1. TMTh:: ARCHYTAS OF TARENTUM MATHEMATICIAN archytas of tarentum (fl. 428347 BC) Life Pythagoreanphilosopher, mathematician and astronomer, Archytas is sometimes http://www.tmth.edu.gr/en/aet/1/14.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN ARCHYTAS OF TARENTUM (fl. 428-347 BC) Life Pythagorean philosopher, mathematician and astronomer, Archytas is sometimes called the father of mathematical mechanics. Aristotle wrote a special treatise on his work, entitled "The Philosophy of Archytas". His theories on the exact sciences are based on two principles: a) that there is no absolute difference between the organic and the inorganic world, and b) that the law of causality cannot interpret phenomena. In mathematics, Archytas was the first to distinguish between arithmetic and geometric progressions; he also found a solution to the problem of doubling the cube. He is thought to be the inventor of the screw and the pulley, and a forefather of mechanical flight. He was a friend of Plato and a teacher of Eudoxus of Cnidus. A valley at the North Pole of the moon has been named "Archytas" in his honour. Work The idea of flight had a perennial and passionate fascination for many ancient peoples; this is especially true of Greece, where not only the gods but also an assortment of demigods and mythical creatures were endowed with this gift. From myth to reality, however, is a long step, even though it was partially spanned by Daedalus with his famous airborne escape from Crete. While the flight of Daedalus and Icarus was probably mythical (opinion is divided), the feat of Archytas by contrast was truly revolutionary: in 425 BC he constructed the first flying machine in history. His "pigeon" (as he called it) was powered by a system of jet propulsion, and in one experiment it flew a distance of 200 metres. Once it fell to the ground, however, this machine could not take off again. Evanghelos Stamatis thinks it must have been some sort of jet-propelled craft driven by a compressed air system.

2. Archytas Of Tarentum - Encyclopedia Article From Britannica.com Search archytas of tarentum at Britannica.com for the Web's best sites, news and magazine articles, and related products. http://www.britannica.com/seo/a/archytas-of-tarentum

Search Archytas Of Tarentum at Britannica.com for the Web's best sites, news and magazine articles, and related products. To view the complete article, sign up for Britannica's premium service - Archytas Of Tarentum Of Tarentum fl. 400, -350 BC, Tarentum, Magna Graecia [now Taranto, Italy] Greek scientist, philosopher, and major Pythagorean mathematician, who is sometimes called the founder of mathematical mechanics. Plato , a close friend, made use of his work in mathematics, and there is evidence that Euclid borrowed from him for Book ... Need more? Complete articles are available to premium service members. Information on site licenses is also available. About Us Advertise With Us Syndication International Publishing ... Help

3. Dupcubfin.html Duplication of the Cube Darrell Mattingly, Cateryn Kiernan Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem Rule and Collapsable Compass Solution archytas of tarentum's Solution archytas of tarentum's Solution. The most interesting and complex of the solutions to the "Delian" Problem is the http://www.ms.uky.edu/~carl/ma330/projects/dupcubfinTOC.html

dupcubfin.mws Duplication of the Cube : Darrell Mattingly, Cateryn Kiernan Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem dupcubfin.mws Duplication of the Cube : Darrell Mattingly, Cateryn Kiernan Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem ... Exercises

4. Plato: Chronology under the leadership of archytas of tarentum. First acquaintance with Dion of Syracuse (brotherin-law of Dionysius I) http://www.csun.edu/~hcfll004/platochron.html

[Archonship of Diotimus] Plato born in Athens, the son of Ariston (son of Aristokles, direct descendant of Solon's brother Exekestiades); his mother was Periktione (sister of Charmides and cousin of Kritias). Plato had two brothers and a sister. His mother married a second time, to Pyrilampes, a member of the Periclean group. The Great Peloponnesian War (Part I). Young Plato received a musical and gymnastic education; he wrote juvenile epigrams and tragedies, but burned them once he became associated with Socrates. Great Peloponnesian War (Part II). He was active politically ( Letter 7 ). His uncle and cousin were among the Thirty Tyrants (404/3), who terrorized the Athenian state after Athens lost the war to Sparta in 404. Conservative coup d' état (The 400), followed later in the summer by a democratic restoration led by Alcibiades. Trial and execution of Socrates. Plato was present at the trial, but not allowed to speak. Plato and other disciples removed themselves to Megara, next door to Athens. There was later a 'Megarean School' of Socratic philosophy: Elkleides of Megara (author of a Crito, Eroticus, Aeschines, Alcibiades

5. Bolt Science - Historical Background To Screw Threads invented in about 400BC by archytas of tarentum (428 BC 350 BC). Archytas is sometimes called the founder of http://www.boltscience.com/pages/screw2.htm

