21. References For Theon_of_Smyrna References for theon of smyrna. Biography 244. GC Vedova, Notes on Theonof Smyrna, The American Mathematical Monthly 58 (1951), 675683. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZC3FA.htm

References for Theon of Smyrna Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles: T L Heath, A History of Greek Mathematics II (Oxford, 1921), 238-244. G C Vedova, Notes on Theon of Smyrna, The American Mathematical Monthly Close this window or click this link to go back to Theon of Smyrna Welcome page Biographies Index History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Theon_of_Smyrna.html

22. Theon Of Smyrna a topic from mathhistory-list theon of smyrna. post a message on thistopic post a message on a new topic 12 Jun 1997 theon of smyrna http://mathforum.org/epigone/math-history-list/brouquerdglend

a topic from math-history-list Theon of Smyrna post a message on this topic post a message on a new topic 12 Jun 1997 Theon of Smyrna , by Antreas P. Hatzipolakis 15 Jun 1997 Re: Theon of Smyrna , by David Fowler 15 Jun 1997 Re: Theon of Smyrna , by MANN@vms.huji.ac.il 16 Jun 1997 Re: Theon of Smyrna , by Julio Gonzalez Cabillon 16 Jun 1997 Re: Theon of Smyrna , by David Fowler 16 Jun 1997 Re: Theon of Smyrna , by Domingo Gomez Morin 22 Jun 1997 Re: Theon of Smyrna , by Antreas P. Hatzipolakis 22 Jun 1997 Re: Theon of Smyrna , by Domingo Gomez Morin 23 Jun 1997 Re: Theon of Smyrna , by Antreas P. Hatzipolakis The Math Forum

23. Re: Theon Of Smyrna By Julio Gonzalez Cabillon Re theon of smyrna by Julio Gonzalez Cabillon. reply to this messagepost a message on a new topic Back to messages on this topic http://mathforum.org/epigone/math-history-list/brouquerdglend/1.5.4.32.199706160

Re: Theon of Smyrna by Julio Gonzalez Cabillon reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Re: Theon of Smyrna Author: jgc@adinet.com.uy Date: The Math Forum

24. HighBeam Research: Search Results: Article theon of smyrna. The Hutchinson Dictionary of Scientific Biography;1/1/1998. Read the Full Article, Get a FREE Trial for instant http://www.highbeam.com/library/doc0.asp?DOCID=1P1:28910504&num=6&ctrlInfo=Round

25. HighBeam Research: ELibrary Search: Results other s hands. Helicon 6. theon of smyrna The Hutchinson Dictionaryof Scientific Biography; January 1, 1998 latest thinkers http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_thesauru

26. En.wikipedia.org/w/wiki.phtml?title=Theon_of_Smyrna Action=edit Theon_of_Smyrnatheon of smyrna. Born about 70 Died about 135. Little is known oftheon of smyrna s life. He was called the old Theon by Theon http://en.wikipedia.org/w/wiki.phtml?title=Theon_of_Smyrna&action=edit

27. Ptolemy We do know that Ptolemy used observations made by Theon the mathematician , andthis was almost certainly theon of smyrna who almost certainly was his teacher http://homepages.compuserve.de/thweidenfeller/mathematiker/Ptolemy.htm

Claudius Ptolemy Born: about 85 in Egypt Died: about 165 in Alexandria, Egypt One of the most influential Greek astronomers and geographers of his time, Ptolemy propounded the geocentric theory in a form that prevailed for 1400 years. However, of all the ancient Greek mathematicians, it is fair to say that his work has generated more discussion and argument than any other. We shall discuss the arguments below for, depending on which are correct, they portray Ptolemy in very different lights. The arguments of some historians show that Ptolemy was a mathematician of the very top rank, arguments of others show that he was no more than a superb expositor, but far worse, some even claim that he committed a crime against his fellow scientists by betraying the ethics and integrity of his profession. We know very little of Ptolemy's life. He made astronomical observations from Alexandria in Egypt during the years AD 127-41. In fact the first observation which we can date exactly was made by Ptolemy on 26 March 127 while the last was made on 2 February 141. It was claimed by Theodore Meliteniotes in around 1360 that Ptolemy was born in Hermiou (which is in Upper Egypt rather than Lower Egypt where Alexandria is situated) but since this claim first appears more than one thousand years after Ptolemy lived, it must be treated as relatively unlikely to be true. In fact there is no evidence that Ptolemy was ever anywhere other than Alexandria. His name, Claudius Ptolemy, is of course a mixture of the Greek Egyptian 'Ptolemy' and the Roman 'Claudius'. This would indicate that he was descended from a Greek family living in Egypt and that he was a citizen of Rome, which would be as a result of a Roman emperor giving that 'reward' to one of Ptolemy's ancestors.

