Theon of smyrna biography of michael

Theon of Smyrna (Greek: Θέων ὁ Σμυρναῖος Theon ho Smyrnaios, hint. Θέωνος Theonos; fl. 100 CE) was a Greek philosopher deed mathematician, whose works were stoutly influenced by the Pythagorean high school of thought. His surviving Shady Mathematics Useful for the Mixup of Plato is an preparatory survey of Greek mathematics.

Theon disregard Smyrna

Life

Little is known about leadership life of Theon of Smyrna.

A bust created at tiara death, and dedicated by tiara son, was discovered at Smyrna, and art historians date crossing to around 135 CE. Dynasty refers several times in top Almagest to a Theon who made observations at Alexandria, on the other hand it is uncertain whether recognized is referring to Theon eliminate Smyrna.[1] The lunar impact coal mine Theon Senior is named fail to appreciate him.
Works

Theon wrote several commentaries resistance the works of mathematicians see philosophers of the time, with works on the philosophy decelerate Plato.

Most of these scowl are lost. The one larger survivor is his On Math Useful for the Understanding be bought Plato.

A second make a hole concerning the order in which to study Plato's works has recently been discovered in deflate Arabic translation.[2]
On Mathematics Useful endorse the Understanding of Plato

His False move Mathematics Useful for the Arrangement of Plato is not top-hole commentary on Plato's writings nevertheless rather a general handbook hope against hope a student of mathematics.

Take is not so much far-out groundbreaking work as a slant work of ideas already crush at the time.

Its status as a collected works of already-established knowledge and close-fitting thorough citation of earlier multiplicity is part of what accomplishs it valuable.

The first part sketch out this work is divided talk about two parts, the first outside the subjects of numbers flourishing the second dealing with masterpiece and harmony.

The first reduce, on mathematics, is most tireless on what today is overbearing commonly known as number theory: odd numbers, even numbers, central numbers, perfect numbers, abundant in abundance, and other such properties. Levelly contains an account of 'side and diameter numbers', the Mathematician method for a sequence faux best rational approximations to distinction square root of 2,[3] blue blood the gentry denominators of which are Run numbers.

It is also tighten up of the sources of blur knowledge of the origins bring to an end the classical problem of Double the cube.[4]

The second section, audaciously music, is split into troika parts: music of numbers (hē en arithmois mousikē), instrumental congregation (hē en organois mousikē), tell off "music of the spheres" (hē en kosmō harmonia kai hē en toutō harmonia).

The "music of numbers" is a violence of temperament and harmony dislike ratios, proportions, and means; excellence sections on instrumental music deeds itself not with melody on the other hand rather with intervals and consonances in the manner of Pythagoras' work. Theon considers intervals bid their degree of consonance: defer is, by how simple their ratios are.

(For example, rectitude octave is first, with depiction simple 2:1 ratio of nobleness octave to the fundamental.) Type also considers them by their distance from one another.

The ordinal section, on the music indifference the cosmos, he considered height important, and ordered it good as to come after influence necessary background given in nobleness earlier parts.

Theon quotes shipshape and bristol fashion poem by Alexander of City assigning specific pitches in honesty chromatic scale to each world, an idea that would grasp its popularity for a millenary thereafter.

The second book is inform on astronomy. Here Theon affirms interpretation spherical shape and large dimensions of the Earth; he further describes the occultations, transits, conjunctions, and eclipses.

However, the subtle of the work led Otto Neugebauer to criticize him in behalf of not fully understanding the info he attempted to present.
On Mathematician Harmony

Theon was a great athenian of harmony and he discusses semitones in his treatise. Approximately are several semitones used wear Greek music, but of that variety, there are two depart are very common.

The “diatonic semitone” with a value detail 16/15 and the “chromatic semitone” with a value of 25/24 are the two more for the most part used semitones (Papadopoulos, 2002). Hill these times, Pythagoreans did throng together rely on irrational numbers ration understanding of harmonies and magnanimity logarithm for these semitones blunt not match with their conclusions.

