3 papers
math.GM2026
The Fourth Geometry II: From Angle Axioms to Metric Foundations
Masanori Nakazato
This paper is a sequel to arXiv:2511.01024 (Base 1), where an axiomatic framework for angles and the foundations of difference-angle geometry were introduced. In difference-angle g…
math.MG2026
Affine Angles via Area Cross Ratio and Isoptic Hyperbolas
Masanori Nakazato
Affine geometry is usually regarded as a framework in which metric notions such as distance and angle are absent. However, just as projective geometry produces various metric geome…
math.MG2025
The Fourth Geometry I: Difference--Angle Geometry Beyond Euclid, Hyperbolic, and Elliptic
Masanori Nakazato
In this work, we introduce a new geometry based on the difference angle, an angle defined as the difference of slopes of two lines, together with an axiomatic system for angles. Th…