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Abstract: These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
Relativity, Special and General represent Time as a linear dimension in a 4-diemnsional spacetime. However, one of the important ways in which time can be distinguished from space is through the exami...
School textbooks play an important role in mathematics education because of their close relation to the teaching and learning process (Valverde et al. 2002, Johansson 2003). Textbooks have a direct in...
We present a method which can produce traditional proofs for a class of geometry statements whose hypotheses can be described constructively and whose conclusions can be represented by polynomial equa...

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