Archytas

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Archytas

Archytas (; 428–347 BC) was an Ancient Greek

Ancient Greece

The term Ancient Greece refers to the period of History of Greece lasting from the Greek Dark Ages ca. 1100 BC and the Dorian invasion, to 146 BC and the Roman Republic conquest of Greece after the Battle of Corinth ....
philosopher, mathematician

Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
, astronomer

Astronomer

An astronomer is a scientist who studies Celestial body such as planets, stars, and Galaxy.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using physical laws....
, statesman

Statesman

A statesman or stateswoman or statesperson is usually a politician or other notable figure of state who has had a long and respected career in politics at the national and international level....
, and strategist

Military strategy

Military strategy is a policy implemented by military organizations to pursue desired Strategic goal s. Derived from the Greek language strategos, strategy when it appeared in use during the 18th century, was seen in its narrow sense as the "art of the general", 'the art of arrangement' of troops....
. He was a scientist of the Pythagorean

Pythagorean

Pythagorean means of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras. See:...
school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato

Plato

Taranto

Taranto is a coastal city in Puglia, Southern Italy. It is the capital of the Province of Taranto and is an important commercial port as well as the main Italian naval base....
, Magna Graecia

Magna Graecia

Magna Graecia is the name of the area in Southern Italy and Sicily that was Colonies in antiquity#Greek colonies by Greek settlers in the eighth century BC, who brought with them the lasting imprint of their Hellenic civilization....
(now Italy

Italy

Italy , officially the Italian Republic , is a country located on the Italian Peninsula in Southern Europe and on the two largest islands in the Mediterranean Sea, Sicily and Sardinia....
) and was the son of Mnesagoras or Histiaeus. For a while, he was taught by Philolaus

Philolaus

Philolaus was a Greeks Pythagoreanism and Presocratic. He argued that all matter is composed of limited and unlimited things, and that the universe is determined by numbers....
, and was a teacher of mathematics to Eudoxus of Cnidus

Eudoxus of Cnidus

Eudoxus of Cnidus was a Ancient Greece astronomer, mathematician, scholar and student of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy....
. Archytas and Eudoxus' student was Menaechmus

Menaechmus

Menaechmus was an ancient Greek mathematician and list of geometers born in Alopeconnesus , who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola....
.

Archytas is believed to be the founder of mathematical mechanics

Mechanics

Mechanics is the branch of physics concerned with the behaviour of physical body when subjected to forces or Displacement , and the subsequent effect of the bodies on their environment....
.

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Archytas (; 428–347 BC) was an Ancient Greek

Ancient Greece

Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
, astronomer

Astronomer

Statesman

Military strategy

Pythagorean

Plato

Life and work

Archytas was born in Tarentum

Taranto

Taranto is a coastal city in Puglia, Southern Italy. It is the capital of the Province of Taranto and is an important commercial port as well as the main Italian naval base....
, Magna Graecia

Magna Graecia

Italy

Philolaus

Eudoxus of Cnidus

Menaechmus

Archytas is believed to be the founder of mathematical mechanics

Mechanics

Mechanics is the branch of physics concerned with the behaviour of physical body when subjected to forces or Displacement , and the subsequent effect of the bodies on their environment....
. As only described in the writings of Aulus Gellius

Aulus Gellius

Aulus Gellius , Latin author and grammarian, possibly of African origin, probably born and certainly brought up at Rome.He studied grammar and rhetoric at Rome and philosophy at Athens, after which he returned to Rome, where he held a judicial office....
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. This machine, which its inventor called The Pigeon, may have been suspended on a wire or pivot for its flight. Archytas also wrote some lost works, as he was included by Vitruvius

Vitruvius

File:Vitruvius.jpgMarcus Vitruvius Pollio was a Ancient Rome writer, architect and engineer , active in the 1st century BC. By his own description Vitruvius served as a Ballista , the third class of arms in the military offices....
in the list of the twelve authors of works of mechanics. Thomas Winter has suggested that the pseudo-Aristotelian Mechanical Problems is an important mechanical work by Archytas, not lost after all, but misattributed.