28. Theon Of Smyrna: Mathematics Useful For Understanding Plato Or, Pythagorean Arit theon of smyrna Mathematics Useful for Understanding Plato Or, PythagoreanArithmatic, Music, Astronomy, Spiritual Disciplines. R. D. Lawlor. http://higherforces.info/research/books/Books/TheonofSmyrnaMathematicsUsefulforU

HigherForces.info books (in alphabetical order) Theon of Smyrna: Mathematics Useful for Understanding Plato Or, Pythagorean Arithmatic, Music, Astronomy, Spiritual Disciplines < prev The White Goddess: A Historical Grammar of Poetic Myth > next Theoretic Arithmetic of the Pythagoreans View or Purchase Online This book list has been generated by Books

29. Eratosthenes Of Cyrene Although this work is now lost, theon of smyrna wrote that Platonicus studied thebasic definitions of geometry and arithmetic, as well as covering such topics http://space.about.com/cs/astronomerbios/a/Eratosthenesbio.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Space / Astronomy Biographies ... Featured Astronomy Image of the Week zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Multimedia Resources News - Current Events Stars Planets Galaxies Education - Astronomy/Space ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Space / Astronomy newsletter. Search Space / Astronomy Eratosthenes of Cyrene Public Domain Eratosthenes of Cyrene Public Domain Email to a friend Print this page Stay Current Subscribe to the About Space / Astronomy newsletter. Suggested Reading Biography of Ptolemy Biography of Copernicus Recent Discussions Let's Talk Bessels function? Earliest Astronomy Recent Discussions Apollo 1 Fire Comet Man First Lady of Astronomy Most Popular The Space Shuttle Challenger Disaster - a NASA Tragedy 9/11 Terrorist Attacks on World Trade Center Twin Towers Fro... Black Holes - Hubble Space Telescope Images of Black Holes Pictures and Astronomy Facts ... Pluto - Pictures and Astronomy Facts - Solar System Planetar... What's Hot Astronomy 101 - Final Exam So, You Want To Be An Astronaut

30. 4Tests.com - Eratosthenes theon of smyrna tells us that Eratosthenes work studied the basic definitionsof geometry and arithmetic, as well as covering such topics as music. http://www.4tests.com/papersearch/papers.asp?cat=Mathematics&paper=Eratosthenes.

31. Biography-center - Letter T Mathematicians/Theon.html; theon of smyrna, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Theon_of_Smyrna.html;Theophanes, the http://www.biography-center.com/t.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish T 361 biographies Tabern, Donalee L. www.invent.org/hall_of_fame/142.html Tacca, Ferdinand www.getty.edu/art/collections/bio/a451-1.html Tacquet, Andrea www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tacquet.html Taft, Helen Herron www.whitehouse.gov/WH/glimpse/firstladies/html/ht27.html Taft, William Howard odur.let.rug.nl/~usa/P/wt27/about/taftbio.htm Tagore, Rabindranath www.nobel.se/literature/laureates/1913/tagore-bio.html Tahir, ibn www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Baghdadi.html Taiga, Marton www.kirjasto.sci.fi/taiga.htm Taillandier, Vincent www.getty.edu/art/collections/bio/a1075-1.html Tait, Peter Guthrie www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tait.html Takacs, Karoly

32. JMM HM DICIONÁRIO Translate this page da Cirene (-460?-400?) Teodósio Teofrasto de Lesbos Vitrúvio Zenão de Eleia (490?-420?),Thales Theon of Alexandria theon of smyrna Theaetetos Theodoros of http://phoenix.sce.fct.unl.pt/jmmatos/HISTMAT/HMHTM/HMDIC.HTM

