DEDUCTIBILITY AND ANALOGY IN THE STUDY OF SOME TRIANGLES (I) - general results
DEDUCTIBILITY AND ANALOGY IN THE STUDY OF SOME TRIANGLES (I) - general results

Author(s): Teodor Dumitru Vălcan
Subject(s): Education, School education, Higher Education
Published by: Editura Eikon
Keywords: deductibility; analogy; triangle; cevian; circle; geometric - trigonometric; identity; inequality;
Summary/Abstract: In this paper we propose, using the relations of logical deductibility and the analogy method, to present some interesting results in the Geometry of the triangle. Thus, we consider a triangle ABC and three cevians, which intersect at point K and intersect the sides of the given triangle at points A, B and C, and the circle circumscribed to the triangle ABC in A1, B1 and C1. Then we will call the triangle ABC the triangle K-cevian attached to the triangle ABC and the point K, and the triangle A1B1C1 we will call the triangle K-circumcevian attached to the triangle ABC and the point K. Using the usual mathematical knowledge, valid in any triangle, we can obtain a series of very uninteresting geometric or trigonometric identities and inequalities, some of them very difficult to prove, synthetically. On the other hand, these new geometric or trigonometric relations introduced in certain derivable or only integrable functions, can lead to a series of identities or inequalities differential or integral, particularly interesting. The paper is exclusively for Didactics of Mathematics and is addressed, equally, to children, students and teachers eager to perform in this field of Mathematics or in Mathematics in general.

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