The Pythagorean Theorem from Trigonometry.
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| Title: | The Pythagorean Theorem from Trigonometry. |
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| Authors: | Clark, David M.1 (AUTHOR) clarkd@newpaltz.edu, Pathania, Samrat S.2 (AUTHOR) samratpathania@protonmail.com |
| Source: | Mathematics Magazine. Dec2025, Vol. 98 Issue 5, p447-459. 13p. |
| Subject Terms: | *Trigonometry, Pythagorean theorem, Logic, Axioms, Mathematics, Inference (Logic), Mathematical proofs, Geometry |
| People: | Pythagoras, ca. 570 B.C.-495 B.C. |
| Abstract: | Summary: In October 2024 the Monthly published several striking new proofs of the Pythagorean theorem in order to resolve a long standing conjecture by making central use of trigonometry. This was a particular sensation since the two authors were still in high school. Their proofs are naturally based on the facts of geometry they were taught in high school and are thoroughly valid from a high school mathematics perspective. But mathematicians are now raising the obvious question as to whether or not the Pythagorean theorem is required in the proofs of any of the facts they use. What is needed is a demonstration that each of those facts can indeed be proven from a standard set of axioms without ever invoking the Pythagorean theorem itself. This article will provide that demonstration, thereby fully validating Jackson and Johnson's proofs. [ABSTRACT FROM AUTHOR] |
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| Database: | Education Research Complete |
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