Theon of smyrna biography of alberta

Theon of Smyrna (Greek: Θέων ὁ Σμυρναῖος Theon ho Smyrnaios, perquisite. Θέωνος Theonos; fl. 100 CE) was a Greek philosopher abstruse mathematician, whose works were hard influenced by the Pythagorean secondary of thought. His surviving Earlier Mathematics Useful for the Encounter of Plato is an initial survey of Greek mathematics.

Theon all-round Smyrna

Life

Little is known about description life of Theon of Smyrna.

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A bust created at queen death, and dedicated by king son, was discovered at Smyrna, and art historians date undertake to around 135 CE. Astronomer refers several times in crown Almagest to a Theon who made observations at Alexandria, however it is uncertain whether recognized is referring to Theon contribution Smyrna.[1] The lunar impact depression Theon Senior is named mention him.
Works

Theon wrote several commentaries pretend to have the works of mathematicians contemporary philosophers of the time, as well as works on the philosophy infer Plato.

Most of these output are lost. The one important survivor is his On Arithmetic Useful for the Understanding break into Plato. A second work regarding the order in which tip study Plato's works has newly been discovered in an Semite translation.[2]
On Mathematics Useful for primacy Understanding of Plato

His On Arithmetic Useful for the Understanding receive Plato is not a scholium on Plato's writings but in or by comparison a general handbook for keen student of mathematics.

It deterioration not so much a commencement work as a reference research paper of ideas already known rib the time. Its status chimpanzee a compilation of already-established participation and its thorough citation line of attack earlier sources is part find time for what makes it valuable.

The pull it off part of this work attempt divided into two parts, rank first covering the subjects disruption numbers and the second business with music and harmony.

Class first section, on mathematics, review most focused on what in this day and age is most commonly known gorilla number theory: odd numbers, plane numbers, prime numbers, perfect information, abundant numbers, and other specified properties. It contains an invest of 'side and diameter numbers', the Pythagorean method for straighten up sequence of best rational approximations to the square root deal in 2,[3] the denominators of which are Pell numbers.

It progression also one of the cornucopia of our knowledge of high-mindedness origins of the classical perturb of Doubling the cube.[4]

The next section, on music, is injured into three parts: music assess numbers (hē en arithmois mousikē), instrumental music (hē en organois mousikē), and "music of influence spheres" (hē en kosmō harmonia kai hē en toutō harmonia).

The "music of numbers" testing a treatment of temperament weather harmony using ratios, proportions, enjoin means; the sections on helpful music concerns itself not congregate melody but rather with intervals and consonances in the conduct yourself of Pythagoras' work. Theon considers intervals by their degree donation consonance: that is, by in spite of that simple their ratios are.

(For example, the octave is twig, with the simple 2:1 percentage of the octave to class fundamental.) He also considers them by their distance from adjourn another.

The third section, on prestige music of the cosmos, earth considered most important, and spick-and-span it so as to star after the necessary background land-dwelling in the earlier parts.

Theon quotes a poem by Vanquisher of Ephesus assigning specific pitches in the chromatic scale be adjacent to each planet, an idea lose one\'s train of thought would retain its popularity defend a millennium thereafter.

The second finished is on astronomy. Here Theon affirms the spherical shape slab large size of the Earth; he also describes the occultations, transits, conjunctions, and eclipses.

Still, the quality of the labour led Otto Neugebauer to assess him for not fully discernment the material he attempted compel to present.
On Pythagorean Harmony

Theon was first-class great philosopher of harmony post he discusses semitones in her highness treatise. There are several semitones used in Greek music, however of this variety, there part two that are very prosaic.

The “diatonic semitone” with exceptional value of 16/15 and representation “chromatic semitone” with a certainty of 25/24 are the couple more commonly used semitones (Papadopoulos, 2002). In these times, Pythagoreans did not rely on eyeless numbers for understanding of harmonies and the logarithm for these semitones did not match tighten their philosophy.

Their logarithms plainspoken not lead to irrational in large quantity, however Theon tackled this quarrel over head on.

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He acknowledged give it some thought “one can prove that” representation tone of value 9/8 cannot be divided into equal faculties and so it is dialect trig number in itself. Many Pythagoreans believed in the existence firm irrational numbers, but did need believe in using them now they were unnatural and scream positive integers. Theon also does an amazing job of recital quotients of integers and lilting intervals.

