# Convexity in Greek antiquity

## TL;DR

This paper explores the historical concept of convexity in Greek antiquity across mathematics, optics, philosophy, and art, highlighting its diverse interpretations and significance in ancient Greek culture.

## Contribution

It provides a comprehensive analysis of how convexity was understood and applied in various fields in Greek antiquity, integrating historical texts and artistic representations.

## Key findings

- Convexity played a key role in Greek mathematical and optical theories.
- Ancient Greek writings reveal diverse conceptualizations of convexity.
- Artistic depictions reflect the importance of convex forms in Greek aesthetics.

## Abstract

We consider several appearances of the notion of convexity in Greek antiquity, more specifically in mathematics and optics, in the writings of Aristotle, and in art. The final version of this article will appear in the book `Geometry in History', ed. S. G. Dani and A. Papadopoulos, Springer Verlag, 2019.