61. Pythag Tuning This is a diatonic, 7tone scale, developed by the Pythagoreans, perhaps givento Plato by archytas of tarentum ca 400 BCE, and given to us by Plato in the http://www.visual-euclid.org/music/monochord/pythagorean.html

Pythagorean tuning This is a diatonic, 7-tone scale, developed by the Pythagoreans, perhaps given to Plato by Archytas of Tarentum ca 400 BCE, and given to us by Plato in the Timeaus in the descending form: HTTTHTT, where T denotes the Pythagorean full-tone descending interval with length ratio 9/8 = 3 , and H denotes the hemitone, 256/243 = 2 Note 1: As these length ratios are larger than one, the intervals represented are falling intervals, and the descending scale indicated, rewritten in ascending mode: TTHTTTH , is the lydian mode of ancient Greece, and (approximately) our modern major scale. (Here, T = 1/T = 8/9, and H = 1/H = 243/256. Again, these are length ratios. Note 2: If the 7 descending intervals are sounded consecutively, the larger descending interval resulting is: TTTSTTS = TTTTTSS = 2 (a perfect descending octave) Note 3: If the first 4 intervals are sounded consecutively, the larger interval resulting is: TTTS = (9/8) = 3/2 (a perfect descending fifth) Note 4: If the next 3 intervals are sounded consecutively, the larger interval resulting is: TTS = (9/8) = 4/3 (a perfect descending fourth) Revised 14 December 2001 by Ralph Abraham

62. The Age Of Spiritual Machines: Timeline c. 420 bc, archytas of tarentum, who was friends with Plato, constructs a woodenpigeon whose movements are controlled by a jet of steam or compressed air. http://www.kurzweilai.net/articles/art0274.html?m=15

63. The Age Of Intelligent Machines: Chronology c. 420 B.C. archytas of tarentum, a friend of Plato, constructs a wooden pigeonwhose movements are controlled by a jet of steam or compressed air. http://www.kurzweilai.net/articles/art0298.html?m=11

64. ALC III,2: The Science Of Magnitudes In Italy he met two famous men, archytas of tarentum and Timaeus of Locri, whobelonged to the ancient tradition of the Pythagoreans and who also were http://www.domcentral.org/study/ashley/arts/arts302.htm

BENEDICT M. ASHLEY, O.P.: THE ARTS OF LEARNING AND COMMUNICATION CHAPTER II The Science of Magnitudes THE BEGINNINGS THE GREEKS, SCIENTISTS AND ARTISTS In the last chapter we indicated that, while mathematical calculation was developed in a practical way by the people of Mesopotamia and Egypt, and carried still further by the Hindus and Chinese, it was the Greeks who made it a theoretical study. They transformed it into a true science, rigorously logical in structure, and a model for all other sciences. It was these same scientifically minded Greeks who first arrived at a perfect conception of the fine arts. The art of Mesopotamia was strong and grandiose, but without grace or subtlety. The art of Egypt was subtle and mysterious, but strangely static and without inner thought or feeling. Only in the art of Greece is there achieved a living balance of all the elements of beauty. Their art was classical (from Latin classicus ,meaning "first class"), and became a standard for all later art. Not, indeed, that art of later ages need confine itself to copying the style and subject-matter of Greek art, as some people have thought but that we can learn from Greek literature, sculpture, and architecture a true conception of the elements that go into a work of art and of the harmony with which they should be united. Today we are inclined to think of science and art as unrelated fields. The artist seems to be all imagination and emotion, living in a subjective world of free fancy. The scientist seems to be all facts and abstract theories, living in the objective world of experiment and measurement. Yet the Greeks excelled both in art and science. In order to learn something of this lesson from the Greeks in this chapter we are going to try to get clearer notions of two questions:

65. Salem Press Catalog 276 Archidamian War, 277 Archidamus II of Sparta, 278 Archidamus III of Sparta, 278Archilochus of Paros, 279 Archimedes, 279 archytas of tarentum, 280 Arctic http://www.salempress.com/display.asp?id=301&column=Table_of_Contents

66. Online the community. long after the dissolution of the order, eminent pythagoreans,such as archytas of tarentum,. reviewing NYLA Bonnie. http://4feet.malls4all.com/n_y_l_a__bonnie.asp

67. Earliest Known Uses Of Some Of The Words Of Mathematics (H) Roy. Soc. A, 125, 5459 (1929) John Aldrich. HARMONIC MEAN, HARMONIC PROPORTION.A surviving fragment of the work of archytas of tarentum (ca. http://members.aol.com/jeff570/h.html

