Challenging Problems in Geometry

by Posamentier, Alfred S.; Salkind, Charles T.

• ISBN13: 9780486691541
• ISBN10: 0486691543
• Format: Paperback
• Copyright: 1996-05-21
• Publisher: Dover Publications

Summary

Stimulating collection of unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and many other topics. Arranged in order of difficulty. Detailed solutions.

Author Biography

Al Posamentier is currently Dean of the School of Education and Professor of Mathematics Education at Mercy College, New York. He is Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was for 40 years. He is the author and co-author of more than 55 mathematics books for teachers, secondary and elementary school students, and the general readership. Dr. Posamentier is also a frequent commentator in newspapers and journals on topics relating to education.

Alfred S. Posamentier: Math's Champion

Dr. Alfred S. Posamentier, Professor Emeritus of Mathematics Education at New York's City College and, from 1999 to 2009, the Dean of City College's School of Education, has long been a tireless advocate for the importance of mathematics in education. He is the author or co-author of more than 40 mathematics books for teachers, students, and general readers including The Fascinating Fibonacci Numbers (Prometheus, 2007) and Mathematical Amazements and Surprises: Fascinating Figures and Noteworthy Numbers (Prometheus, 2009)

His incisive views on aspects of mathematics education may often be encountered in the Letters columns and on the op-ed pages of The New York Times and other newspapers and periodicals. For Dover he provided, with co-author Charles T. Salkind, something very educational and also fun, two long-lived books of problems: Challenging Problems in Geometry and Challenging Problems in Algebra, both on the Dover list since 1996.

Why solve problems? Here's an excerpt from a letter Dr. Posamentier sent to The New York Times following an article about Martin Gardner’s career in 2009:

"Teachers shouldn't think that textbook exercises provide problem-solving experiences — that's just drill. Genuine problem solving is what Mr. Gardner has been espousing. Genuine problem solving provides a stronger command of mathematics and exhibits its power and beauty. Something sorely lacking in our society."

Table of Contents

Introduction
Preparing to Solve a Problem
SECTION I A New Twist on Familiar Topics
1. Congruence and Parallelism
2. Triangles in Proportion
3. The Pythagorean Theorem
4. Circles Revisited
5. Area Relationships
SECTION II Further Investigations
6. A Geometric Potpourri
7. Ptolemy and the Cyclic Quadrilateral
8. Menelaus and Ceva: Collinearity and Concurrency
9. The Simson Line
10. The Theorem of Stewart
Hints
"Appendix I: Selected Definitions, Postulates, and Theorems"
Appendix II: Selected Formulas