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Actual infinity and pure calculation : the legacy of Archimedes through the Palimpsest of Codex C

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Title: Actual infinity and pure calculation : the legacy of Archimedes through the Palimpsest of Codex C
Author: Bergbower, Emily Anne Smith
Type: Thesis
Issue Date: 2011
Abstract: The Archimedes Palimpsest, otherwise known as Codex C, contains two new treatises of the great mathematician and mechanical engineer, Archimedes of Syracuse. The first treatise, The Method of Mechanical Theorems, was read in part by J.L. Heiburg in 1906, but its critically important proposition 14 was first read in the last decade using modern imaging techniques. Proposition 14 indicates that Archimedes knew certain principles of infinite summation, calculated with actual infinity, and foresaw modern Set Theory. These are critical concepts to the development of calculus and advanced mathematics, and they also undermine the nature of what historians of science have long believed of ancient Greek mathematics. The second treatise found in the palimpsest is the Stomachion in which Archimedes relies on a 14 piece tangram puzzle to perform pure calculations and use combinatorics. The content of these two treatises create a new and more developed role for Archimedes within the history of science as they show him to be both the father of calculus and the father of combinatorics. This paper assesses the content of these treatises, their importance within the history of science, and how they alter our perception of Archimedes.
Subject: Combinatorial analysis
Subject: Archimedes codex
Subject: Palimpsests
Subject: Archimedes
Permanent URL: http://hdl.handle.net/10066/7070

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Citation

Bergbower, Emily Anne Smith. "Actual infinity and pure calculation : the legacy of Archimedes through the Palimpsest of Codex C". 2011. Available electronically from http://hdl.handle.net/10066/7070.

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