November 17, 2025GeometryOpen Access

Side-Angle-Side, Side-Angle-Angle, and the Non-Continuous Absolute Plane

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The framework demonstrates new axioms can replace traditional geometric axioms for absolute planes.
Important findings include the viability of angle addition and angle bisectors with defined axioms.
Analysis eliminated the Side-Angle-Side axiom while establishing an absolute plane conceptually.
The study highlights limits of traditional geometry, broadening axiomatic possibilities in mathematical theory.

Implication

Proves an absolute plane using Side-Angle-Angle and angle addition, suggesting alternative axioms in geometry.

Abstract

We prove that if we start with a non-continuous absolute plane, remove Side-Angle-Side as an axiom, and replace it with the three new axioms, Side-Angle-Angle, angle addition, and the existence of angle bisectors, then the result is also an absolute plane.

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John Donnelly (2025) studied this question.

synapsesocial.com/papers/692509e8c0ce034ddc3527ad https://doi.org/10.3390/geometry2040019

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Implication

Proves an absolute plane using Side-Angle-Angle and angle addition, suggesting alternative axioms in geometry.

Side-Angle-Side, Side-Angle-Angle, and the Non-Continuous Absolute Plane

Key Points

Implication

Abstract

Discussion

Cite This Study

Side-Angle-Side, Side-Angle-Angle, and the Non-Continuous Absolute Plane

Key Points

Implication

Abstract

Discussion

Cite This Study

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