Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point - no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating.
The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.
Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry.
Alfred S. Posamentier
About Alfred S. Posamentier
Alfred S. Posamentier is dean of the School of Education and professor of mathematics education at Mercy College in Dobbs Ferry, New York. Previously, he had the same positions at the City College of the City University of New York for forty years. He has published over fifty-five books in the area of mathematics and mathematics education, including, most recently, Numbers: Their Tales, Types, and Treasures (with Bernd Thaller) and Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments (with Ingmar Lehmann).
“[Y]et another fine collection of mathematical insights, intriguing relationships, and surprising results focused on the triangle…. [A]n incredibly rich compendium of results that will lead the reader to consistently react in surprise about and appreciation of the richness and unexpected depth of triangular relationships…. [T]he illustrations are excellent. Highly Recommended.”
-Choice: Current Reviews for Academic Libraries
"A fascinating look at the geometrical. While this may not be a 'read on the beach' novel, it would prove to be an indispensible classroom companion for those wading into the fascinating subject for the first time."
- Astro Guyz
"[A] joyously nerdy celebration of the history of geometry and trigonometry, exploring the dozens and dozens of curiosities sitting just beneath the surface of a seemingly ordinary triangle…. By no means a casual read, The Secrets of Triangles is nonetheless worth a look, if only to blow your mind."
- Sacramento/San Francisco Book Review
"Any science or math holding, especially those catering to lay readers, will find this a winner!"
- Midwest Book Review
The Secrets of Triangles by Alfred S. Posamentier and Ingmar Lehmann