**Theon** was a Greek philosopher who described how prime numbers, geometrical numbers such as squares, progressions, music and astronomy are interrelated.

- He was called 'the old Theon' by Theon of Alexandria and 'Theon the mathematician' by Ptolemy.
- The date of his birth is little better than a guess, but we do have some firm data about dates in his life.
- We know that he was making astronomical observations of Mercury and Venus between 127 and 132 since Ptolemy lists four observations which Theon made in 127, 129, 130 and 132.
- From these observations Theon made estimates of the greatest angular distance that Mercury and Venus can reach from the Sun.
- Theon's most important work is Expositio rerum mathematicarum ad legendum Platonem utilium.
- Its rather curious title means that it was intended as an introduction to a study of the works of Plato, but this is rather fanciful.
- the book has little to offer the specialist student of Plato's mathematics.
- The most important feature of the work is the wide range of citations of earlier sources.
- Its worst feature is its lack of originality.
- One who had become skilled in all geometry and all music and astronomy would be reckoned most happy on making acquaintance with the writings of Plato, but this cannot be come by easily or readily, for it calls for a very great deal of application from youth upwards.
- The work begins with a collection of theorems which Theon says will be useful for the study of arithmetic, music, geometry, and astronomy in Plato.
- However his coverage of geometry is none too good and later in the book he makes an excuse for this saying that anyone who reads his book, or the works of Plato, will have already studied elementary geometry.
- In the section on numbers Theon adopts a Pythagorean approach, writing about odd numbers, even numbers, prime numbers, composite numbers, square numbers, oblong numbers, triangular numbers, polygonal numbers, circular numbers, spherical numbers, solid numbers with three factors, pyramidal numbers, perfect numbers, deficient numbers and abundant numbers.
- The best section of Expositio rerum mathematicarum is the astronomy section which teaches that the Earth is spherical, that mountains are negligible in height compared with the Earth etc.
- It includes knowledge of conjunctions, eclipses, occultations and transits.
- Unfortunately it is also clear that Theon has not fully digested the material he is presenting to his readers.
- Theon also wrote commentaries on the main authorities of mathematics and astronomy.
- Whether his work on the ancestry of Plato is a separate work or a section of one of his commentaries on Plato's work, it is impossible to say.

Born about AD 70, Smyrna (now Izmir), Turkey. Died about AD 135.

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Ancient Greek, Astronomy, Geometry, Origin Turkey, Physics

Epochs: 1

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive