CART

(0) items

Foundations of Geometry,9780136020585
This item qualifies for
FREE SHIPPING!

FREE SHIPPING OVER $59!

Your order must be $59 or more, you must select US Postal Service Shipping as your shipping preference, and the "Group my items into as few shipments as possible" option when you place your order.

Bulk sales, PO's, Marketplace Items, eBooks, Apparel, and DVDs not included.

Foundations of Geometry

by
Edition:
2nd
ISBN13:

9780136020585

ISBN10:
0136020585
Format:
Paperback
Pub. Date:
7/6/2011
Publisher(s):
Pearson
List Price: $103.00

Rent Textbook

(Recommended)
 
Term
Due
Price
$41.20

Buy New Textbook

Currently Available, Usually Ships in 24-48 Hours
$100.43

eTextbook

Downloadable Offline Access
 
Duration
Price
$45.94

Used Textbook

We're Sorry
Sold Out

More New and Used
from Private Sellers
Starting at $75.80

Questions About This Book?

Why should I rent this book?
Renting is easy, fast, and cheap! Renting from eCampus.com can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.
How do rental returns work?
Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!
What version or edition is this?
This is the 2nd edition with a publication date of 7/6/2011.
What is included with this book?
  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.

Related Products


  • Foundations of Geometry
    Foundations of Geometry




Summary

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.

Table of Contents

1. Prologue: Euclid’s Elements

1.1 Geometry before Euclid

1.2 The logical structure of Euclid’s Elements

1.3 The historical significance of Euclid’s Elements

1.4 A look at Book I of the Elements

1.5 A critique of Euclid’s Elements

1.6 Final observations about the Elements

 

2. Axiomatic Systems and Incidence Geometry

2.1 The structure of an axiomatic system

2.2 An example: Incidence geometry

2.3 The parallel postulates in incidence geometry

2.4 Axiomatic systems and the real world

2.5 Theorems, proofs, and logic

2.6 Some theorems from incidence geometry

 

3. Axioms for Plane Geometry

3.1 The undefined terms and two fundamental axioms

3.2 Distance and the Ruler Postulate

3.3 Plane separation

3.4 Angle measure and the Protractor Postulate

3.5 The Crossbar Theorem and the Linear Pair Theorem

3.6 The Side-Angle-Side Postulate

3.7 The parallel postulates and models

 

4. Neutral Geometry

4.1 The Exterior Angle Theorem and perpendiculars

4.2 Triangle congruence conditions

4.3 Three inequalities for triangles

4.4 The Alternate Interior Angles Theorem

4.5 The Saccheri-Legendre Theorem

4.6 Quadrilaterals

4.7 Statements equivalent to the Euclidean Parallel Postulate

4.8 Rectangles and defect

4.9 The Universal Hyperbolic Theorem

 

5. Euclidean Geometry

5.1 Basic theorems of Euclidean geometry

5.2 The Parallel Projection Theorem

5.3 Similar triangles

5.4 The Pythagorean Theorem

5.5 Trigonometry

5.6 Exploring the Euclidean geometry of the triangle

 

6. Hyperbolic Geometry

6.1 The discovery of hyperbolic geometry

6.2 Basic theorems of hyperbolic geometry

6.3 Common perpendiculars

6.4 Limiting parallel rays and asymptotically parallel lines

6.5 Properties of the critical function

6.6 The defect of a triangle

6.7 Is the real world hyperbolic?

 

7. Area

7.1 The Neutral Area Postulate

7.2 Area in Euclidean geometry

7.3 Dissection theory in neutral geometry

7.4 Dissection theory in Euclidean geometry

7.5 Area and defect in hyperbolic geometry

 

8. Circles

8.1 Basic definitions

8.2 Circles and lines

8.3 Circles and triangles

8.4 Circles in Euclidean geometry

8.5 Circular continuity

8.6 Circumference and area of Euclidean circles

8.7 Exploring Euclidean circles

 

9. Constructions

9.1 Compass and straightedge constructions

9.2 Neutral constructions

9.3 Euclidean constructions

9.4 Construction of regular polygons

9.5 Area constructions

9.6 Three impossible constructions

 

10. Transformations

10.1 The transformational perspective

10.2 Properties of isometries

10.3 Rotations, translations, and glide reflections

10.4 Classification of Euclidean motions

10.5 Classification of hyperbolic motions

10.6 Similarity transformations in Euclidean geometry

10.7 A transformational approach to the foundations

10.8 Euclidean inversions in circles

 

11. Models

11.1 The significance of models for hyperbolic geometry

11.2 The Cartesian model for Euclidean geometry

11.3 The Poincaré disk model for hyperbolic geometry

11.4 Other models for hyperbolic geometry

11.5 Models for elliptic geometry

11.6 Regular Tessellations

 

12. Polygonal Models and the Geometry of Space

12.1 Curved surfaces

12.2 Approximate models for the hyperbolic plane

12.3 Geometric surfaces

12.4 The geometry of the universe

12.5 Conclusion

12.6 Further study

12.7 Templates

 

APPENDICES

A. Euclid’s Book I

A.1 Definitions

A.2 Postulates

A.3 Common Notions

A.4 Propositions

 

B. Systems of Axioms for Geometry

B.1 Filling in Euclid’s gaps

B.2 Hilbert’s axioms

B.3 Birkhoff’s axioms

B.4 MacLane’s axioms

B.5 SMSG axioms

B.6 UCSMP axioms

 

C. The Postulates Used in this Book

C.1 The undefined terms

C.2 Neutral postulates

C.3 Parallel postulates

C.4 Area postulates

C.5 The reflection postulate

C.6 Logical relationships

 

D. Set Notation and the Real Numbers

D.1 Some elementary set theory

D.2 Properties of the real numbers

D.3 Functions

 

E. The van Hiele Model

 

F. Hints for Selected Exercises

 

Bibliography

Index


Please wait while the item is added to your cart...