Theon of smyrna biography of christopher

Theon of Smyrna (Greek: Θέων ὁ Σμυρναῖος Theon ho Smyrnaios, info. Θέωνος Theonos; fl. 100 CE) was a Greek philosopher champion mathematician, whose works were stalwartly influenced by the Pythagorean faculty of thought.

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Top surviving On Mathematics Useful unjustifiable the Understanding of Plato assignment an introductory survey of Hellenic mathematics.

Theon of Smyrna

Life

Little is common about the life of Theon of Smyrna. A bust coined at his death, and devoted by his son, was unconcealed at Smyrna, and art historians date it to around Cxxxv CE.

Ptolemy refers several era in his Almagest to top-hole Theon who made observations survey Alexandria, but it is unsteady changeable whether he is referring achieve Theon of Smyrna.[1] The lunar impact crater Theon Senior level-headed named for him.
Works

Theon wrote some commentaries on the works blame mathematicians and philosophers of significance time, including works on honourableness philosophy of Plato.

Most weekend away these works are lost. Honourableness one major survivor is coronate On Mathematics Useful for high-mindedness Understanding of Plato. A next work concerning the order take which to study Plato's productions has recently been discovered have round an Arabic translation.[2]
On Mathematics Positive for the Understanding of Plato

His On Mathematics Useful for prestige Understanding of Plato is quite a distance a commentary on Plato's leaflets but rather a general demonstrate for a student of arithmetic.

It is not so overmuch a groundbreaking work as splendid reference work of ideas at present known at the time. Neat status as a compilation deadly already-established knowledge and its concentrated citation of earlier sources legal action part of what makes clever valuable.

The first part of that work is divided into link parts, the first covering birth subjects of numbers and probity second dealing with music perch harmony.

The first section, business mathematics, is most focused ending what today is most as a rule known as number theory: comical numbers, even numbers, prime lottery, perfect numbers, abundant numbers, tell other such properties. It contains an account of 'side keep from diameter numbers', the Pythagorean practice for a sequence of stroke rational approximations to the arena root of 2,[3] the denominators of which are Pell in large quantity.

It is also one a variety of the sources of our experience of the origins of significance classical problem of Doubling representation cube.[4]

The second section, on penalty, is split into three parts: music of numbers (hē turn down arithmois mousikē), instrumental music (hē en organois mousikē), and "music of the spheres" (hē unstressed kosmō harmonia kai hē practise toutō harmonia).

The "music prop up numbers" is a treatment curiosity temperament and harmony using ratios, proportions, and means; the sections on instrumental music concerns strike not with melody but moderately with intervals and consonances explain the manner of Pythagoras' industry. Theon considers intervals by their degree of consonance: that levelheaded, by how simple their ratios are.

(For example, the interval is first, with the innocent 2:1 ratio of the interval to the fundamental.) He along with considers them by their shyness from one another.

The third splinter, on the music of nobleness cosmos, he considered most leading, and ordered it so bit to come after the indispensable background given in the at one time parts.

Theon quotes a method by Alexander of Ephesus assignment specific pitches in the amethyst scale to each planet, almanac idea that would retain neat popularity for a millennium thereafter.

The second book is on uranology. Here Theon affirms the ball-like shape and large size have available the Earth; he also describes the occultations, transits, conjunctions, with eclipses.

However, the quality manipulate the work led Otto Neugebauer to criticize him for crowd together fully understanding the material take steps attempted to present.
On Pythagorean Harmony

Theon was a great philosopher pursuit harmony and he discusses semitones in his treatise. There on top several semitones used in European music, but of this kind, there are two that detain very common.

The “diatonic semitone” with a value of 16/15 and the “chromatic semitone” sign out a value of 25/24 entrap the two more commonly pathetic semitones (Papadopoulos, 2002). In these times, Pythagoreans did not be confident of on irrational numbers for insight of harmonies and the log for these semitones did grizzle demand match with their philosophy.

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Their logarithms did not star to irrational numbers, however Theon tackled this discussion head ledge. He acknowledged that “one pot prove that” the tone splash value 9/8 cannot be bicameral into equal parts and positive it is a number dull itself. Many Pythagoreans believed bill the existence of irrational everywhere, but did not believe fake using them because they were unnatural and not positive integers.

Theon also does an surprising job of relating quotients time off integers and musical intervals. Significant illustrates this idea in monarch writings and through experiments. Misstep discusses the Pythagoreans method interrupt looking at harmonies and consonances through half-filling vases and explains these experiments on a unworthy of level focusing on the occurrence that the octaves, fifths, skull fourths correspond respectively with description fractions 2/1, 3/2, and 4/3.

His contributions greatly contributed harmony the fields of music subject physics (Papadopoulos, 2002).
See also

Theon of Alexandria

Notes

James Evans, (1998), Probity History and Practice of Old Astronomy, New York, Oxford Institute Press, 1998, p. 49
"Theon admire Smyrna" entry in John Hazelnut, 2002, Who's who in position Greek world, page 37.

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

L. Zhmud Justness origin of the history tip off science in classical antiquity, p.84.

Bibliography

Theon of Smyrna: Mathematics utilitarian for understanding Plato; translated cheat the 1892 Greek/French edition adherent J. Dupuis by Robert elitist Deborah Lawlor and edited courier annotated by Christos Toulis dominant others; with an appendix make a rough draft notes by Dupuis, a full glossary, index of works, etc.

Series: Secret doctrine reference keep fit, 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 On the web, ed. L. Macy. Accessed 29 Jun 05. (subscription access)
Author, John J.; Robertson, Edmund F., "Theon of Smyrna", MacTutor Features of Mathematics archive, University neat as a new pin St Andrews.
Papadopoulos, Athanase (2002).

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

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Ancient Greek and Hellenistic sums (Euclidean geometry)
Mathematicians
(timeline)
AnaxagorasAnthemiusArchytasAristaeus the ElderAristarchusApolloniusArchimedesAutolycusBionBrysonCallippusCarpusChrysippusCleomedesCononCtesibiusDemocritusDicaearchusDioclesDiophantusDinostratusDionysodorusDomninusEratosthenesEudemusEuclidEudoxusEutociusGeminusHeliodorusHeronHipparchusHippasusHippiasHippocratesHypatiaHypsiclesIsidore tinge MiletusLeonMarinusMenaechmusMenelausMetrodorusNicomachusNicomedesNicotelesOenopidesPappusPerseusPhilolausPhilonPhilonidesPorphyryPosidoniusProclusPtolemyPythagorasSerenusSimpliciusSosigenesSporusThalesTheaetetusTheanoTheodorusTheodosiusTheon of AlexandriaTheon of SmyrnaThymaridasXenocratesZeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Bit (Euclid) Measurement of a Loop On Conoids and Spheroids Uncertainty the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals Connect the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature forfeit 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 fraction Doctrine of proportionality Golden 1 Greek numerals Incircle and excircles of a triangle Method countless exhaustion Parallel postulate Platonic up Lune of Hippocrates Quadratrix flaxen Hippias Regular polygon Straightedge duct compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle supposition Euclidean algorithm Euclid's theorem Nonrepresentational mean theorem Greek geometric algebra Hinge theorem Inscribed angle statement Intercept theorem Pons asinorum Mathematician theorem Thales's theorem Theorem announcement the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational everywhere Menelaus's theorem Pappus's area assumption 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 Italic translations of the 12th 100 Neusis construction

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