The Secrets of Triangles: A Mathematical Journey by Alfred S. Posamentier (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐This book should be in every university library. It deals with the simplest of mathematical objects, namely the triangles. Despite studying mathematics for 50 years or so, I learned something new by page 21. The book is not at high school level, nor is it too technical. For someone like me who loves mathematics, it’s enjoyable to read. It’s well written; my hard back copy is well bound and nicely printed, with large font – which is great for someone who is as old as I am; excellent clear diagrams. Congratulations to the authors and the publisher. I’d give it 3/3.

⭐Dr. Posamentier is a man who loves math. There is no end to his explication of it. The facts pour forth for the interested student of mathematics. The good professor writes for the interested mathematics student. The texts of Dr. Posamentier are always written to be read and understood. Teachers need him for the continual discourse, the whys and the wherefores of mathematics; to be more interesting teachers, read Dr. Posamentiers books of which there are many.

⭐I’m still reading the book and enjoying it immensely. Great book, brings back memories of my high school geometry, but starts out where that left off and discusses many new and interesting theorems that relate to triangles.

⭐The book is more for mathematicians who enjoy learning about complicated details about triangles.

⭐This is a brilliant book. It outshines others by the clarity and topicality of its writing, and especially the diagrams, which are meticulous and relevant to the discussion. Helpful bibliography as well.

⭐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.

⭐I would have loved to have had this book when I was still in school . It would have been a good challenge!

⭐This is the book which everyone should Study if he/she is from engineering, mathematics, Physics etc backgroundI have read many books but this was one of the best book in geometry

⭐Must read book..if one loves Olympiad geometry,just go with this book.one will find new questions & innovation concepts

⭐Curiosity is the point, I didn’t expect that much, If you want to dig and have it all, this is a book about triangle you have to read…or study in fact

⭐El contenido del libro es bueno, pero me llego con defectos. Varias paginas sobrasalian, y no se les ocurrio otra cosa que doblarlas hacia dentro para disimularlo. Asi que tengo las paginas dobladas y he tenido que cortar lo que sobrasalia. Llevo muchos años comprando en amazon y ya me han llegado varios libros defectuosos. No volvere a comprar mas si siguen asi.

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