Geometry in the Euclidean Plane: Algebraization, Axiomatization and Interfaces with School Mathematics - Max Hoffmann

In this textbook, the authors present an axiomatic approach to plane geometry that offers a structural alternative to, for example, Hilbert's axiom system or other commonly used approaches, along with several pedagogical advantages. Based on metric spaces, this approach is developed in a thoroughly motivated and pedagogically effective way. Particular attention is paid to integrating the mathematical training of future teachers with the school curriculum. In addition to the axiomatic perspective, the book also shows how plane geometry can be approached using tools from linear algebra, thereby creating a bridge to analytic geometry at the upper secondary level.

As a further link between school mathematics and axiomatic geometry, the topics of congruence and symmetry are explored in greater depth. In doing so, the authors make explicit the key connections between isometries, congruence, and symmetry, and embed them in contexts typical of school mathematics.

This book is a translation of the original German edition Ebene euklidische Geometrie, 1st edition, by Max Hoffmann, Joachim Hilgert, and Tobias Weich, published by Springer-Verlag GmbH, Germany, in 2024. The translation was produced with the support of an AI-based tool and subsequently carefully reviewed and revised for accuracy of content, clarity of language, and consistency of references.