Euclidean and Non-Euclidean Geometries
Fourth Edition   ©2008

Euclidean and Non-Euclidean Geometries

Development and History

Marvin J. Greenberg (University of California, Santa Cruz)

  • ISBN-10: 0-7167-9948-0; ISBN-13: 978-0-7167-9948-1; Format: Cloth Text, 512 pages

Additional Coverage
This edition offers greater coverage of key events and contributors throughout history including additional information on the Pythagoreans, Plato, Euclid, Proclus, Saccheri and Bolyai.

Revised Coverage
This edition offers clearer coverage of Models, Isomorphism of Models, Axioms of Betweenness, Axioms of Congruence, Geometry without a Parallel Axiom, Measures of Angles and Segments, Angle Sum of a Triangle, Similar Triangles, and Saccheri and Lambert Quadrilaterals.

New Coverage
A new section has been added to discuss pi (Chapter 1)
New section on Straightedge and Compass, Constructions (Chapter1)
New Section on "Brief Historical Remarks" (Chapter 2)
New Section on "Consistency" (Chapter 2)
New Section on "Brief History of Real Projective Geometry" (Chapter 2)
New section on "Equidistant Curves" (Chapter 5)
New section on the "Beltrami’s Interpretation" (Chapter 7)
New section on the "Fruitfulness of Hyperbolic Geometry for Other Branches of Mathematics, Cosmology, and Art" (Chapter 8)
New Section on “Bolyai's Constructions in the Hyperbolic Plane” (Chapter 10)

More than 50% additional projects added to the text, plus new exercises included in every chapter.