Abstract

ARTEAGA B, José Ricardo. Relationship between geometry and algebra (Erlangen program). Rev. Fac. Cienc. Tecnol. [online]. 2012, n.32, pp.143-148. ISSN 0121-3814.

The three key documents for study geometry are: 1) '' The Elements'' of Euclid, 2) the lecture by B. Riemann at Göttingen in 1854 entitled ''Über die Hypo thesen welche der Geometriezu Grun deliegen''(On the hypotheses which underlie geometry) and 3) the ''Erlangen Program'', a document written by F. Klein (1872) on his income as professor at the Faculty of Philosophy and the Senate of the Erlangen University. The latter document F. Klein introduces the concept of group as a tool to study geometry. The concept of a group of transformations of space was known at the time. The purpose of this informative paper is to show a relationship between geometry and algebra through an example, the projective plane. Erlangen program until today continues being a guideline of how to study geometry.

Keywords : Euclidean Geometry; Erlangen program; proyective plane; algebra.

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