The equivalence of side-angle-side and side-angle-angle in the absolute plane (Q601729)
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scientific article; zbMATH DE number 5808433
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The equivalence of side-angle-side and side-angle-angle in the absolute plane |
scientific article; zbMATH DE number 5808433 |
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The equivalence of side-angle-side and side-angle-angle in the absolute plane (English)
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29 October 2010
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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.''
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absolute plane
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continuous absolute plane
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foundations of geometry
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axiomatic approach
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congruence
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triangles
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