SALE ON NOW! PROMOTIONS

Close Notification

Your cart does not contain any items

Euclidean Geometry and its Subgeometries by Edward John Specht at Abbey's Bookshop,
Euclidean Geometry and its Subgeometries
— —
Edward John Specht Harold Trainer Jones

Euclidean Geometry and its Subgeometries

Edward John Specht,  Harold Trainer Jones,  Keith G. Calkins ,  Donald H. Rhoads

$291.95   $233.16

Hardback

Not in-store but you can order this
How long will it take?
English
Birkhauser Verlag AG
12 January 2016
Euclidean geometry
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 the book at www.springer.com. 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 Hilbert's work, filling a gap in the existing literature.
By:   , , ,
Imprint:   Birkhauser Verlag AG
Country of Publication:   Switzerland
Edition:   1st ed. 2015
Dimensions:   Height: 235mm,  Width: 155mm,  Spine: 30mm
Weight:   9.398kg
ISBN:   9783319237749
ISBN 10:   3319237748
Pages:   527
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  A / AS level ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active
Preface.- ​Preliminaries and Incidence Geometry (I).- Affine Geometry: Incidence with Parallelism (IP).- Collineations of an Affine Plane (CAP).- Incidence and Betweenness (IB).- Pasch Geometry (PSH).- Ordering a Line in the Pasch Plane (ORD).- Collineations Preserving Betweenness (COBE).- Neutral Geometry (NEUT).- Free Segments of a Neutral Plane (FSEG).- Rotations about a Point of a Neutral Plane (ROT).- Euclidean Geometry Basics (EUC).- Isometries of a Euclidean Plane (ISM).- Dilations of a Euclidean Plane (DLN).- Every Line in a Euclidean Plane is an Ordered Field (OF).- Similarity on a Euclidean Plane (SIM).- Axial Affinities of a Euclidean Plane (AX).- Rational Points on a Line (QX).- A Line as Real Numbers (REAL); Coordinatization of a Plane (RR).- Belineations on a Euclidean/LUB Plane (AA).- Ratios of Sensed Segments (RS).- Consistency and Independence of Axioms; Other Matters Involving Models.- References.- Index.

Reviews for Euclidean Geometry and its Subgeometries

“This is the most detailed undergraduate textbook on the axiomatic foundation of Euclidean geometry ever written.” (Victor V. Pambuccian, Mathematical Reviews, July, 2016) “The authors do a commendable job of writing out proofs in detail and attempting to make the text accessible to undergraduates. … It makes a very useful reference source, and … there aren’t very many current textbooks that discuss geometry from this particular point of view. I commend this book to the attention of instructors with an interest in the foundations of geometry, and to university librarians.” (Mark Hunacek, MAA Reviews, maa.org, March, 2016)


See Also

Euclidean Geometry and its Subgeometries

Abstract Chiral Polytopes

Daniel Pellicer (Universidad Nacional...

Hardback

$259.95 

Not in-store but you can order this

ADD +
Euclidean Geometry and its Subgeometries

Metric Diophantine Approximation...

V. I. Bernik (National Academy of...

Hardback

$214.95 

Not in-store but you can order this

ADD +
Euclidean Geometry and its Subgeometries

Geometry

Plane and Fancy

David A. Singer

Hardback

$130.95  $105.07

Not in-store but you can order this

ADD +
Euclidean Geometry and its Subgeometries

Analysis of Spherical Symmetries...

Claus Müller

Hardback

$260.95  $208.95

Not in-store but you can order this

ADD +
Euclidean Geometry and its Subgeometries

An Introductory Course in Commutative...

Chatters

Paperback

$104.95 

Not in-store but you can order this

ADD +
Euclidean Geometry and its Subgeometries

Geometry and Topology of Configuration...

Edward R. Fadell

Hardback

$251.95  $201.58

Not in-store but you can order this

ADD +