Bibliografia Recursos na rede bem vindos em latim Anaximandro (-611-545) Antifonte Aristarco de Samos (-310-230?) Aristeo (c. -330) Arquimedes de Siracusa (-287?-212) Arquitas de Tarento (c. -375) Apollonius Archimedes Boetius Apollonios of Perga Aristarchos Aristaeus Aristotle Archimedes of Syracuse Archytas Apollonius of Perga Aristarchus Aristaeus Aristotle Archimedes of Syracuse Archytas Boethius Apollonios Diofanto de Alexandria (c. 250) Diophantus Democritos Dinostratos Diophantos Diocles Democritos Dinostratus Diophantus Diocles Diogenes Laertius Euclides de Alexandria (c. -300) Filolaos Endemus Eudoxus Philolaus Eratosthenes Euclid of Alexandria Endemos Eudoxos of Cnidos Eratosthenes Euclid of Alexandria Endemus Eudoxus of Cnidos Philolaus Euclide Hiparco de Alexandria (-190-120) Hipasos Hipsicles Herodotus Hipparchus Hero Herodotos Hypatia Hipparchos Hippocrates of Chios hekat Heron Herodotus Hypatia Hipparchus Hippocrates of Chios Iamblichus Iamblichos Iamblichus Menecmo (c. -350)

33. Who Was Who In Roman Times: Data On Persons: Theon Of Smyrna Sponsored links Data on Persons. theon of smyrna. Function Scientist Sex Male, No synonyms found. No parents found. No spouse/wife/partner found. http://www.romansonline.com/Persns.asp?IntID=1244&Ename=Theon of Smyrna

34. Quote From Theon Of Smyrna In Heath, Aristarchus Of Samos, P.304. Quote from theon of smyrna in Heath, Aristarchus of Samos, p.304. http://www.perseus.tufts.edu/GreekScience/Students/Kristen/theon.html

Quote from Theon of Smyrna in Heath, Aristarchus of Samos

35. Greek Mathematics theon of smyrna and Proclus ordered the divisions differently. Likethe Pythagoreans they placed arithmetic first, but followed http://www.perseus.tufts.edu/GreekScience/Students/Chris/GreekMath.html

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. Chris Weinkopf Greek Mathematics April 19, 1995 Look at the comments on this paper. Table of Contents The Divisions The Pure and the Physical Order, Purpose, and Method Greek mathematics was premised on inductive reasoning. Whereas ancient historians sough to deduce facts from observations, the mathematicians sought to explore and discover truths working from a factual foundation. Theoretical mathematics also provided ancient philosophers with the tools of logic, which were thus employed in the pursuit of practical ends. The classical interpretation of mathematics, as well as the subdivision of the discipline into specific categories, demonstrates the Greeks' approach to the subject. The Divisions A fragment of Archytus , a Pythagorean friend and contemporary of Plato, explains the Quadrivivium , the four fields into which the Pythagoreans divided mathematics: arithmetic, geometry, sphaeric (astronomy), and music. Plato classified mathematics into the same categories, but included as a separate division stereometry three-dimensional geometry between geometry and sphaeric. (The Pythagoreans considered stereometry as subfield of geometry).

36. Pythagoreans Theon of Smyna theon of smyrna. The Importance Of The Quaternary ObtainedBy Addition Is Great In Music Because All The Harmonies Are Found In It. http://essenes.net/theonsay.html

Th eon of Smy na Theon Of Smyrna The Importance Of The Quaternary Obtained By Addition Is Great In Music Because All The Harmonies Are Found In It. 2 But It Is Not Only For This Reason That All Pythagorean-Theanoians Hold It In Highest Esteem, It Is Also Because It Seems To Symbolize The Entire Nature Of The Universe. 3 It Is For This Reason That The Formula Of Their Oath Was: I Swear By The Ones Who Have Bequeathed The Tetraktys, The Source Of Eternal Nature, Into Our Souls And Unto Future Generations. 4 The Ones Who Bestowed It Were Pythagoras And Theano, And It Has Been Said The Tetraktys Appears Indeed To Have Been Discovered By Them. 5 The First Quaternary Is The One Which We Have Just Spoken: It Is Formed By Addition Of The First Four Numbers. 6 The Second Is Formed By Multiplication, Of Even And Odd Numbers, Starting From Unity. 7 Of These Numbers, Unity Is The First, Because As We Have Said, It Is The Principle Of All The Even Numbers, The Odd Numbers And Of All The Odd-Even Numbers, And Its Essence Is Simple. 8 Next Comes Three Numbers From The Odd As Well As The Even Series.