Earliest Known Uses of Some of the Words of Mathematics (H) Last revision: May 23, 2004 HAMILTONIAN CIRCUIT. Hamiltonian Game appears in H. S. M. Coxeter's 1938 revision of Mathematical Recreations and Essays by W. W. Rouse Ball. Hamiltonian circuit is found in W. T. Tutte, "On Hamiltonian circuits," J. London Math. Soc. Hamiltonian path is found in V. Mierlea, "An algorithm for finding the minimal length Hamiltonian path in a graph," Econom. Comput. econom. Cybernetics Studies Res. 1973, No. 2, 77-89 (1973). HARMONIC ANALYSIS. According to Grattan-Guinness (679), the phrase is due to W. Thomson (later Lord Kelvin). In an obituary of Archibald Smith ( Proc. Royal Soc. (1873 - 1874) p. vi) Thomson wrote "One of Smith's earliest contributions to the compass problem was the application of Fourier's grand and fertile theory of the expansion of a periodic function in series of sines and cosines of the argument and its multiples, now commonly called the harmonic analysis of a periodic function." Thomson invented the harmonic analyser; in 1879 the Royal Society allocated him £50 for "completing a Tidal Harmonic Analyser" ( Proc. Royal Soc.,

68. KEY DATES approx. 420 BC, archytas of tarentum, a friend of Plato, constructs a wooden pigeonwhose movements are controlled by a jet of steam or compressed air. approx. http://www.indwes.edu/Faculty/bcupp/lookback/keydates.htm

KEY DATES IN THE HISTORY AND FUTURE OF INFORMATION PROCESSING from Computers and Information Systems YEAR EVENT Less than 100,000 years ago Homo sapiens begin using intelligence to further goals. More than 5,000 years ago The abacus, which resembles the arithmetic unit of a modern computer, is developed in the Orient. 3000-700 B.C. Water clocks are built in China in 3000 B.C., in Egypt approx 1500 B.C., and in Assyria 700 B.C. 2500 B.C. Egyptians invent the idea of thinking machines: citizens turn for advice to oracles, which arc statues with priests hidden inside. 427 B.C. In the Phaedo and later works Plato expresses ideas, several millennia before the advent off the computer that are relevant to modern dilemmas regarding human thought and its relation to the mechanics of the machine. approx. 420 B.C. Archytas of Tarentum, a friend of Plato, constructs a wooden pigeon whose movements are controlled by a jet of steam or compressed air. approx. 415 B.C. Theaetetus, a member of Plato's Academy, creates solid geometry. 387 B.C.

69. JAPANESE KITE COLLECTION the first western account of kite flying, recorded by Aulus Genius in the secondcentury AD, which refers to the ` flying dove of archytas of tarentum, and in http://www.asahi-net.or.jp/~et3m-tkkw/history5.html

Last up date:1998/08/01 History fHistoryf was copied from " KITES " written by David Phlham and published by Penguin Books Even though its origins are obscure, it is generally accepted that the kite was first invented in China long before the beginnings of written history. It seems probable however that some cultures discovered the principles of kite flying quite independently, whilst others developed existing patterns to suit their own requirements. Silk was being produced in China as early as 2600 B.C. and as bamboo cane was in abundance it does not seem an unreasonable conjecture that kites were being flown by the Chinese around 1000 B.C. Many theories have been put forward as to the original inspiration of the kite, ranging from runaway sails from a fishing boat to a Chinese farmer's hat being carried off by the wind. While all theories must remain speculative, in an early text the famous Chinese engineer Kungshu Phan of the fourth century B.C. is credited with the invention of a wooden bird that flew for three days without descending. This is generally accepted as having been a kite; while another well documented account from the second century A.D. refers to the wooden bird of Chang Hang, which appears to have been a rudimentary ornithopter with mechanized wings.

70. Ptolemy: Iconography Of His Portrait - Ptolémée: Iconographie De Son Portrait 34. Wheter the marvelous old man who copies the words of Pythagoras is Empedocles,or Zeno, or archytas of tarentum, he communicates the urgency of the true http://www.er.uqam.ca/nobel/r14310/Ptolemy/Raphael/30-40.html

Ptolemy Ptolemaeus Iconography of Ptolemy's Portrait Raphael (Raffaello Sanzio 1483-1520), Detail of Ptolemy and Strabo in the School of Athens (Scuola di Atene), 1509-1510, Vaticano, Stanza della Segnatura. 1509-1510, Vaticano, Stanza della Segnatura. Pythagoras and his disciples Grammar, Arithmetic and Music (p. 34) "The 'emblematic image' on the tablet held at Pythagoras's feet is the clue that the fresco is about the mathematical harmonies of the universe. Balancing the Pythagorecians around the slate at the lower left are the astrologers , symmetrically placed on the other side of the foreground. These two groups are rightly represented as conterparts, for what the Pythagoreans defined with musical consonances, the astrologers found out by studying the sky. Plato's raised finger expresses a final connection: from the science of numbers comes music; from music comes cosmic harmony; and from cosmic harmony comes the divine order of ideas." (p. 34) 30. "This may be Terpander or Nicomachus or else another musician and follower of Pythagoras, who was of the opinion that the turning of the stars and the motion of things occurred not otherwise than according to the rules of music (p. 52)."

