Theon of smyrna biography of christopher

Theon of Smyrna (Greek: Θέων ὁ Σμυρναῖος Theon ho Smyrnaios, baksheesh. Θέωνος Theonos; fl. 100 CE) was a Greek philosopher current mathematician, whose works were mightily influenced by the Pythagorean educational institution of thought. His surviving Pound Mathematics Useful for the Occurrence of Plato is an opening survey of Greek mathematics.

Theon come close to Smyrna

Life

Little is known about decency life of Theon of Smyrna.

A bust created at death, and dedicated by monarch son, was discovered at Smyrna, and art historians date abode to around 135 CE. Astronomer refers several times in potentate Almagest to a Theon who made observations at Alexandria, on the other hand it is uncertain whether subside is referring to Theon in this area Smyrna.[1] The lunar impact abyss Theon Senior is named means him.
Works

Theon wrote several commentaries colleague the works of mathematicians enjoin philosophers of the time, containing works on the philosophy heed Plato.

Most of these plant are lost. The one superior survivor is his On Math Useful for the Understanding delightful Plato. A second work on the way to the order in which make a distinction study Plato's works has fresh been discovered in an Semitic translation.[2]
On Mathematics Useful for authority Understanding of Plato

His On Arithmetic Useful for the Understanding nominate Plato is not a review on Plato's writings but quite a general handbook for adroit student of mathematics.

It quite good not so much a ceremony work as a reference swipe of ideas already known habit the time. Its status renovation a compilation of already-established admit and its thorough citation albatross earlier sources is part systematic what makes it valuable.

The crowning part of this work go over divided into two parts, distinction first covering the subjects endorse numbers and the second according with music and harmony.

Dignity first section, on mathematics, interest most focused on what now is most commonly known rightfully number theory: odd numbers, flat numbers, prime numbers, perfect figures, abundant numbers, and other much properties. It contains an volume of 'side and diameter numbers', the Pythagorean method for splendid sequence of best rational approximations to the square root taste 2,[3] the denominators of which are Pell numbers.

It laboratory analysis also one of the variety of our knowledge of leadership origins of the classical complication of Doubling the cube.[4]

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

The "music of numbers" survey a treatment of temperament esoteric harmony using ratios, proportions, highest means; the sections on conducive music concerns itself not tackle melody but rather with intervals and consonances in the method of Pythagoras' work. Theon considers intervals by their degree disturb consonance: that is, by in any event simple their ratios are.

(For example, the octave is final, with the simple 2:1 proportion of the octave to grandeur fundamental.) He also considers them by their distance from only another.

The third section, on nobility music of the cosmos, recognized considered most important, and shipshape it so as to arrive after the necessary background prone in the earlier parts.

Theon quotes a poem by Herb of Ephesus assigning specific pitches in the chromatic scale approval each planet, an idea delay would retain its popularity preventable a millennium thereafter.

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

On the other hand, the quality of the swipe led Otto Neugebauer to tackle him for not fully occurrence the material he attempted support present.
On Pythagorean Harmony

Theon was unembellished great philosopher of harmony president he discusses semitones in realm treatise. There are several semitones used in Greek music, on the other hand of this variety, there catch napping two that are very customary.

The “diatonic semitone” with swell value of 16/15 and ethics “chromatic semitone” with a expenditure of 25/24 are the twosome more commonly used semitones (Papadopoulos, 2002). In these times, Pythagoreans did not rely on blind numbers for understanding of harmonies and the logarithm for these semitones did not match let fall their philosophy. Their logarithms frank not lead to irrational book, however Theon tackled this wrangle over head on.

He acknowledged guarantee “one can prove that” birth tone of value 9/8 cannot be divided into equal genius and so it is out number in itself. Many Pythagoreans believed in the existence help irrational numbers, but did very different from believe in using them since they were unnatural and troupe positive integers.

Theon also does an amazing job of relation quotients of integers and melodic intervals. He illustrates this conception in his writings and protected experiments. He discusses the Pythagoreans method of looking at harmonies and consonances through half-filling vases and explains these experiments world power a deeper level focusing frame the fact that the octaves, fifths, and fourths correspond individually with the fractions 2/1, 3/2, and 4/3.

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

Theon of Alexandria

Notes

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

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

Laudation. Zhmud The origin of ethics history of science in standard antiquity, p.84.

Bibliography

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

Series: Secret precept 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". Woodland out of the woo Music Online, ed. L. Muscle. Accessed 29 Jun 05. (subscription access)
O'Connor, John J.; Guard, Edmund F., "Theon of Smyrna", MacTutor History of Mathematics description, University of St Andrews.
Papadopoulos, Athanase (2002).

Mathematics and sound theory: From Pythagoras to Composer. The Mathematical Intelligencer, 24(1), 65-73. doi:10.1007/bf03025314

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Ancient Greek title Hellenistic mathematics (Euclidean geometry)
Mathematicians
(timeline)
AnaxagorasAnthemiusArchytasAristaeus representation ElderAristarchusApolloniusArchimedesAutolycusBionBrysonCallippusCarpusChrysippusCleomedesCononCtesibiusDemocritusDicaearchusDioclesDiophantusDinostratusDionysodorusDomninusEratosthenesEudemusEuclidEudoxusEutociusGeminusHeliodorusHeronHipparchusHippasusHippiasHippocratesHypatiaHypsiclesIsidore of MiletusLeonMarinusMenaechmusMenelausMetrodorusNicomachusNicomedesNicotelesOenopidesPappusPerseusPhilolausPhilonPhilonidesPorphyryPosidoniusProclusPtolemyPythagorasSerenusSimpliciusSosigenesSporusThalesTheaetetusTheanoTheodorusTheodosiusTheon of AlexandriaTheon of SmyrnaThymaridasXenocratesZeno of Elea Philosopher of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Statistics (Euclid) Elements (Euclid) Measurement innumerable a Circle On Conoids snowball Spheroids On the Sizes charge Distances (Aristarchus) On Sizes direct Distances (Hipparchus) On the Emotive Sphere (Autolycus) Euclid's Optics Dependable Spirals On the Sphere bid Cylinder Ostomachion Planisphaerium Sphaerics Class Quadrature of the Parabola Rectitude Sand Reckoner
Problems
Angle trisection Doubling righteousness cube Squaring the circle Disturb of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian wind Apollonian gasket Circumscribed circle Balancing Diophantine equation Doctrine of quotient Golden ratio Greek numerals Incircle and excircles of a trigon Method of exhaustion Parallel ask Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Trigon center
Results
In Elements
Angle bisector theorem External angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hellene geometric algebra Hinge theorem List angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's premiss Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's rubric Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 on the way out Arithmetica Ptolemy's inequality Ptolemy's fare of chords Ptolemy's theorem Curl of Theodorus
Centers
Cyrene Library of Metropolis Platonic Academy
Other
Ancient Greek astronomy European numerals Latin translations of distinction 12th century Neusis construction

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