Modernizing Archimedes’ Construction of <i>π</i>
In his famous work, “Measurement of a Circle,” Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern approaches for defining <inline-formula><math display...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2204 |
| _version_ | 1797544987895791616 |
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| author | David Weisbart |
| author_facet | David Weisbart |
| author_sort | David Weisbart |
| collection | DOAJ |
| description | In his famous work, “Measurement of a Circle,” Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern approaches for defining <inline-formula><math display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> eschew his method and instead use arguments that are easier to justify, but they involve ideas that are not elementary. This paper makes Archimedes’ measurement procedure rigorous from a modern perspective. In so doing, it brings a rigorous and geometric treatment of the differential properties of the trigonometric functions into the purview of an introductory calculus course. |
| first_indexed | 2024-03-10T14:09:17Z |
| format | Article |
| id | doaj.art-eaad24fb39024a478fdece92568cc498 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:09:17Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-eaad24fb39024a478fdece92568cc4982023-11-21T00:23:56ZengMDPI AGMathematics2227-73902020-12-01812220410.3390/math8122204Modernizing Archimedes’ Construction of <i>π</i>David Weisbart0Department of Mathematics, University of California, Riverside, CA 92521, USAIn his famous work, “Measurement of a Circle,” Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern approaches for defining <inline-formula><math display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> eschew his method and instead use arguments that are easier to justify, but they involve ideas that are not elementary. This paper makes Archimedes’ measurement procedure rigorous from a modern perspective. In so doing, it brings a rigorous and geometric treatment of the differential properties of the trigonometric functions into the purview of an introductory calculus course.https://www.mdpi.com/2227-7390/8/12/2204euclidean geometryArchimedesMeasurement of a Circle |
| spellingShingle | David Weisbart Modernizing Archimedes’ Construction of <i>π</i> Mathematics euclidean geometry Archimedes Measurement of a Circle |
| title | Modernizing Archimedes’ Construction of <i>π</i> |
| title_full | Modernizing Archimedes’ Construction of <i>π</i> |
| title_fullStr | Modernizing Archimedes’ Construction of <i>π</i> |
| title_full_unstemmed | Modernizing Archimedes’ Construction of <i>π</i> |
| title_short | Modernizing Archimedes’ Construction of <i>π</i> |
| title_sort | modernizing archimedes construction of i π i |
| topic | euclidean geometry Archimedes Measurement of a Circle |
| url | https://www.mdpi.com/2227-7390/8/12/2204 |
| work_keys_str_mv | AT davidweisbart modernizingarchimedesconstructionofipi |