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Elementary Geometry for College Students, by Daniel C. Alexander, Geralyn M. Koeberlein
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Building on the success of its first five editions, the Sixth Edition of the market-leading text explores the important principles and real-world applications of plane, coordinate, and solid geometry. Strongly influenced by both NCTM and AMATYC standards, the text includes intuitive, inductive, and deductive experiences in its explorations. Goals of the authors for the students include a comprehensive development of the vocabulary of geometry, an intuitive and inductive approach to development of principles, and the strengthening of deductive skills that leads to both verification of geometric theories and the solution of geometry-based real world applications. Updates in this edition include the addition of 150 new problems, new applications, new Discover! activities and examples and additional material on select topics such as parabolas and a Three-Dimensional Coordinate System.
- Sales Rank: #25656 in Books
- Published on: 2014-01-01
- Original language: English
- Number of items: 1
- Dimensions: 10.90" h x 1.00" w x 8.60" l, 2.95 pounds
- Binding: Hardcover
- 624 pages
Review
Chapter 1 Line and Angle Relationships 1.1 Sets, Statements and Reasoning 1.2 Informal Geometry and Measurement 1.3 Early Definitions and Postulates 1.4 Angles and Their Relationships 1.5 Introduction to Geometric Proof 1.6 Relationships: Perpindicular Lines 1.7 The Formal Proof of a Theorem PERSPECTIVE ON HISTORY: The Development of Geometry PERSPECTIVE ON APPLICATION: Patterns Summary Review Exercises Chapter Test Chapter 2 Parallel Lines 2.1 The Parallel Postulate and Special Angles 2.2 Indirect Proof 2.3 Proving Lines Parallel 2.4 The Angles of a Triangle 2.5 Convex Polygons 2.6 Symmetry and Transformations PERSPECTIVE ON HISTORY: Sketch of Euclid PERSPECTIVE ON APPLICATION: Non-Euclidean Geometries Summary Review Exercises Chapter Test Chapter 3 Triangles 3.1 Congruent Triangles 3.2 Correspondening Parts of Congruent Triangles 3.3 Isosceles Triangles 3.4 Basic Constructions Justified 3.5 Inequalities in a Triangle PERSPECTIVE ON HISTORY: Sketch of Archimedes PERSPECTIVE ON APPLICATION: Pascal's Triangle Summary Review Exercises Chapter Test Chapter 4 Quadrilaterals 4.1 Properties of a Parallelogram 4.2 The Parallelogram and Kite 4.3 The Rectangle, Square, and Rhombus 4.4 The Trapezoid PERSPECTIVE ON HISTORY: Sketch of Thales PERSPECTIVE ON APPLICATION: Square Numbers as Sums Summary Review Exercises Chapter Test Chapter 5 Similar Triangles 5.1 Ratios, Rates and Proportions 5.2 Similar Polygons 5.3 Proving Triangles Similar 5.4 The Pythagorean Theory 5.5 Special Right Triangles 5.6 Segments Divided Proportionally PERSPECTIVE ON HISTORY: Ceva's Proof PERSPECTIVE ON APPLICATION: An Unusual Application of Similar Triangles Summary Review Exercises Chapter Test Chapter 6 Circles 6.1 Circles and Related Segments and Angles 6.2 More Angle Measures in the Circle 6.3 Line and Segment Relationships in the Circle 6.4 Some Construction and Inequalities in the Circle PERSPECTIVE ON HISTORY: Circumference of the Earth PERSPECTIVE ON APPLICATION: Sum of the Interior Angles of a Polygon Summary Review Exercises Chapter Test Chapter 7 Locus and Concurrence 7.1 Locus of Points 7.2 Concurrence of Lines 7.3 More About Regular Polygons PERSPECTIVE ON HISTORY: The Value of p (Pi) PERSPECTIVE ON APPLICATION: The Nine-Point Circle Summary Review Exercises Chapter Test Chapter 8 Areas of Polygons and Circles 8.1 Areas and Initial Postulates 8.2 Perimeter and Area of Polygons 8.3 Regular Polygons and Area 8.4 Circumference and Area of a Circle 8.5 More Area Relationships in the Circle PERSPECTIVE ON HISTORY: Sketch of Pythagoras PERSPECTIVE ON APPLICATION: Another Look at the Pythagorean Theorem Summary Review Exercises Chapter Test Chapter 9 Surfaces and Solids 9.1 Prisms, Area, and Volume 9.2 Pyramids, Area, and Volume 9.3 Cylinders and Cones 9.4 Polyhedrons and Spheres PERSPECTIVE ON HISTORY: Sketch of Rene Descartes PERSPECTIVE ON APPLICATION: Birds in Flight Summary Review Exercises Chapter Test Chapter 10 Analytical Geometry 10.1 The Rectangular Coordinate System 10.2 Graphs of Linear Equations and Slope 10.3 Preparing to do Analytic Proofs 10.4 Analytic Proofs 10.5 Equations of Lines 10.6 A Three-Dimensional Coordinate System PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox PERSPECTIVE ON APPLICATION: The Point-of-Division Formulas Summary Review Exercises Chapter Test Chapter 11 Introduction to Trigonometry 11.1 The Sine Ratio and Applications 11.2 The Cosine Ratio and Applications 11.3 The Tangent Ratio and Other Ratios 11.4 Applications with Acute Triangles PERSPECTIVE ON HISTORY: Sketch of Plato PERSPECTIVE ON APPLICATION: Radian Measure of Angles Summary Review Exercises Chapter Test Appendix A: Algebra Review Appendix B: Summaries of Constructions, Postulates, Theorems, and Corollaries Answers Glossary Index