Information on Screw Threads Historical Background Bolt Science is committed to providing expertise in bolted joint technology and to this end we present the following information for education purposes. It is considered by some that the screw thread was invented in about 400BC by Archytas of Tarentum (428 BC - 350 BC). Archytas is sometimes called the founder of mechanics and was a contemporary of Plato. One of the first applications of the screw principle were in presses for the extraction of oils from olives and juice from grapes. The oil presses in Pomeii were worked by the screw principle. Archimedes (287 BC - 212 BC) developed the screw principle and used it to construct devices to raise water. The water screw may have originated in Egypt before the time of Archimedes was constructed from wood and was used for land irrigation and to remove bilge-water from ships. The Romans applied the Archimedean screw to mine drainage. The screw was described in the first century AD in Mechanica of Heron of Alexandria. The construction of the screw thread depended upon the eye and skill of the craftsman. Advances on this occurred in the eighteenth century. Antoine Thiout around 1750 introduced the innovation of equipping a lathe with a screw drive allowing the tool carriage to be moved longitudinally semi-automatically. Screws with fine pitches are essential in a wide variety of instruments - such as micrometers. To construct such a thread a lathe was essential. Jesse Ramsden in 1770 made the first satisfactory screw-cutting lathe. Using his lathes a long screw cut be cut from a carefully cut small original. Precision screws allowed precision instruments to be made to allow the construction of steam engines and machines tools. By their use in surveying instruments they assisted in the construction and development of canals, roads and bridges.

6. Archytas archytas of tarentum. Born about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) http://sfabel.tripod.com/mathematik/database/Archytas.html

Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Archytas was a mathematician, statesman and philosopher. He worked on the harmonic mean and gave it that name. The reason he worked on this was his interest in the problem of duplicating the cube, finding the side of a cube with volume twice that of a given cube. Hippocrates reduced the problem to finding mean proportionals. Archytas solved the problem with a remarkable geometric solution (not of course a ruler and compass construction). He is sometimes called the founder of mechanics and Plato , a close friend, made use of his mathematics. Euclid also borrowed his work for Book 8 of the Elements References (6 books/articles) References elsewhere in this archive: There is a Crater Archytas on the moon. There is also a Rima Archytas . You can see a list of lunar features named after mathematicians. Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996

7. Archytas archytas of tarentum. Born about 428 BC in Tarentum (now Taranto),Magna Graecia (now Italy) Died about 350 BC. Click the picture http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Archytas.html

Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Archytas of Tarentum was a mathematician, statesman and philosopher who lived in Tarentum in Magna Graecia, an area of southern Italy which was under Greek control in the fifth century BC. The Pythagoreans, who had at one stage been strong throughout Magna Graecia, were attacked and expelled until only the town of Tarentum remained a stronghold for them. Archytas led the Pythagoreans in Tarentum and tried to unite the Greek towns in the area to form an alliance against their non-Greek neighbours. He was commander in chief of the forces in Tarentum for seven years despite there being a law that nobody could hold the post for more than a year. Plato , who became a close friend, made his acquaintance while saying in Magna Graecia. Heath writes in [4]:- ... he is said, by means of a letter, to have saved

8. Archytas Biography of Archytas (428BC350BC) archytas of tarentum. Born about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archytas.html

Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Archytas of Tarentum was a mathematician, statesman and philosopher who lived in Tarentum in Magna Graecia, an area of southern Italy which was under Greek control in the fifth century BC. The Pythagoreans, who had at one stage been strong throughout Magna Graecia, were attacked and expelled until only the town of Tarentum remained a stronghold for them. Archytas led the Pythagoreans in Tarentum and tried to unite the Greek towns in the area to form an alliance against their non-Greek neighbours. He was commander in chief of the forces in Tarentum for seven years despite there being a law that nobody could hold the post for more than a year. Plato , who became a close friend, made his acquaintance while saying in Magna Graecia. Heath writes in [4]:- ... he is said, by means of a letter, to have saved

9. Chronology For 500BC To 1AD number. (See this History Topic.). 387BC Plato founds his Academy inAthens. About 375BC archytas of tarentum develops mechanics. He http://www-gap.dcs.st-and.ac.uk/~history/Chronology/500BC_1AD.html

Chronology for 500BC to 1AD Previous page Chronology index Full chronology Next page About 500BC The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets. (See this History Topic About 500BC Panini 's work on Sanskrit grammar is the forerunner of the modern formal language theory. About 465BC Hippasus writes of a "sphere of 12 pentagons", which must refer to a dodecahedron About 450BC Greeks begin to use written numerals. (See this History Topic About 450BC Zeno of Elea presents his paradoxes. About 440BC Hippocrates of Chios writes the Elements which is the first compilation of the elements of geometry. About 430BC Hippias of Elis invents the quadratrix which may have been used by him for trisecting an angle and squaring the circle About 425BC Theodorus of Cyrene shows that certain square roots are irrational . This had been shown earlier but it is not known by whom. About 400BC Babylonians use a symbol to indicate an empty place in their numbers recorded in cuneiform writing. There is no indication that this was in any way thought of as a number. (See this History Topic Plato founds his Academy in Athens About 375BC Archytas of Tarentum develops mechanics. He studies the "classical problem" of