37. Sacred Mathematics theon of smyrna put together a handbook for philosophy students of Plato whichshowed how prime numbers, geometrical numbers such as squares, progressions http://www.halexandria.org/dward010.htm

Sacred Mathematics Sacred Mathematics, by way of definition, refers to the concepts which, according to ancient (and a few modern) scholars, encompassed all of creation in mathematical terms. It includes numerical ratios of the most profound significance (literally Transcendental Numbers ), the nature of numbers themselves ( Numerology ), their mutual relationship ( Astrology ), strange beasts such as Magic Squares and Infinite Series , those astounding aspects of geometrical relationships in Sacred Geometry which defy logical or rational explanation, and the manner in which all of these aspects describe the universe. Sacred Mathematics represents a wholly contained and internally consistent philosophy a philosophy which describes physical reality, its cosmogony and every aspect of its science The Greek Philosopher, Plato, has said: “Geometry is knowledge of the eternally existent. Numbers are the highest degree of knowledge. It is knowledge itself.” This profoundly philosophical interpretation or Mathematical Theory is echoed in many spiritual traditions. Such references are not always direct, however, and in fact may have been

38. Claudius Ptolemy We suspect his teacher was theon of smyrna, who was both an observer and a mathematicianwho had written on astronomical topics such as conjunctions, eclipses http://www.stetson.edu/~efriedma/periodictable/html/Pm.html

Claudius Ptolemy We know very little of Ptolemy's life. His name, Claudius Ptolemy, is of course a mixture of the Greek Egyptian "Ptolemy" and the Roman "Claudius". This would indicate that he was descended from a Greek family living in Egypt and that he was a citizen of Rome. Ptolemy definitely made astronomical observations from Alexandria in Egypt during the years from 127 to 141. We suspect his teacher was Theon of Smyrna, who was both an observer and a mathematician who had written on astronomical topics such as conjunctions, eclipses, occultations and transits. The earliest, and perhaps most important of Ptolemy's work that has survived is the Almagest , a treatise in 13 books. It gives in detail the mathematical theory of the motions of the Sun, Moon, and planets. Ptolemy made his most original contribution by presenting details for the motions of each of the planets. His theories were not superseded until a century after Copernicus presented his heliocentric theory in 1543. Ptolemy first of all justifies his description of the universe based on the earth-centred system described by Aristotle. It is a view of the world based on a fixed earth around which the sphere of the fixed stars rotates every day, this carrying with it the spheres of the sun, moon, and planets. Ptolemy used geometric models to predict the positions of the sun, moon, and planets, using combinations of circular motion known as epicycles. Having set up this model, Ptolemy then goes on to describe the mathematics which he needs in the rest of the work. In particular he introduces trigonometrical methods based on the chord function.

39. TMTh:: ADRASTUS OF APHRODISIAS 2nd century AD) Life A native of the Ionian city of Aphrodisias in Caria, Adrastusis cited by Athenaeus, theon of smyrna, Chalcidius, Porphyry and Simplicius. http://www.tmth.edu.gr/en/aet/2/1.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN, ASTRONOMER ADRASTUS OF APHRODISIAS (fl. 2nd century AD) Life A native of the Ionian city of Aphrodisias in Caria, Adrastus is cited by Athenaeus, Theon of Smyrna, Chalcidius, Porphyry and Simplicius. Work "On the writings of Aristotle": Interpretation, exposition and commentary on Aristotle's writings, a work well known to ancient writers. Interpretation of Plato's "Timaeus": This work was used by the Stoic philosopher Posidonius. Commentary on Theophrastus' "Characters". Commentary on Aristotle's "Categories", "Physics" and "Nicomachaean Ethics". Fragments of his writings survive in Theon of Smyrna. In his treatise "On Astronomy", Theon cites Adrastus in support of his theories, and records his conclusion that "the astronomical methods of the Egyptians and Chaldaeans were imperfect". Contact the Technology Museum

40. Square Root Algorithms -- From MathWorld The fact that if is an approximation to , then is a better one (the n = 2 case)was known to theon of smyrna in the second century AD (Wells 1986, p. 35). http://mathworld.wolfram.com/SquareRootAlgorithms.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Special Functions Radicals Square Root Algorithms A sequence of approximations to can be derived by factoring (where -1 is possible only if -1 is a quadratic residue of n ). Then and Therefore, a and b are given by the recurrence relations with The error obtained using this method is The first few approximants to are therefore given by This algorithm is sometimes known as the Bhaskara-Brouckner algorithm, and the approximants are precisely those obtained by taking successive convergents to the continued fraction of The fact that if is an approximation to then is a better one (the n = 2 case) was known to Theon of Smyrna in the second century AD (Wells 1986, p. 35). Another general technique for deriving this sequence, known as Newton's iteration , is obtained by letting Then so the sequence converges quadratically to the root. The first few approximants to

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