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The Secrets of Triangles: A Mathematical Journey, by Alfred S. Posamentier, Ingmar Lehmann
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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. 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.
- Sales Rank: #666697 in eBooks
- Published on: 2012-08-28
- Released on: 2012-08-28
- Format: Kindle eBook
Review
"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
About the Author
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 The Fabulous Fibonacci Numbers (with Ingmar Lehmann).
Ingmar Lehmann is retired from the mathematics faculty at Humboldt University in Berlin. For many years he led the Berlin Mathematics Student Society for gifted secondary-school students, with which he is still closely engaged today. He is the coauthor with Alfred S. Posamentier of The Secrets of Triangles, The Glorious Golden Ratio, and three other books.
Most helpful customer reviews
38 of 38 people found the following review helpful.
A valuable contribution to the literature of mathematics
By Gerry
Alfred Posamentier, mostly with co-author Ingmar Lehmann, has written books about pi, the golden ratio, the Pythagorean theorem and Fibonacci numbers. Now these two authors have outdone themselves. The Secrets of Triangles: A Mathematical Journey (Prometheus) provides the reader with far deeper insights into concepts related to triangles than does the usual school or even college course.
But this is also a book accessible to the interested general reader requiring no more than a reasonable background in school algebra and geometry.
In addition to familiar topics like centroids, nine point circles and Euler lines, we meet pedal triangles; Gergonne, Fermat, Brocard, Miguel and Nagel points; and Ptolemy's, Menelaus's, Napoleon;s, Simpson's and Morley's theorems. There is a useful chapter on constructions and an interesting extension to fractals that includes the Sierpinski triangle and the chaos game.
The omission of projective geometry from this text I consider appropriate and my sole concern is that the authors have not included any of the nice applications of transformation geometry to the study of triangles.
The figures in this book are one of its best features. Today much of that art can be duplicated and generalized by readers through the use of computer-based programs like Geometer's Sketchpad, Cinderella and GeoGebra.
One of the best uses of this book will be by school classroom teachers of geometry but it also provides an excess of pleasure for the general reader.
0 of 0 people found the following review helpful.
Good and interesting Content, poor physical quality of the book (hard cover).
By Amazon Customer
The contents of the book are interesting and the explanations are mostly easy to follow, recommended for anybody with general interest in the properties of Triangles and geometry as such. Although I have to say that some of the print in the figures is really rather small and a larger size of book would general be more suitable for geometry texts.
A request/ to the authors: I have recently come across the book "A treatise on the Circle and the Sphere" by J.L. Coolidge (1916). A real treasure trove (and obviously a step up in level). It is however very difficult to follow the text because of a real lack of figures. Apart from the triangle, the circle and sphere are the other shapes that everybody can relate to and which have many amazing properties and uses. (Although circles are encountered in The Secrets of Triangles, they are only used in connection to the Triangle geometry.) It would be a real challenge to produce a modernized version of Coolidge's great text, now exactly 100 years old. I'd sign up in advance for a copy!
The reason for 4 stars instead of 5 stars is the physical quality of the book that I received. It looked fine upon receipt but after two (!!) days the front cover simply tore apart while I was holding the book in my hands. No overstretching or overfolding, it just started to make a funny noise and halve the front cover (hard cover!) separated from the rest. Shame on you Prometheus!
I also happen to have the authors' books on Pi and the Golden Ratio, also hard covers from Prometheus and these are fine after several months and frequent reading. Maybe I just got a bad specimen this time.. I live too far away to bother with return/replacement.
7 of 7 people found the following review helpful.
great overview
By Honest Abe
My husband loves this book and he teaches geometry to elementary school children. Highly recommend as a basic yet beautifully explained and illustrated guide to geometry.
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