10. TMTh:: Ancient Greek Technologists PHYSICIANS PHYSICISTS, ADRASTUS OF APHRODISIAS AETHRA OF TROEZEN APOLLONIUS OF PERGAARATUS OF SOLI ARCHIMEDES OF SYRACUSE archytas of tarentum ARISTAEUS THE http://www.tmth.edu.gr/en/aet/1.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ARTISTS ASTRONOMERS ... ZENO OF ELEA Read about the life and Work of Ancient Greek Scientists. Choose the desired category from the list on the left and the desired scientist from the list on the right Based on the Greek book: K. Georgakopoulos, "Ancient Greek Scientists", Athens, 1995 Contact the Technology Museum

11. Encyclopædia Britannica Encyclopædia Britannica. archytas of tarentum. Encyclopædia Britannica Article http://www.britannica.com/eb/article?eu=9411

12. Encyclopædia Britannica Search Tips. Your search archytas of tarentum. Log In or Subscribe Now. Expand yoursearch on archytas of tarentum with these databases Journals and magazines. http://www.britannica.com/search?query=archytas of tarentum&seo

13. Archytas Of Tarentum © 1998 Bernard SUZANNE, Last updated December 5, 1998. Plato and hisdialogues Home Biography - Works - History of interpretation http://plato-dialogues.org/tools/char/archytas.htm

Bernard SUZANNE Last updated December 5, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations . . . . WORK IN PROGRESS - PLEASE BE PATIENT . . . To Perseus general lookup encyclopedia mentions in ancient authors Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author First published January 4, 1998 - Last updated December 5, 1998

14. Dupcubfin.html archytas of tarentum's Solution. The most interesting and complex of the solutions to the "Delian" Problem is the http://www.ms.uky.edu/~carl/ma330/projects/dupcubfin.html

Sorry, this document requires that your browser support frames. This link will take you to a non-frames presentation of the document.

15. ªüº¸§Æ¶ð´µ¡£Archytas Of Tarentum¡¤ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/3/3_78.htm

Archytas of Tarentum ¤½¤¸«e ¥ª¥k¡A¥j§Æ¾ §Æ¾¼Æ¾Ç®a¡B­õ¾Ç®a¡Bª«²z¾Ç®a¡A¥Í¥­¤£¸Ô¡C¬ù¤½¤¸«e ¦~¬¡°Ê©ó¥LªL´°¡£¤µ·N¤j§Q¶ðÄõ¦«¡¤¡Cªüº¸§Æ¶ð´µ¬O²¦¹F­ô©Ô´µ¾Ç¬£±ß´Á­«­nªº¦¨­û¡A¥L¹ï¼Æ¾Ç¤ÎÀ³¥Î¼Æ¾Çªº°^Äm¬O«Ü¤jªº¡C ¥­§¡­È²z½×©M¤ñ¨Ò²z½×¬Oªüº¸§Æ¶ð´µ¹ï¼Æ¾Çªº¥D­n°^Äm¡A¥L¹ï½×¤F¤TºØ¥­§¡­È¡Gºâ³N¥­§¡¡B´X¦ó¥­§¡©M½Õ©M¥­§¡¡A«ü¥X¡§®t¼Æ¬° ªº¨â¼Æ¤§¶¡¨S¦³¡£¦³²z¡¤´X¦ó¥­§¡­È¡¨¡A¼Ú´X¨½¼w¡m´X¦ó­ì¥»¡n¨÷ VIII Ptolemy ¡¤ÅA¬°²¦¹F­ô©Ô´µ¾Ç¬£³Ì­«­nªº­µ¼Ö²z½×®a¡C ªü«´¶ð³ÌµÛ¦Wªº¼Æ¾Ç°^Äm¬O­¿¥ß¤èÅé°ÝDªº¨D¸Ñ¡A¥L§Q¥Î¤TºûªÅ¶¡ªº¥ßÅé¼Ò«¬¨Ó¸Ñ¨M³o¤@°ÝD¡A¦¨¬°¸û¦­¬ã¨s³o¤@°ÝDªº¼Æ¾Ç®a¡C­¿¥ß¤èÅé°ÝD¬ã¨sªº²Ä¤@¨B¶i®i¬O¥Ñ²¦¤ó¾Ç¬£ªº¦¨­û§Æªi§J©Ô©³°µ¥Xªº¡A¥L±N³o­Ó°ÝDÂkµ²¬°¨D½u¬q a »P