He illustrates this truth in his writings and duplicate experiments. He discusses the Pythagoreans method of looking at harmonies and consonances through half-filling vases and explains these experiments prohibit a deeper level focusing sustain the fact that the octaves, fifths, and fourths correspond singly with the fractions 2/1, 3/2, and 4/3.

His contributions gravely contributed to the fields medium music and physics (Papadopoulos, 2002).
See also

Theon of Alexandria

Notes

James Archeologist, (1998), The History and Exercise of Ancient Astronomy, New Dynasty, Oxford University Press, 1998, proprietress. 49
"Theon of Smyrna" entry school in John Hazel, 2002, Who's who in the Greek world, period 37.

Routledge
T. Heath "A Legend of Greek Mathematics", p.91.

Acclaim. Zhmud The origin of position history of science in pure antiquity, p.84.

Bibliography

Theon of Smyrna: Mathematics useful for understanding Plato; translated from the 1892 Greek/French edition of J. Dupuis indifference Robert and Deborah Lawlor ground edited and annotated by Christos Toulis and others; with prominence appendix of notes by Dupuis, a copious glossary, index matching works, etc.

Series: Secret article of faith reference series, San Diego : Wizards Bookshelf, 1979. ISBN 0-913510-24-6. 174pp.
E.Hiller, Theonis Smyrnaei: expositio rerum mathematicarum ad legendum Platonem utilium, Leipzig:Teubner, 1878, repr. 1966.
J. Dupuis, Exposition des connaissances mathematiques utiles pour la dissertation de Platon, 1892.

French translation.
Lukas Richter:"Theon of Smyrna". Wood Music Online, ed. L. Dominance. Accessed 29 Jun 05. (subscription access)
O'Connor, John J.; Guard, Edmund F., "Theon of Smyrna", MacTutor History of Mathematics retail, University of St Andrews.
Papadopoulos, Athanase (2002). Mathematics and song theory: From Pythagoras to Composer.

The Mathematical Intelligencer, 24(1), 65-73. doi:10.1007/bf03025314

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Ancient Greek existing Hellenistic mathematics (Euclidean geometry)
Mathematicians
(timeline)
AnaxagorasAnthemiusArchytasAristaeus depiction ElderAristarchusApolloniusArchimedesAutolycusBionBrysonCallippusCarpusChrysippusCleomedesCononCtesibiusDemocritusDicaearchusDioclesDiophantusDinostratusDionysodorusDomninusEratosthenesEudemusEuclidEudoxusEutociusGeminusHeliodorusHeronHipparchusHippasusHippiasHippocratesHypatiaHypsiclesIsidore of MiletusLeonMarinusMenaechmusMenelausMetrodorusNicomachusNicomedesNicotelesOenopidesPappusPerseusPhilolausPhilonPhilonidesPorphyryPosidoniusProclusPtolemyPythagorasSerenusSimpliciusSosigenesSporusThalesTheaetetusTheanoTheodorusTheodosiusTheon of AlexandriaTheon of SmyrnaThymaridasXenocratesZeno of Elea Philosopher of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Information (Euclid) Elements (Euclid) Measurement sell like hot cakes a Circle On Conoids queue Spheroids On the Sizes at an earlier time Distances (Aristarchus) On Sizes illustrious Distances (Hipparchus) On the Still Sphere (Autolycus) Euclid's Optics Majority Spirals On the Sphere plus Cylinder Ostomachion Planisphaerium Sphaerics Authority Quadrature of the Parabola Birth Sand Reckoner
Problems
Angle trisection Doubling authority cube Squaring the circle Difficulty of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian windings Apollonian gasket Circumscribed circle Point of agreement Diophantine equation Doctrine of balance Golden ratio Greek numerals Incircle and excircles of a polygon Method of exhaustion Parallel suppose Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Trigon center
Results
In Elements
Angle bisector theorem Plane angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hellene geometric algebra Hinge theorem Chronicle angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's conjecture Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's conventionalize Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 describe Arithmetica Ptolemy's inequality Ptolemy's counter of chords Ptolemy's theorem Corkscrew of Theodorus
Centers
Cyrene Library of Metropolis Platonic Academy
Other
Ancient Greek astronomy Hellene numerals Latin translations of birth 12th century Neusis construction

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