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.

Introduces and represents a novel axiomatic approach to plane geometry Places a special focus on the integration and link of teacher training in mathematics and the school curriculum Tested and tried out in many lectures

Autorentext

Dr. Max Hoffmann is a trained teacher of mathematics and computer science. He currently teaches and researches mathematics and its didactics at Paderborn University (Germany), and is active in mathematics outreach.

Prof. Dr. Joachim Hilgert is emeritus professor at Paderborn University (Germany) and previously led the research group on Lie theory.

Prof. Dr. Tobias Weich carries out research and teaches at Paderborn University (Germany), where he leads a research group on spectral analysis.

Inhalt

Part I: Plane Geometry through the Lens of Linear Algebra.- 1 Congruence, Reflection and SSS.- 2 Classification of Eucledian Isometries of R^2.- 3 Congruence.- Part II: Axiomatic Plane Geometry.- 4 Elementary Geometric Concepts in Metric Spaces.- 5 Plane Neutral Geometry in Metric Spaces.- 6 Deep Dives into Neutral Planes.- 7 Symmetry.- Part III: The Parallel Postulate: Geometry in the Euclidean Plane.- 8 Parallelism in the Neutral Plane.- 9 Euclidean Planes.- 10 Deepening on Euclidean Planes.