According to Eutocius, Archytas solved the problem of doubling the cube

Doubling the cube

Doubling the cube is one of the three most famous geometry problems unsolvable by compass and straightedge construction. It was known to the Egyptian mathematics, Greek mathematics, and Indian mathematics....
in his manner with a geometric construction. Hippocrates of Chios

Hippocrates of Chios

Hippocrates of Chios was an ancient Greece mathematician, , and astronomer, who lived c. 470 – c. 410 Common Era.He was born on the isle of Chios, where he originally was a merchant....
before, reduced this problem to finding mean proportionals

Proportionality (mathematics)

In mathematics, two quantity are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio....
. Archytas' theory of proportions is treated in book VIII of Euclid

Euclid

Euclid , floruit 300 BC, also known as Euclid of Alexandria, was a Greek mathematics and is often referred to as the Father of Geometry. He was active in Alexandria during the reign of Ptolemy I ....
's Elements
Euclid's Elements

Euclid's Elements is a mathematics and geometry treatise consisting of 13 books written by the Greek mathematics Euclid in Alexandria circa 300 BC....
, where is the construction for two proportional means, equivalent to the extraction of the cube root

Cube root

In mathematics, a cube root of a number, denoted or x1/3, is a number a such that a3 = x. All real numbers have exactly one real number cube root and a pair of complex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots....
. According to Diogenes Laertius

Diogenes Laertius

Diogenes La?rtius , the biographer of the Greece philosophers, is supposed by some to have received his surname from the town of Laerte in Cilicia, Asia Minor, and by others from the Roman Empire family of the La?rtii....
, 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. 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

Pericles

Pericles was a prominent and influential statesman, orator, and general of History of Athens during the city's Age of Pericles?specifically, the time between the Greco-Persian Wars and Peloponnesian War wars....
in Athens

Athens

Athens , the Capital and largest city of Greece, dominates the Attica periphery; as one of the List of cities by time of continuous habitation, its recorded history spans around 3,400 years....
a half-century earlier. The Tarentines elected him strategos
Strategos

The term strategos is used in Greek language to mean "general". In the Hellenistic and Byzantine Empires the term was also used to describe a military governor....
, '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

Plato

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
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

Philosopher king

Philosopher kings are the hypothetical rulers, or Guardians, of Plato's Utopian Kallipolis. If his ideal city-state is to ever come into being, "philosophers [must] become kings?or those now called kings [must]?genuinely and adequately philosophize" ....
, 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

Mattinata

Mattinata is a famous seaside resort town and commune municipality in the Apulia region, southern Italy....
. 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

Styx (mythology)

In Greek mythology, the "River Styx" was a river which formed the boundary between Earth and the Underworld . It circles Hades nine times. The rivers Styx, Phlegethon, Acheron and Cocytus all converge at the center of Hades on a great swamp....
for a hundred years, such the virtue of a little dust, munera pulveris, as Horace

Horace

This article is about the Roman poet Horace. For other uses, see Horace .Quintus Horatius Flaccus, , known in the English language world as Horace, was the leading Roman Empire Lyric poetry during the time of Augustus....
calls it.

The crater Archytas

Archytas (crater)

Archytas is a moon impact crater that protrudes into the northern edge of Mare Frigoris. To the northwest is the comparably sized crater Timaeus , and the smaller Protagoras lies in the opposite direction to the southeast....
on the Moon

Moon

The Moon is Earth's only natural satellite and the List of natural satellites by diameter satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is km, about thirty times the diameter of the Earth....
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) and then rotating the semicircle about the cylinder's diameter. This rotation will cut out a portion of the cylinder forming the Archytas Curve. Another, less mathematical, way of thinking of this construction is that the Archytas Curve is basically the result of cutting out 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.

External links

by Giannis Stamatellos
- Greek text and English translation

Archytas

Life and work

The Archytas Curve

External links

Further reading