Geometry

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These three volumes represent the first complete English translation of Felix Klein’s influential series “Elementarmathematik vom höheren Standpunkte aus.” This translation is significant for two reasons: it includes the previously untranslated volume III and offers a complete revised version of volumes I and II, which had omitted parts of the original. First published between 1902 and 1908, these volumes are based on lecture notes from Klein’s courses for future mathematics teachers, introducing a teacher training approach that remains relevant today. Klein encourages students to adopt a comprehensive and methodological perspective on school mathematics. Volume II exemplifies Klein’s concept of elementarisation, showcasing how various geometries, particularly those developed since the early 19th century, can be unified within a restructured geometry framework. Klein famously asserted that “Projective geometry is all geometry,” and this volume illustrates how non-Euclidean geometry fits into this unifying vision. Additionally, a separate chapter discusses the teaching of geometry, providing valuable insights into its historical context and an international comparison.