About the Author
Daniel C. Alexander, now retired, taught mathematics at the secondary and college levels for over 40 years. His final 25 years of teaching were at Parkland College in Champaign, Illinois; before retirement, his position at Parkland College was as mathematics professor emeritus. Although Professor Alexander held undergraduate and graduate degrees from Southern Illinois University, he also completed considerable post graduate course work as well. He delivered many talks and participated in various panel discussions at mathematics conferences of IMACC, AMATYC, and ICTM. Further, he had numerous published articles in the ICTM, NCTM,and AMATYC mathematics journals.
Geralyn M. Koeberlein, now retired, taught mathematics at Mahomet-Seymour High School in Mahomet, Illinois for 34 years. She taught several levels of math, from Algebra I to AB Calculus. In the last few years of her career, Geralyn was also Chair of the Math and Science Department. After receiving her Master's Degree from the University of Illinois early in her teaching years, Geralyn continued her education by receiving over 90 hours of post graduate credit. She was a member of the the ICTM and the NCTM.
Most helpful customer reviews
4 of 5 people found the following review helpful.
there are People who hold Geometry as their Favorite and most Formative Discipline
By Leo Volont
I was a bit afraid of getting this book. I knew I needed Geometry. My Hobby since Retirement (getting fired from Age Discrimination) had been studying Mathematics. And, well, it seems that usual progression to Calculus is via Algebra and Trig. Nobody makes much of a fuss about Geometry... Except! Well, there are People who hold Geometry as their Favorite and most Formative Discipline... Proving Everything and all of that. But the word "Elementary" threw me off. For that kind of money, I did not want an Elementary Anything... I wanted the Full 10 Gage Goose Gun of Geometry (oh, note... '10 gage goose guns are virtual cannons'... even the hardcore Street Thugs stick with the smaller 12 gages). But the Reviews seems good, and, well, there was Really Nothing Much out there... that didn't get horrible reviews... but were significantly cheaper. Here is a Hint. If you are going to sit at the Table Every Day and go through a Math Text Book.... because you think that Should Be Fun... well, you need a Special Math Text Book. A Cheap and Irritatingly Limited Math Book, at a fraction of the Price, would still take you 3 or 4 Months to get through. But the cheap book would be annoying. You would have to run to your computer all the time to get cross references and explanations. The Better Book at even its far greater Price is a Bargain after all. A good Text Book is something you actually Love. a cheap Text Book is something you quickly learn to loath and despise.
I Love this Geometry Book. Well, yes, It turns out that I am more of an Algebra Guy. More than half the Axioms and Theorems seem to be So Obvious as not needing to be Stated. It reminds me of Reviews I had read about Euclid's Books on Geometry... that back in his Dark Ancient Days where nobody knew any better, He left out what were considered Essential Proofs. Now I understand that even Euclid thought some things were just too plain and obvious to need some, well, Idiotically labored 'Proof'... such as "A Line Equals Itself'.... Duh!? who would have it any other way?
So, I am Doing the book, paying attention to only what I feel are the Essential Proofs... and Thank God I am not doing this book in a college course, or it would take me a bit longer to go through the Exercises. Oh, yes, many Exercises, and answers in the back for the Odd Problems, and great Examples... a Real College Book!
Its been Great Fun!
0 of 0 people found the following review helpful.
Textbook
By Kelley
It's a textbook. Need I say more?
0 of 0 people found the following review helpful.
Five Stars
By IRENE DELGADILLO
GREAT
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