The Spiral of Theodorus

Spiral of Theodorus Source: https://commons.wikimedia.org/wiki/File:Spiral_of_Theodorus.svg
The root spiral of Theodorus Source

In Plato’s dialogue, Theaetetus (p. 147d), there is a cryptic description of a complicated geometrical diagram that the geometrician, Theodorus, drew for his students. Down through the centuries there has been much speculation about exactly what Theodorus was supposed to have drawn.

We know that it involved the roots of square areas in the natural number series up the area of 17, and so √17. But then at √17 Theodorus stopped, so we are told, because after that the diagram got ‘entangled’ (enescheto).

What happened after √17?

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Platonism and Buddhism

Ancient Gandhara Source: https://upload.wikimedia.org/wikipedia/commons/thumb/9/94/Gandhara_map.jpg/640px-Gandhara_map.jpg
Ancient Gandhara in the upper Indus valley is where a Hellenistic culture turn Buddhist. Source

Session 4 of Reading Plato comes to the Phaedo’s myth of the soul’s transmigration, where students are often astonished by the similarities with Buddhist doctrine. This raises the question of whether Platonism influenced Buddhism, or whether Plato and Buddhism share a common source.

This question has been raised many times down through the centuries and continues to be asked by modern scholars. Much of the interest centres around the ancient Gandharan civilisation of the northern Indus valley in modern day Pakistan. Gandhara was part of the great Persian Empire until Alexander’s conquest, when it came under Hellenistic influence in its art and culture. But then it turned to Buddhism.

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