Pythagoras is just a special case

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A simple theorem developed by one of Napoleon's generals encompasses the Pythagorean Theorem as a special case. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Sean McKee

doi:10.1080/10724117.2026.2676779

August 25, 2026Math HorizonsOpen Access

Pythagoras is just a special case

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Key Points

Examine a broader geometric theorem formulated by a Napoleonic general that includes the Pythagorean theorem as a specific case.
Conducted a geometric derivation and historical analysis of triangle side and angle properties.
Evaluated the formulation across both orthogonal and non-orthogonal geometric configurations.
Demonstrated that the traditional Pythagorean equation represents a constrained subset of a generalized triangle theorem.
Established a unified geometric framework that accounts for side-length relationships across arbitrary triangle angles.

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Implication

Mathematical exposition reveals a generalized geometric theorem encompassing the Pythagorean theorem, indicating broader structural rules across general triangles.

Abstract

It was a great surprise to me to discover through a golfing pal from St. Andrews that one of Napoleon’s generals was responsible for a simple theorem that has the Pythagorean Theorem as a special c...

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Cite This Study

Sean McKee (2026) studied this question.

synapsesocial.com/papers/6a9145ead15324a1df3a9225 https://doi.org/10.1080/10724117.2026.2676779

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Pythagoras is just a special case

Key Points

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Implication

Abstract

Discussion

Cite This Study

Pythagoras is just a special case

Key Points

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Implication

Abstract

Discussion

Cite This Study

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