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Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

Betweenness plane geometry and its relationship with convex, linear, and projective plane geometries; 233-251

Full article in PDF format | 10.3176/phys.math.2007.3.01

Author
√úlo Lumiste

Abstract

In a previous paper the author recapitulated betweenness geometry, developed in 1904–64 by O. Veblen, J. Sarv, J. Hashimoto, and the author. The relationship of this geometry with join geometry (by W. Prenowitz) was investigated. Now this relationship will be extended to convex and linear geometry. The achievements of the well-developed projective plane geometry are used to enrich betweenness plane geometry with coordinates, ternary operation, algebraic extension, Lenz–Barlotti classification, translation, and Moufang type. The final statement is that every Moufang-type betweenness plane is Desarguesian.


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