October 20, 2025Open Access

Theorem of three squares across three geometries

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This exploration identifies can reveal expressions in spherical and hyperbolic formats.
Key findings indicate meaningful analogies between the three different geometrical properties.
The approach utilized a conceptual framework highlighting geometric principles across dimensions.
This work suggests a unified view of geometry may enhance understanding of spatial relationships.

Implication

Exploration of the theorem shows parallels in spherical and hyperbolic geometries, suggesting broader applications.

Abstract

In Euclidean geometry, the Pythagorean theorem is presented as an equation involving three squares. This paper explores how analogous expressions may be identified in spherical and hyperbolic geometries.

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Cite This Study

Ichihara et al. (2025) studied this question.

synapsesocial.com/papers/68f6379bb481a140a36cf7b9 https://doi.org/10.48550/arxiv.2506.15416

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Implication

Exploration of the theorem shows parallels in spherical and hyperbolic geometries, suggesting broader applications.

Theorem of three squares across three geometries

Key Points

Implication

Abstract

Discussion

Cite This Study

Theorem of three squares across three geometries

Key Points

Implication

Abstract

Discussion

Cite This Study

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