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From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

AIP Conference Proceedings, 2017
In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems – considered as tasks inviting the use of problem solving and reasoning ...
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Computer Algebra Systems and Dynamic Geometry for Mathematical Thinking

2021
Marcelo de Carvalho-Borba   +4 more
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Algebra, Geometry and Mathematical Physics

2011
We discuss the consequences of the Poincaré duality, versus AS-Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poincaré duality property implies the existence of twisted potentials which characterize the corresponding algebras while in the case of quadratic linear Koszul algebras, the ...
Makhlouf, Abdenacer   +3 more
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The principle of topological economy in algebraic geometry

2005
This part of the lecture is not related to the first part, so it can be understood independently. We start with an example. Example 1. In ℂP n , consider two algebraic varieties X and Y of complementary dimensions. In general position, they intersect in finitely many points. Let [ X ] and [ Y ] be the homology classes realized by the varieties
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Studies in Algebraic Geometry (M.A.A. Studies in Mathematics, Vol. 20).

The American Mathematical Monthly, 1983
Kenneth R. Mount, A. Seidenberg
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Categories in Algebra, Geometry and Mathematical Physics

2007
Michael Batanin   +4 more
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