Geometric representations of irrational algebraic numbers in Hungarian high school mathematics education

Abstract

Irrational numbers are present in our everyday life but their exact values cannot be given in a form that students easily understand. Therefore in this paper we show geometrical constructions and calculations in which non-rational numbers naturally arise and gain meaning. We look at numbers which are expressible with at maximum two roots and are present in the Hungarian curriculum. For each number we present how they appear in Hungarian textbooks, and show multiple problems and solutions in which they arise. These solutions differ in their level of mathematical complexity, from elementary geometry to higher algebra. Introducing these solutions to students, shows them, that the different areas of mathematics are interrelated. This approach may inspire students to use their mathematical knowledge not only from the area in which the problem was presented.