The geometry in Plato's Meno

TL;DR

This paper offers a comprehensive geometric analysis of Plato's Meno, explaining two passages from ancient and modern perspectives, and resolving a long-standing geometric puzzle that has puzzled scholars for over 2,400 years.

Contribution

It provides the first complete explanation of the second geometrical passage in Plato's Meno, bridging ancient and modern geometric interpretations.

Findings

Resolved a 2,400-year-old geometric puzzle in Plato's Meno.

Provided a unified geometric interpretation from ancient and modern viewpoints.

Clarified the geometrical passages for better understanding of Plato's dialogue.

Abstract

In this paper, we analyze the two geometrical passages in Plato's Meno, (81c -- 85c) and (86e4 -- 87b2), from the points of view of a geometer in Plato's time and today. We give, in our opinion, a complete explanation of the difficult second geometrical passage. Our explanation solves an ingenious geometry puzzle that has baffled readers of Plato's Meno for over 2,400 years.