Foundations of Geometry

ISBN-10: 0136020585

ISBN-13: 9780136020585

Edition: 2nd 2012 (Revised)

Authors: Gerard Venema

List price: $117.80
eBook available
30 day, 100% satisfaction guarantee

If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost.

Learn more about our returns policy


Foundations of Geometry, Second Editionimplements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers ;and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Editionstreamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra.
eBooks Starting from $23.99
Rent eBooks
Buy eBooks
what's this?
Rush Rewards U
Members Receive:
You have reached 400 XP and carrot coins. That is the daily max!
Study Briefs

Limited time offer: Get the first one free! (?)

All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.

Add to cart
Study Briefs
Periodic Table Online content $4.95 $1.99
Add to cart
Study Briefs
Calculus 1 Online content $4.95 $1.99
Add to cart
Study Briefs
Algebra Online content $4.95 $1.99
Customers also bought

Book details

List price: $117.80
Edition: 2nd
Copyright year: 2012
Publisher: Addison Wesley
Publication date: 7/6/2011
Binding: Paperback
Pages: 408
Size: 7.75" wide x 9.50" long x 0.50" tall
Weight: 1.892
Language: English

Prologue: Euclid's Elements
Geometry before Euclid
The logical structure of Euclid's Elements
The historical significance of Euclid's Elements
A look at Book I of the Elements
A critique of Euclid's Elements
Final observations about the Elements
Axiomatic Systems and Incidence Geometry
The structure of an axiomatic system
An example: Incidence geometry
The parallel postulates in incidence geometry
Axiomatic systems and the real world
Theorems, proofs, and logic
Some theorems from incidence geometry
Axioms for Plane Geometry
The undefined terms and two fundamental axioms
Distance and the Ruler Postulate
Plane separation
Angle measure and the Protractor Postulate
The Crossbar Theorem and the Linear Pair Theorem
The Side-Angle-Side Postulate
The parallel postulates and models
Neutral Geometry
The Exterior Angle Theorem and perpendiculars
Triangle congruence conditions
Three inequalities for triangles
The Alternate Interior Angles Theorem
The Saccheri-Legendre Theorem
Statements equivalent to the Euclidean Parallel Postulate
Rectangles and defect
The Universal Hyperbolic Theorem
Euclidean Geometry
Basic theorems of Euclidean geometry
The Parallel Projection Theorem
Similar triangles
The Pythagorean Theorem
Exploring the Euclidean geometry of the triangle
Hyperbolic Geometry
The discovery of hyperbolic geometry
Basic theorems of hyperbolic geometry
Common perpendiculars
Limiting parallel rays and asymptotically parallel lines
Properties of the critical function
The defect of a triangle
Is the real world hyperbolic?
The Neutral Area Postulate
Area in Euclidean geometry
Dissection theory in neutral geometry
Dissection theory in Euclidean geometry
Area and defect in hyperbolic geometry
Basic definitions
Circles and lines
Circles and triangles
Circles in Euclidean geometry
Circular continuity
Circumference and area of Euclidean circles
Exploring Euclidean circles
Compass and straightedge constructions
Neutral constructions
Euclidean constructions
Construction of regular polygons
Area constructions
Three impossible constructions
The transformational perspective
Properties of isometries
Rotations, translations, and glide reflections
Classification of Euclidean motions
Classification of hyperbolic motions
Similarity transformations in Euclidean geometry
A transformational approach to the foundations
Euclidean inversions in circles
The significance of models for hyperbolic geometry
The Cartesian model for Euclidean geometry
The Poincar� disk model for hyperbolic geometry
Other models for hyperbolic geometry
Models for elliptic geometry
Regular Tessellations
Polygonal Models and the Geometry of Space
Curved surfaces
Approximate models for the hyperbolic plane
Geometric surfaces
The geometry of the universe
Further study
Euclid's Book I
Common Notions
Systems of Axioms for Geometry
Filling in Euclid's gaps
Hilbert's axioms
Birkhoff's axioms
MacLane's axioms
SMSG axioms
UCSMP axioms
The Postulates Used in this Book
The undefined terms
Neutral postulates
Parallel postulates
Area postulates
The reflection postulate
Logical relationships
Set Notation and the Real Numbers
Some elementary set theory
Properties of the real numbers
The van Hiele Model
Hints for Selected Exercises
Free shipping on orders over $35*

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

Learn more about the TextbookRush Marketplace.