16. ¤Hª« (Zeno of Elea), ?(archytas of tarentum).?(Hippocrates of Chios), ?(Plato). http://www.edp.ust.hk/math/history/3/

ªð¦^¥D­¶ ¼Æ¾Ç¥v¦~ªí ¤¤¥~¼Æ¾Ç¥v ¤Hª« »y¿ý ¾Ç¬ì¥v ¦WD»P²q·Q ÄvÁÉ»P¼ú¶µ µØ»y¤åÄm¯Á¤Þ ¾¥¤l ´f¬I ±i»a ¼BÝõ ... §JµÜ¦] ¡A¢Û¡D¢Û¡D¡]Kline, Morris¡^

17. Title archytas of tarentum Ca. One of the last prominent Pythagoreans, Archytas ofTarentum was a mathematician, teacher, philosopher, and military leader. http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/archytastext.html

ARCHYTAS OF TARENTUM Ca. 430 BCE to 350 BCE One of the last prominent Pythagoreans , Archytas of Tarentum was a mathematician, teacher, philosopher, and military leader. Archytas was also a contemporary and good friend of Plato , and is even credited with saving his life! Archytas' main contribution to mathematics was his work involving the harmonic mean, which he used to discover a geometric way of duplicating the cube . That is, given any cube, construct another cube with exactly double the volume. This problem is also referred to as the Delian Problem. Archytas' other major contribution to mathematics was his eminence as a teacher. Archytas was involved with teaching at Plato's Academy. Menaechmus , a student of Eudoxus , who in turn was a student of Archytas was also interested in the Delian problem and found an independent geometric solution.

18. Dupcubfin.html archytas of tarentum's Solution The most interesting and complex of the solutionsto the Delian Problem is the solution developed by archytas of tarentum. http://www.ms.uky.edu/~carl/ma330/projects/dupcubfin1.html

Duplication of the Cube : Darrell Mattingly, Cateryn Kiernan The ancient Greeks originated numerous mathematical questions, most of which they learned to solve using simple mathematical tools, such as the straight edge and the collapsable compass. Three of these problems persist today, challenging students in contemporary classrooms. This triology of problems, the trisection of a given angle, the squaring of a circle, and the duplication of the cube, have since been proved impossible using exclusively the straight edge and the compass. In the quest to solve these problems using those specific tools, however, mathematicians developed numerous alternate solutions using other mathematical tools. The last problem of the trilogy is the focus of this discussion, and it challenged mathematicians for centuries, due to the restriction of using only the aforementioned tools. Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem After centuries of mathematicians had worked on this problem, a proof developed that it could not be done using exclusively the straight edge and compass. This proof is based on theorems about the powers of degrees of subfields generated by the x and y coordinates of the side of the cube to be duplicated. Although the desired point can be approximated, it cannot in fact be found based on these theorems.

19. CATHOLIC ENCYCLOPEDIA: Pythagoras And Pythagoreanism (Catholic Encyclopedia)Category Society Religion and Spirituality P...... around the name of Pythagoras, many tenets were ascribed him which were in factintroduced by later Pythagoreans, such as Philolaus and archytas of tarentum. http://www.newadvent.org/cathen/12587b.htm

Home Encyclopedia Summa Fathers ... P > Pythagoras and Pythagoreanism A B C D ... Z Pythagoras and Pythagoreanism Pythagoras, the Greek philosopher and mathematician and founder of the Pythagorean school, flourished about 530 B. C. Very little is known about the life and personality of Pythagoras. There is an abundance of biographical material dating from the first centuries of the Christian era, from the age of neo-Pythagoreanism, but, when we go back to the centuries nearer to Pythagoras's time, our material becomes very scanty. It seems to be certain that Pythagoras was born at Samos about the year 550 or 560 B. C. miracles , pronounced prophecies, and did many other wonderful things, belong to legend, and seem to have no historical foundation. Similarly the story of his journey into Egypt, Asia Minor, and even to Babylon is not attested by reliable historians. To the region of fable belongs also the description of the learned works which he wrote and which were long kept secret in his school. It is certain, however, that he founded a school, or, rather, a religious philosophical society, for which he drew up a rule of life. In this rule are said to have been regulations imposing secrecy, a protracted period of silence, celibacy , and various kinds of abstinence. The time-honoured tradition that Pythagoras forbade his disciples to eat beans, for which various reasons, more or less ingenious, were assigned by ancient and medieval writers, has been upset by some recent writers, who understand the phrase, "Abstain from beans" (

20. History Of Mathematics: Greece 460370); Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?);archytas of tarentum (of Taras) (c. 428-c. 347); Plato (427-347 http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 1     1-20 of 97    1  | 2  | 3  | 4  | 5  | Next 20