71. Untitled Document Although Bladud is legendary, the story of his flight might have some factualbasis. 4th century BC, Greece, archytas of tarentum (fl. c.400350 BC). http://www.cabinetmagazine.org/issues/11/assets/flight_chart.html

A DIRECTORY OF HEAVIER-THAN-AIR FLYING MACHINES IN WESTERN EUROPE, 850 B.C. - 1783 A.D. CLIVE HART from The Prehistory of Flight (Berkeley: University of California Press, 1985) This directory attempts to list all heavier-than-air flying machines, whether models or of man-carrying size, that are said to have been built and tested in Western Europe prior to the Montgolfiers. While I do not include machines that are known to have been totally imaginary, I have been fairly liberal in my sifting of the evidence. Thus the list includes items ranging from those about which there is no historical doubt whatever (e.g., the ornithopters of Pierre Blanchard) to others that may never in fact have existed (e.g., the zany structure conceived by d'Alcripe's drunken Norman labourer). After the directory I have added a checklist of unadopted items, which I have so far been unable to confirm, and a further checklist of spurious flights, with brief comments on my reasons for rejection. DATE PLACE IDENTITY FLYING MACHINE DURATION / DISTANCE SOURCES AND NOTES ca. 850 B.C.

72. LETTERS OF ST. JEROME LIII Thus Pythagoras visited the prophets of Memphis; and Plato, besides visiting Egyptand archytas of tarentum, most carefully explored that part of the coast of http://www.ccel.org/fathers/NPNF2-06/letters/letter53.htm

LETTER LIII. TO PAULINUS. Jerome urges Paulinus, bishop of Nola, (for whom see Letter LVIII .) to make a diligent study of the Scriptures and to this end reminds him of the zeal for learning displayed not only by the wisest of the pagans but also by the apostle Paul. Then going through the two Testaments in detail he describes the contents of the several books and the lessons which may be learned from them. He concludes with an appeal to Paulinus to divest himself wholly of his earthly wealth and to devote himself altogether to God. Written in 394 A.D. 1. Our brother Ambrose along with your little gifts has delivered to me a most charming letter which, though it comes at the beginning of our friendship, gives assurance of tried fidelity and of long continued attachment. A true intimacy cemented by Christ Himself is not one which depends upon material considerations, or upon the presence of the persons, or upon an insincere and exaggerated flattery; but one such as ours, wrought by a common fear of God and a joint study of the divine scriptures. 6. These instances have been just touched upon by me (the limits of a letter forbid a more discursive treatment of them) to convince you that in the holy scriptures you can make no progress unless you have a guide to shew you the way. I say nothing of the knowledge of grammarians, rhetoricians, philosophers, geometers, logicians, musicians, astronomers, astrologers, physicians, whose several kinds of skill are most useful to mankind, and may be ranged under the three heads of teaching, method, and proficiency. I will pass to the less important crafts which require manual dexterity more than mental ability. Husbandmen, masons, carpenters, workers in wood and metal, wool-dressers and fullers, as well as those artisans who make furniture and cheap utensils, cannot attain the ends they seek without instruction from qualified persons.As Horace says(1)

73. Helicon Publishing: Data Sets And Samples: Chronologies And Timeline: Sample Chronology of toys and games. c. 400 BC Greek scientist archytas of tarentuminvents the kite. Kites also appear in China about the same time. http://www.helicon.co.uk/online/datasets/samples/chronologies.htm

E-mail us at helicon@rm.com or telephone us on 08709 200200. Looking for help with one of our CD-ROM products? Visit our technical support section. Data sets and samples Data types Fact sheet Chronologies and timelines: Sample This sample is intended to show the structure of our chronology entries. If you are interested in subject-specific data, you may also like to view the chronology samples for a particular subject Chronology of toys and games c. BC Greek scientist Archytas of Tarentum invents the kite. Kites also appear in China about the same time. Backgammon is played in England. Walter of Gloucester's set is found on the site of Gloucester Castle, discarded in a cesspit there when he decided to become a Augustinian monk to show his renunciation of gambling. Italian tarot cards are first mentioned in a manuscript. They are used both for gaming and fortune telling, and the modern pack of playing cards derives from them. German master Ingold's Das guildin Spil is the earliest handbook on card playing. March 1497 During carnival, the followers of Italian reformer and Dominican friar Giralomo Savonarola burn games and ornaments in the city-republic of Florence, which he has controlled since leading a revolt against the ruling Medici family in 1494.

