Theorem of three squares across three geometries | Synapse
October 20, 2025Open Access
Theorem of three squares across three geometries
Key Points
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.
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.