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The Pythagorean Theorem from Trigonometry.

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Title: The Pythagorean Theorem from Trigonometry.
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]
Copyright of Mathematics Magazine is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Education Research Complete
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PubType: Academic Journal
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  Data: The Pythagorean Theorem from Trigonometry.
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  Data: *<searchLink fieldCode="DE" term="%22Trigonometry%22">Trigonometry</searchLink><br /><searchLink fieldCode="DE" term="%22Pythagorean+theorem%22">Pythagorean theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Logic%22">Logic</searchLink><br /><searchLink fieldCode="DE" term="%22Axioms%22">Axioms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Inference+%28Logic%29%22">Inference (Logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+proofs%22">Mathematical proofs</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink>
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  Label: Abstract
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  Data: 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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  Data: <i>Copyright of Mathematics Magazine is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=190863622
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      – Type: doi
        Value: 10.1080/0025570X.2025.2558493
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 447
    Subjects:
      – SubjectFull: Trigonometry
        Type: general
      – SubjectFull: Pythagorean theorem
        Type: general
      – SubjectFull: Logic
        Type: general
      – SubjectFull: Axioms
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      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Inference (Logic)
        Type: general
      – SubjectFull: Mathematical proofs
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      – SubjectFull: Geometry
        Type: general
      – SubjectFull: Pythagoras, ca. 570 B.C.-495 B.C.
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      – TitleFull: The Pythagorean Theorem from Trigonometry.
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              M: 12
              Text: Dec2025
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