The equivalence of Side-Angle-Side and Side-Angle-Angle in the absolute plane
Copyright policy )The equivalence of Side-Angle-Side and Side-Angle-Angle in the absolute plane
The following abstract of the author summarizes, nicely, content of the paper: ``Following the approach of G. D. Birkhoff, we develop a new axiom system for a continuous absolute plane. In this new axiom system we remove Side-Angle-Side as an axiom and replace it with Side-Angle-Angle as a new axiom. We prove that the new axiom system is also a continuous absolute plane, and in particular, that Side-Angle-Side holds in the new axiom system. In addition, we give new proofs of well known results. These new proofs do not depend on Side-Angle-Side, but instead use Side-Angle-Angle.''
- University of Southern Indiana United States
Absolute planes in metric geometry, axiomatic approach, congruence, continuous absolute plane, foundations of geometry, triangles, absolute plane
Absolute planes in metric geometry, axiomatic approach, congruence, continuous absolute plane, foundations of geometry, triangles, absolute plane
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