Foundations of Geometry, 3rd edition
Your access includes:
 Search, highlight, and take notes
 Easily create flashcards
 Use the app for access anywhere
 14day refund guarantee
$10.99per month
4month term, pay monthly or pay $43.96
Learn more, spend less

Study simpler and faster
Use flashcards and other study tools in your eTextbook

Listen on the go
Learn how you like with full eTextbook audio

Special partners and offers
Enjoy perks from special partners and offers for students

Find it fast
Quickly navigate your eTextbook with search

Stay organized
Access all your eTextbooks in one place
Overview
Foundations of Geometry will enrich your understanding of math and encourage a smooth transition into more advanced courses. The text assumes calculus and linear algebra as prerequisites.
Published by Pearson (July 30th 2021)  Copyright © 2022
ISBN13: 9780136845294
Subject: Geometry
Category: Introductory Geometry
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 A New View of the Foundations
1.7 Some 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 RealWorld
2.5 Theorems, Proofs, and Logic
2.6 Some Theorems from Incidence Geometry
3. A System of Axioms for Plane Geometry
3.1 The Undefined Terms and Two Fundamental Axioms
3.2 Distance and the Ruler Postulate
3.3 The Plane Separation Postulate
3.4 Angle Measure and the Protractor Postulate
3.5 The Crossbar Theorem and the Linear Pair Theorem
3.6 The SideAngleSide Postulate
3.7 The Parallel Postulates and Models for Neutral Geometry
4. Neutral Geometry
4.1 The Exterior Angle Theorem
4.2 Triangle Congruence Conditions
4.3 Three Inequalities for Triangles
4.4 The Alternate Interior Angles Theorem
4.5 The SaccheriLegendre 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 Geometry of Euclidean Triangles
6. Hyperbolic Geometry
6.1 Basic Theorems of Hyperbolic Geometry
6.2 Common Perpendiculars
6.3 The Angle of Parallelism
6.4 Limiting Parallel Rays
6.5 Asymptotic Triangles
6.6 The Classification of Parallels
6.7 The Critical Function
6.8 The Defect of a Triangle
6.9 Is the Real World Hyperbolic?
7. Area
7.1 The Neutral Area Postulate
7.2 Area in Euclidean Geometry
7.3 Dissection Theory
7.4 Proof of the Dissection Theorem in Euclidean Geometry
7.5 The Associated Saccheri Quadrilateral
7.6 Area and Defect in Hyperbolic Geometry
7.7 The Euclidean Area Postulate Reconsidered
8. Circles
8.1 Circles and Lines in Neutral Geometry
8.2 Circles and Triangles in Neutral Geometry
8.3 Circles in Euclidean Geometry
8.4 Circular Continuity
8.5 Circumference and Area of Euclidean Circles
8.6 Exploring Euclidean Circles
9. Constructions
9.1 Compass and Straightedge Constructions in Geometry
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 Isometries of the Plane
10.2 Rotations, Translations, and Glide Reflections
10.3 Classification of Euclidean Motions
10.4 Classification of Hyperbolic Motions
10.5 A Transformational Approach to the Foundations
10.6 Similarity Transformations in Euclidean Geometry
10.7 Euclidean Inversions in Circles
11. Models
11.1 The Cartesian Model for Euclidean Geometry
11.2 The Poincaré Disk Model for Hyperbolic Geometry
11.3 Other Models for Hyperbolic Geometry
11.4 Models for Elliptic Geometry
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
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 Hilbert's Axioms
B.2 Birkhoff's Axioms
B.3MacLane'sAxioms
B.4 SMSG Axioms
B.5 UCSMP Axioms
C. The Postulates Used in This Book
C.1 Criteria Used in Selecting the Postulates
C.2 Statements of the Postulates
C.3 Logical Relationships
D. The Van Hiele Model of the Development of Geometric Thought
E. Set Notation and the Real Numbers
E.1 Some Elementary Set Theory
E.2 Axioms for the Real Numbers
E.3 Properties of the Real Numbers
E.4 OnetoOne and Onto Functions
E.5 Continuous Functions
F. Hints for Selected Exercises
Bibliography
Index
Your questions answered
Pearson+ is your onestop shop, with eTextbooks and study videos designed to help students get better grades in college.
A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.
Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.
When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.
If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.
To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.
Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.
Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.
When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.
When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.
We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.