Theon of Smyrna

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Theon of

philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving On Mathematics Useful for the Understanding of Plato is an introductory survey of Greek mathematics
.

Life

Little is known about the life of Theon of Smyrna. A bust created at his death, and dedicated by his son, was discovered at Smyrna, and art historians date it to around 135 CE. Ptolemy refers several times in his Almagest to a Theon who made observations at Alexandria, but it is uncertain whether he is referring to Theon of Smyrna.[1] The lunar impact crater Theon Senior is named for him.

Works

Theon wrote several commentaries on the works of mathematicians and philosophers of the time, including works on the philosophy of

Arabic translation.[2]

On Mathematics Useful for the Understanding of Plato

His On Mathematics Useful for the Understanding of Plato is not a commentary on Plato's writings but rather a general handbook for a student of mathematics. It is not so much a groundbreaking work as a reference work of ideas already known at the time. Its status as a compilation of already-established knowledge and its thorough citation of earlier sources is part of what makes it valuable.

The first part of this work is divided into two parts, the first covering the subjects of numbers and the second dealing with music and

even numbers, prime numbers, perfect numbers, abundant numbers, and other such properties. It contains an account of 'side and diameter numbers', the Pythagorean method for a sequence of best rational approximations to the square root of 2,[3] the denominators of which are Pell numbers. It is also one of the sources of our knowledge of the origins of the classical problem of Doubling the cube.[4]

The second section, on music, is split into three parts: music of numbers (hē en arithmois mousikē), instrumental music (hē en organois mousikē), and "music of the spheres" (hē en kosmō harmonia kai hē en toutō harmonia). The "music of numbers" is a treatment of temperament and harmony using ratios, proportions, and means; the sections on instrumental music concerns itself not with melody but rather with intervals and consonances in the manner of Pythagoras' work. Theon considers intervals by their degree of consonance: that is, by how simple their ratios are. (For example, the octave is first, with the simple 2:1 ratio of the octave to the fundamental.) He also considers them by their distance from one another.

The third section, on the music of the cosmos, he considered most important, and ordered it so as to come after the necessary background given in the earlier parts. Theon quotes a poem by

Alexander of Ephesus
assigning specific pitches in the chromatic scale to each planet, an idea that would retain its popularity for a millennium thereafter.

The second book is on

Otto Neugebauer
to criticize him for not fully understanding the material he attempted to present.

On Pythagorean Harmony

Theon was a great philosopher of

consonances
through half-filling vases and explains these experiments on a deeper level focusing on the fact that the octaves, fifths, and fourths correspond respectively with the fractions 2/1, 3/2, and 4/3. His contributions greatly contributed to the fields of music and physics (Papadopoulos, 2002).

See also

Notes

  1. ^ James Evans, (1998), The History and Practice of Ancient Astronomy, New York, Oxford University Press, 1998, p. 49
  2. ^ "Theon of Smyrna" entry in John Hazel, 2002, Who's who in the Greek world, page 37. Routledge
  3. ^ T. Heath "A History of Greek Mathematics", p.91.
  4. ^ L. Zhmud The origin of the history of science in classical antiquity, p.84.

Bibliography

External links

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