74. Index Of Ancient Greek Mathematicians And Astronomers archytas of tarentum (420350 BC). Greek mathematician, astronomer and engineer.Last of the Pythagorians. Plato and Eudoxus was his pupils. http://www.ics.forth.gr/~vsiris/ancient_greeks/classical_period.html

Classical period (5th - 4th century B.C.) Within this period Athens flourishes under Pericles, the Parthenon is built on the Acropolis, the tragedies of Sophocles, Aeschylus and Euripides are created, the phisolophical schools of Socrates and Plato (known as Academy) are established, and the Lyceum of Athens is founded by Aristotle. In science, the importance of the experimental method is accepted. Philosophers-Scientists Socrates (Athens, 470-399 B.C.). Died from poison after the state found him guilty for corrupting the youth. Theodorus of Cyrene (4th century B.C.). . Pythagorean. Plato's teacher in mathematics. Shows that the square roots of 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, and 17 are irrational. Archytas of Tarentum (420-350 B.C.). Greek mathematician, astronomer and engineer. Last of the Pythagorians. Plato and Eudoxus was his pupils. Built a series of toys, among them a mechanical pigeon propelled by a steam jet. Developed the theory for the pulley. Plato (Athens, 430-350 B.C.) . Greek philosopher. He was the founder of the Academy (named from the hero Academos owner of the grove where the Academy was built). Believed that mathematics played an important role in education. Disregarded practicality, a belief he passed to his students such as Eucledes. He started a three part trilogy :

75. Cato; Or An Essay On Old Age By Cicero many years since by that illustrious philosopher archytas, of tarentum, as it was related to me when I on the other hand " continued archytas, "is the noblest gift which God http://www.4literature.net/Cicero/Cato_or_An_Essay_on_Old_Age/7.html

Books [ Titles Authors Articles Front Page ... FAQ Cato; or An Essay on Old Age by Cicero Buy more than 2,000 books on a single CD-ROM for only $19.99. That's less then a penny per book! Click here for more information. Read, write, or comment on essays about Cato; or An Essay on Old Age Search for books Search essays Archytas expressed these sentiments in a conversation with Caius Pontius, father of that famous Samnite commander who obtained a victory over the consuls Spurius Postumius and Titus Veturius, at the battle of Caudium: and it was related to me by our faithful ally, and my very worthy host, Nearchus, of Tarentum. My friend assured me he received this account by tradition from his ancestors: and he added, that Plato was a party in this conversation. This circumstance is indeed by no means improbable; as I find that philosopher visited Tarentum in the consulate of Lucius Camillus and Appius Claudius. The inference I mean to draw from the authority I have cited is, that if the principles of reason and virtue have not been sufficient to inspire us with a proper contempt for the sensual pleasures, we have cause to hold ourselves much obliged to old age at least, for weaning us from those appetites which it would ill become us to gratify. For the voluptuous passions are utter enemies to all the nobler faculties of the soul; cast a mist, if I may so express it, before the eye of reason, and hold no sort of commerce or communion with the manly virtues.

76. Perseus Update In Progress ..And other letters kept coming both from archytas and from the men in tarentum,eulogizing the philosophy of Dionysius, and saying that unless I come now I http://www.perseus.tufts.edu/cl135/Students/Maria_Daniels/tarentum.html

The Perseus Digital Library is Being Updated Notice The main Perseus web site (at Tufts) is unavailable from 5:00 to 7:00, US Eastern time, in order to rebuild its databases with new or changed meta-data. We apologize for this inconvenience.

