Vol.13, No.1 | [Article] Plato’s Geometric Figure and Thales Theorem: Meno 86e-87b

This paper discusses the geometry dialogue between Socrates and Meno (86e-87b). Plato's vague expression in the geometry dialogue has caused a lot of controversy about figures. In order to estimate the geometric figure used in the dialogue between Socrates and Meno, we need to consider the tacit knowledge of Plato related to the dialectic of the dialogue. I argue that the geometry in the dialogue is related to Thales Theorem (an angle inscribed in a semicircle is a right angle) and his method of proof, called Allman–Heath’s conjecture. Also, I discuss Butcher, Wilson, and Knorr’s interpretations regarding similarity, and present competitive plausibility that the techniques of geometric measurement from the Old Babylonians and ancient Egyptians related to the geometry dialogue between Socrates and Meno may have flowed to the Greeks through the Eastern Mediterranean.