College Geometry: A Problem Solving Approach with Applications

College Geometry: A Problem Solving Approach with Applications, 1/e

Gary L. Musser, Oregon State University
Lynn Trimpe

Published March, 1994 by Prentice Hall Engineering/Science/Mathematics

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Geometry-Mathematics

Summary

This book exposes readers to many practical applications of geometry, especially those involving measurement. A three-part organization divides topics into Problem Solving, Geometric Shapes, and Measurement; Formal Synthetic Euclidean Geometry; and Alternate Approaches to Plane Geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections.

Features

The authors provide a wealth of pedagogical aids, including over 1,000 exercises, problems, proofs, and applications with answers.
Begins with informal experiences and gradually moves toward more formal proofs.
Part I, Problem Solving, Geometric Shapes, and Measurement, provides readers with a fresh start in geometry through problem solving and applications in measurement.
Part II, Formal Synthetic Euclidean Geometry, contains an extensive, if somewhat informal, treatment of geometric shapes where initial postulates and basic course terminology are introduced.
Part III, Alternate Approaches to Plane Geometry, approaches problem solving/applications in geometry via coordinates and transformations.
Special topics sections at the end of the book cover Real Numbers, Logic, Non-Euclidean Geometry, and Inequalities.
A rich collection of applied problems appears throughout.
Exercises and problems, together with various combinations of proof and application problems, appear at the end of most sections.
Each section begins with an applied problem whose solution becomes accessible as the section material unfolds. (A complete solution appears at the end of the section.)
A "Geometry Around Us" feature appears just before the problem set at the end of each section.
A wealth of helpful pedagogy includes chapter-opening historical tidbits, "People In Geometry" vignettes, over 1,500 figures, display boxes highlighting postulates and theorems, paragraph and statement-reason proofs, tips for getting started, and thorough reviews, "Writing for Understanding" ideas, and practice tests in each chapter along with functional use of color throughout.
Over 1,000 exercises, problems, proofs, and applications with answers for odd exercises, problems, and applications provided in the book, and to even ones provided in the Instructor's Manual.
Most theorems are displayed in three modes: (i) written, (ii) pictorial, and (iii) symbolic.

Table of Contents
I. PROBLEM SOLVING, GEOMETRIC SHAPES, AND MEASUREMENT.

1. Problem Solving in Geometry.
2. Geometric Shapes and Measurement.
3. Perimeter, Area, and Volume.

II. FORMAL SYNTHETIC EUCLIDEAN GEOMETRY.

III. ALTERNATE APPROACHES TO PLANE GEOMETRY.