Schön irrational! – Irrational schön?

Ein klassischer Unterrichtsgegenstand aus mathematikästhetischer Perspektive

Abstract

Aesthetical categories like beauty, elegance or ugliness are of special interest in mathematical practice. By presenting a geometrical and an arithmetical version of the proof of the irrationality of √2 a classical subject is shown as prime example of mathematical beauty. Based on general research in the philosophy of mathematics four sets of characteristics of mathematical beauty can be identified and further substantiated by the presented example. The resulting sketch of general didactical perspectives of mathematical aesthetics offers consequences concerning problem solving and the personal attitude towards mathematics as a science as well as the selection of special contents and methods in school.