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osu1338326658.pdf (4.36 MB)
ETD Abstract Container
Abstract Header
The Greek Method of Exhaustion: Leading the Way to Modern Integration
Author Info
DeSouza, Chelsea E.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658
Abstract Details
Year and Degree
2012, Master of Science, Ohio State University, Mathematics.
Abstract
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.
Committee
Herb Clemens, PhD (Advisor)
Rodica Costin, PhD (Committee Chair)
Pages
65 p.
Subject Headings
Mathematics
Keywords
archimedes quadrature of the parabola
;
method of exhaustion
;
constructing regular polygons
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Citations
DeSouza, C. E. (2012).
The Greek Method of Exhaustion: Leading the Way to Modern Integration
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658
APA Style (7th edition)
DeSouza, Chelsea.
The Greek Method of Exhaustion: Leading the Way to Modern Integration.
2012. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658.
MLA Style (8th edition)
DeSouza, Chelsea. "The Greek Method of Exhaustion: Leading the Way to Modern Integration." Master's thesis, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658
Chicago Manual of Style (17th edition)
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Document number:
osu1338326658
Download Count:
11,071
Copyright Info
© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.