From Plato's Rational Diameter to Proclus' Elegant Theorem
George Baloglou, Yannis Thomaidis
TL;DR
This paper explores the historical and philosophical plausibility of deriving an infinite sequence of geometric ratios through inductive arithmetic methods, based on interpretations of ancient texts by Proclus and Plato.
Contribution
It offers a new analysis of ancient mathematical reasoning, connecting philosophical commentary with potential mathematical derivations in a historical context.
Findings
Proclus' commentary suggests a possible inductive approach to geometric ratios.
The paper debates the historical plausibility of rigorous arithmetical derivations in ancient Greece.
It provides interpretative insights into the mathematical thinking of Proclus and Plato.
Abstract
We debate, departing from 2-3 readings of a single sentence in Proclus' Commentary to Plato's Republic, the plausibility of a rigorous (inductive) arithmetical derivation of an infinite sequence of pairs of side and diameter numbers by Proclus.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.