X, 12.9 at LacusCurtius
  3. ^ ARCHYTAS OF TARENTUM, Technology Museum of Thessaloniki, Macedonia, Greece
  4. ^ Modern rocketry
  5. ^ Automata history
  6. ^ Vitruvius, De architectura, vii.14.
  7. ^ Thomas Nelson Winter, "The Mechanical Problems in the Corpus of Aristotle," DigitalCommons@University of Nebraska - Lincoln, 2007.
  8. ^ Eutocius, commentary on Archimedes' On the sphere and cylinder.
  9. ^ Plato blamed Archytas for his contamination of geometry with mechanics (Plutarch, Questionum convivialium libri iii, 718E-F): And therefore Plato himself dislikes Eudoxus, Archytas, and Menaechmus for endeavoring to bring down the doubling the cube to mechanical operations; for by this means all that was good in geometry would be lost and corrupted, it falling back again to sensible things, and not rising upward and considering immaterial and immortal images, in which God being versed is always God.

External links

Further reading

  • von Fritz, Kurt (1970). "Archytas of Tarentum". Dictionary of Scientific Biography. 1. New York: Charles Scribner's Sons. pp. 231–233. ISBN 0684101149.  
  • Carl A. Huffman, "Archytas of Tarentum", Cambridge University Press, 2005, ISBN 0521837464
Advertisements

1911 encyclopedia

Up to date as of January 14, 2010

From LoveToKnow 1911

ARCHYTAS (c. 428-347 B.C.), of Tarentum, Greek philosopher and scientist of the Pythagorean school, famous as the intimate friend of Plato, was the son of Mnesagoras or Histiaeus. Equally distinguishedin natural science,philosophy and the administration of civic affairs, he takes a high place among the versatile savants of the ancient Greek world. He was a man of high character and benevolent disposition, a fine flute-player, and a generous master to his slaves, for whose children he invented the rattle. He took a prominent part in state affairs, and, contrary to precedent, was seven times elected commander of the army. Under his leadership, Tarentum fought with unvarying success against the Messapii, Lucania and even Syracuse. After a life of high intellectual achievement and uninterrupted public service, he was drowned (according to a tradition suggested by Horace, Odes, i. 28) on a voyage across the Adriatic, and was buried, as we are told, at Matinum in Apulia. He is described as the eighth leader of the Pythagorean school, and was a pupil (not the teacher, as some have maintained) of Philolaus. In mathematics, he was the first to draw up a methodical treatment of mechanics with the aid of geometry; he first distinguished harmonic progression from arithmetical and geometrical progressions. As a geometer he is classed by Eudemus, the greatest ancient authority, among those who "have enriched the science with original theorems, and given it a really sound arrangement." He evolved an ingenious solution of the duplication of the cube, which shows considerable knowledge of the generation of cylinders and cones. The theory of proportion, and the study of acoustics and music were considerably advanced by his investigations. He was said to be the inventor of a kind of flying-machine, a wooden pigeon balanced by a weight suspended from a pulley, and set in motion by compressed air escaping from a valve.' Fragments of his ethical and metaphysical writings are quoted by Stobaeus, Simplicius and others. To portions of these Aristotle has been supposed to have been indebted for his doctrine of the categories and some of his chief ethical theories. It is, however, certain that these fragments are mainly forgeries, attributable to the eclecticism of the 1st or 2nd century A.D., of which the chief characteristic was a desire to father later doctrines on the old masters. Such fragments as seem to be authentic are of small philosophical value. It is important to notice that Archytas must have been famous as a philosopher, inasmuch as Aristotle wrote a special treatise (not extant) On the Philosophy of Archytas. Some positive idea of his speculations may be derived from two of his observations: the one in which he notices that the parts of animals and plants are in general rounded in form, and the other dealing with the sense of hearing, which, in virtue of its limited receptivity, he compares ' If this be the proper translation of Aulus Gellius, Noctes Atticae, x. 12.9,". .. simulacrum columbae e ligno. factum; ita erat scilicet libramentis suspensum et aura spiritus inclusa atque occulta concitum." (See Aeronautics.) with vessels, which when filled can hold no more. Two important principles are illustrated by these thoughts, (1) that there is no absolute distinction between the organic and the inorganic, and (2) that the argument from final causes is no explanation of phenomena. Archytas may be quoted as an example of Plato's perfect ruler, the philosopher-king, who combines practical sagacity with high character and philosophic insight.

See G. Hartenstein, De Arch. Tar. frag. (Leipzig, 1833); O. F. Gruppe, U ber d. Frag. d. Arch. (1840); F. Beckmann, De Pythag. reliq. (Berlin, 1844, 1850); Egger, De Arch. Tar. sit., op. Phil.; Ed. Zeller, Phil. d. Griech.; Theodor Gomperz, Greek Thinkers, ii. 259 (Eng. trans. G. G. Berry, Lond., 1905); G. J. Allman, Greek Geometry from Thales to Euclid (1889); Florian Cajori, History of Mathematics (New York, 1894); M. Cantor, Gesch. d. gr. Math. (1894 foil.). The mathematical fragments are collected by Fr. Blass, Melanges Graux (Paris, 1884). For Pythagorean mathematics see further Pythagoras.


<< Archpriest

Arcis-Sur-Aube >>


Advertisements






Got something to say? Make a comment.
Your name
Your email address
Message