Modern View of Geometry (eBook)

Leonard M. Blumenthal (Autor)

eBook Download: EPUB

2017
208 Seiten
Dover Publications (Verlag)
978-0-486-82113-9 (ISBN)

Infos

Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.

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"e;On the required reading list for all thoughtful students who wish to see mathematics from the 'higher standpoint.' "e; — American Mathematical MonthlyElegant and original, this exposition explores the foundations and development of both Euclidean and non-Euclidean geometry, particularly the postulational geometry of planes. Emphasis is placed upon the coordination of affine and projective planes as well as the basic unity of algebra and geometry.Geared toward undergraduate and graduate students, the treatment begins with a brief but engaging sketch of the historical background of Euclidean geometry and an elementary summary of set theory and propositional calculus. Subsequent chapters explore coordinates in an affine plane, including those with Desargues and Pappus properties, and coordinatizing projective planes. The final two chapters contain detailed developments of simple sets of postulates for the Euclidean and non-Euclidean planes.

Autor

Leonard M. Blumenthal (1901–84) was Professor of Mathematics at the University of Missouri. In addition to this volume, he wrote Theory and Applications of Distance Geometry.

Inhalt

I. Historical Development of the Modern View.II. Sets and Propositions.III. Postulational Systems.IV. Coordinates in an Affine Plane.V. Coordinates in an Affine Plne with Desargues and Pappus Properties.VI. Coordinatizing Projective Planes.VII. Metric Postulates for the Euclidean  Plane.VIII. Postulates for the Non-euclidean PlaneIndex

Produkt-Details

• Erscheint lt. Verlag: 19.4.2017
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 263 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Abstract Sets • Desarguesian Planes • Desargues Properties • finite sets • hyperbolic plane • Infinite Sets • Metric Space • Non-Euclidean geometry • Pappian Planes • Pappus Properties • Postulational geometry • The Affine Plane • Veblen-Wedderburn Planes
• ISBN-10: 0-486-82113-7 / 0486821137
• ISBN-13: 978-0-486-82113-9 / 9780486821139