### A proposition from algebra – how would Pythagoras phrase it?

#### Abstract

The paper presents three methods from different branches of mathematics for the solution of the same task. Originally this is an algebraic problem, and therefore the first solution presented is the one utilizing the algebraic method. Subsequently, the question was “translated” into a geometric language, with an “interesting” presentation of the problem – “how would Pythagoras phrase and solve the problem?” Later, we bring the geometric and trigonometric solution deal with a special triangle whose angles are a, 2a, 4a – a geometric progression. Solution of the same problem using different methods contributes to the enrichment of the “mathematical toolbox” of the student and exemplifies to the student the beauty of mathematics as a field composed of intertwining branches.

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