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DeSouza, Chelsea E.
The Greek *Method* of *Exhaustion*: Leading the Way to Modern
Integration.

Degree: MS, Mathematics, 2012, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658

This paper is a critical look at the Method of
Exhaustion and how it is related to some of the more modern
techniques of integration. This text moves through the development
of the Method of Exhaustion to some applications. These
applications include estimating the area of a circle using the
Method of Exhaustion, and finding the exact area of a parabolic
region by Archimedes quadrature of the parabola. These ideas are
extensively developed and all constructions and proofs are given in
the text and appendices. Similar techniques are then suggested to
the reader to extend these results to find certain volumes in the
appendix. Finally, a comparison is drawn between the Method of
Exhaustion and integration techniques taught in modern classroom
settings.
*Advisors/Committee Members: Costin, Rodica (Committee Chair), Clemens, Herb (Advisor).*

Subjects/Keywords: Mathematics; archimedes quadrature of the parabola; method of exhaustion; constructing regular polygons

…paper examines the Greekās idea *of* the
*Method* *of* *Exhaustion* and how this *method* could have… …*of* *Exhaustion*.
This text seeks to: historically look at what the *Method* *of* *Exhaustion* was… …used
for, look at how to apply the *Method* *of* *Exhaustion* to find useful results, and examine… …similarities between the *Method* *of* *Exhaustion* and the techniques *of* modern integration.
The *Method* *of*… …*Method* *of* *Exhaustion* to approximate the area
*of* a circle and find an exact formula for the area…

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APA (6^{th} Edition):

DeSouza, C. E. (2012). The Greek Method of Exhaustion: Leading the Way to Modern Integration. (Masters Thesis). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658

Chicago Manual of Style (16^{th} Edition):

DeSouza, Chelsea E. “The Greek Method of Exhaustion: Leading the Way to Modern Integration.” 2012. Masters Thesis, The Ohio State University. Accessed April 03, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658.

MLA Handbook (7^{th} Edition):

DeSouza, Chelsea E. “The Greek Method of Exhaustion: Leading the Way to Modern Integration.” 2012. Web. 03 Apr 2020.

Vancouver:

DeSouza CE. The Greek Method of Exhaustion: Leading the Way to Modern Integration. [Internet] [Masters thesis]. The Ohio State University; 2012. [cited 2020 Apr 03]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658.

Council of Science Editors:

DeSouza CE. The Greek Method of Exhaustion: Leading the Way to Modern Integration. [Masters Thesis]. The Ohio State University; 2012. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658