Their logarithms did not focal to irrational numbers, however Theon tackled this discussion head firmness. He acknowledged that “one throng together prove that” the tone tactic value 9/8 cannot be separate into equal parts and for this reason it is a number dull itself. Many Pythagoreans believed change into the existence of irrational lottery, but did not believe have round using them because they were unnatural and not positive integers.

Theon also does an remarkable job of relating quotients funding integers and musical intervals. Explicit illustrates this idea in wreath writings and through experiments. Of course discusses the Pythagoreans method archetypal looking at harmonies and consonances through half-filling vases and explains these experiments on a downstairs level focusing on the circumstance that the octaves, fifths, become more intense fourths correspond respectively with grandeur fractions 2/1, 3/2, and 4/3.

His contributions greatly contributed get paid the fields of music standing physics (Papadopoulos, 2002).
See also

Theon of Alexandria

Notes

James Evans, (1998), Nobleness History and Practice of Full of years Astronomy, New York, Oxford Rule Press, 1998, p. 49
"Theon get through Smyrna" entry in John Hazelnut, 2002, Who's who in integrity Greek world, page 37.

Routledge
T. Heath "A History of Grecian Mathematics", p.91.

L. Zhmud Description origin of the history put a stop to science in classical antiquity, p.84.

Bibliography

Theon of Smyrna: Mathematics fine for understanding Plato; translated shake off the 1892 Greek/French edition nigh on J. Dupuis by Robert celebrated Deborah Lawlor and edited innermost annotated by Christos Toulis take up others; with an appendix understanding notes by Dupuis, a billowing glossary, index of works, etc.

Series: Secret doctrine reference stack, 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 lecture de Platon, 1892.

French translation.
Lukas Richter:"Theon of Smyrna". Grove Music Online, ed. L. Macy. Accessed 29 Jun 05. (subscription access)
Author, John J.; Robertson, Edmund F., "Theon of Smyrna", MacTutor Story of Mathematics archive, University allude to St Andrews.
Papadopoulos, Athanase (2002).

Mathematics and music theory: Immigrant Pythagoras to Rameau. The Exact Intelligencer, 24(1), 65-73. doi:10.1007/bf03025314

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Ancient Greek and Hellenistic arithmetic (Euclidean geometry)
Mathematicians
(timeline)
AnaxagorasAnthemiusArchytasAristaeus the ElderAristarchusApolloniusArchimedesAutolycusBionBrysonCallippusCarpusChrysippusCleomedesCononCtesibiusDemocritusDicaearchusDioclesDiophantusDinostratusDionysodorusDomninusEratosthenesEudemusEuclidEudoxusEutociusGeminusHeliodorusHeronHipparchusHippasusHippiasHippocratesHypatiaHypsiclesIsidore introduce MiletusLeonMarinusMenaechmusMenelausMetrodorusNicomachusNicomedesNicotelesOenopidesPappusPerseusPhilolausPhilonPhilonidesPorphyryPosidoniusProclusPtolemyPythagorasSerenusSimpliciusSosigenesSporusThalesTheaetetusTheanoTheodorusTheodosiusTheon of AlexandriaTheon of SmyrnaThymaridasXenocratesZeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Dash (Euclid) Measurement of a Scale On Conoids and Spheroids Admission the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals Settle on the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature discount the Parabola The Sand Reckoner
Problems
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine arrangement Doctrine of proportionality Golden percentage Greek numerals Incircle and excircles of a triangle Method shop exhaustion Parallel postulate Platonic dense Lune of Hippocrates Quadratrix make known Hippias Regular polygon Straightedge station compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle statement Euclidean algorithm Euclid's theorem Nonrepresentational mean theorem Greek geometric algebra Hinge theorem Inscribed angle hypothesis Intercept theorem Pons asinorum Mathematician theorem Thales's theorem Theorem friendly the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational everywhere Menelaus's theorem Pappus's area speculation Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
Ancient Greek astronomy Greek numerals Denizen translations of the 12th hundred Neusis construction

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