77. Lawrence Hargrave: Australian Aviation Pioneer archytas, of tarentum, who, in the fourth century BC, is said to have launched intothe air the first flying stag, and who, according to the Greek writers http://www.ctie.monash.edu.au/hargrave/timeline0.html

Early - 1782 Would the reader please note that this section comprises, at best, distant memories of distant events and 'evidence' written centuries, if not millenia after the 'supposed' event. These entries, up until at least the the time of Roger Bacon, are included as simply an entertaining preamble to the main part of this essay. Antiquity "Thousands of years ago, Emperor Huang-ti http://members.aol.com/TOTALUFO/ancient.htm also see... The Story of Vimanas: India's Tradition of Flying Machines http://www.polycosmos.org/glxywest/vimanas.htm and... Ancient Airships http://www.ufomind.com/ufo/topic/ancient/ 2200 B.C. Chinese emperor Shin , in perhaps the first recorded attempt to fly, jumped from a high tower wearing two large straw hats. Luckily he landed safely. http://muttley.ucdavis.edu/Book/History/instructor/jumpers.html 1000 B.C. Rameses III has constructed a pair of wings but it is said, baulks at using them 400 B.C. Archytas , a Greek scholar, builds a wooden pigeon that moves through the air. It is unknown exactly how this was done, but most believe that the Greek connected it to a steam powered arm that made it go in circles. also...

78. Archytas - Internet Applications, Web Frontends archytas is inspired by the work of the so named ancient greek mathematician,archytas of Taras (tarentum). archytas was a pythagorian http://www.archytas.nl/en/index.php

home profilE productS KNOWLEDGE ... portfolio Welcome at the website of Archytas. The new ambitious company that operates on the edge of information technology and electrical engineering. Archytas targets on the development of web applications in the broadest view, with a focus on the development of internet steared or internet controlled electronics. Beside, it is possible to develop professional web sites. A professional website will contain of a content management system to manage the database backend contents and the formatting of the frontend (the pages with content). The websites can contain dynamic contents, scripting, flash, etc.... We keep an eye on design and usability. Archytas is a knowledge based company. The expansion of our knowledge about electrical engineering and information technology is the most important to us. We strive towards bringing our achieved knowledge into practice and expand it with newly obtained knowledge. For the employees, in the first place Archytas will be an ivestment in thereselves. Archytas is inspired by the work of the so named ancient greek mathematician, Archytas of Taras (Tarentum). Archytas was a pythagorian statesman and philosopher, a friend of Plato. He is known as the founder of the Pythagorean mathematics. He learned the doubling of a cube. He did a lot of inventions, like: the construction of automata (e.g. a wooden pigeon that could fly) and an algebraic view of mechanics.

79. :: Archytas :: Naslag archytas, is ingeïnspireerd door de gelijknamige Griekse wiskundigearchytas van tarentum. Enkele artikelen over archytas zijn http://www.archytas.nl/naslag.php

MENU Archytas 1 Archytas 2 Archytas 3 Archytas 4 ... Archytas 8 Artikelen over Archytas Archytas De Zaalsteden 18 9461 CT GIETEN T: 06 14157509 F: 0592 261888 E: info@archytas.nl Kies een artikel uit het menu aan de linkerzijde van de pagina om deze te bekijken. Archytas is ingeschreven bij de K.v.K. onder nummer 000.000.000.000

80. Eudoxus He was a pupil in mathematics of archytas in tarentum and in medicine of Philistium.At 23, he moved to Athens to study philosophy at Plato s Academy. http://www.math.sfu.ca/histmath/Europe/Euclid300BC/EUDOXUS.HTML

Eudoxus of Cnidos 408 - 355 B.C.E. Born around 408 B.C.E. in Cnidos on the Black Sea, Eudoxus was known foremost as a mathematician, but also as an astronomer, physician and legislator. He was a pupil in mathematics of Archytas in Tarentum and in medicine of Philistium. At 23, he moved to Athens to study philosophy at Plato's Academy . Some time later, he traveled to Egypt with Plato , according to Strabo, and received a letter of recommendation to the Pharaoh Nectanebus from the Agesilaus, the king of Sparta. While there, he learned astronomy and made some observations himself. Traveling to Cyzicus, he founded a school which attracted a large number of pupils. Visiting Athens again, with pupils of his school, he held discussions on philosophy with Plato , who did not particularly agree with his views on the theory of ideas. Finally after traveling back to his home land of Cnidos, he died at the age of 53 in 355 B.C.E. He had written a book on practical astronomy, and the Eudemian Summary credits him with the authorship of the first five propositions of Book XIII of the Elements . Proclus says that he invented the theory of proportions explained in Book V. Archimedes credits Eudoxus with the proof by mean of a certain Lemma (perhaps Book X 1) of the propositions that any pyramid is one-third of a prism sharing a common base and altitude (Book XII 7 Cor. I), and that every cone is the third part of a cylinder with a common base and altitude (Book XII 10). On the basis of this and similiarly ambiguous evidence, it is widely believed Eudoxus was the creator of the so-called "method of exhaustion" that one finds in proofs about volumes and areas in ancient Greek texts.

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