Description: Euclidean Geometry and Its Subgeometries, Hardcover by Specht, Edward John; Jones, Harold Trainer; Calkins, Keith G.; Rhoads, Donald H., ISBN 3319237748, ISBN-13 9783319237749, Like New Used, Free shipping in the US In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties.
There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for th at . Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem.
Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilberts work, filling a gap in the existing literature.
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Book Title: Euclidean Geometry and Its Subgeometries
Number of Pages: Xix, 527 Pages
Publication Name: Euclidean Geometry and Its Subgeometries
Language: English
Publisher: Springer International Publishing A&G
Subject: History & Philosophy, Geometry / General
Publication Year: 2016
Item Weight: 331.5 Oz
Type: Textbook
Subject Area: Mathematics
Item Length: 9.3 in
Author: Keith G. Calkins, Donald H. Rhoads, Harold Trainer Jones, Edward John Specht
Item Width: 6.1 in
Format: Hardcover
