Felix Klein

This comprehensive treatment features analytic formulas, enabling precise formulation of geometric facts, and it covers geometric manifolds and transformations, concluding with a systematic discussion of fundamentals. 1939 edition. Includes 141 figures.

Geometry

Elementary Mathematics from an Advanced Standpoint

Arithmetic, Algebra, Analysis (Dover Books on Mathematics)

Albert Einstein

Heinrich Behnke

David Hilbert

Bartel Leendert Waerden

Alfred Clebsch

Carl Neumann

Adolph Mayer

Otto Blumenthal

Constantin Carathéodory

Erich Hecke

Publishes original contributions from the entire field of mathematics.

MathAnnalen

Conr. Müller

Vierter Band: Mechanik

Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen

Elementarmathematik vom höheren Standpunkte aus: Geometrie

Mathematische Annalen

Elementarmathematik vom höheren Standpunkte aus

Einleitung in die höhere geometrie ...

Vorlesung gehalten während des Sommersemesters 1891-92

Riemann'sche Flächen

These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English. The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics./div This volume II presents a paradigmatic realisation of Klein’s approach of elementarisation for teacher education. It is shown how the various geometries, elaborated particularly since the beginning of the 19th century, are revealed as becoming unified in a new restructured geometry. As Klein liked to stress: “Projective geometry is all geometry”. Non-Euclidean geometry proves to constitute a part of this unifying process. The teaching of geometry is discussed in a separate chapter, which provides moreover important information on the history of geometry teaching and an international comparison.

Volume II: Geometry

Elementary Mathematics from a Higher Standpoint

Felix Klein

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