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Challenging Problems in Geometry (Repost): Alfred S. Posamentier, Charles T. Salkind

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.

Review:

Posamentiers' book is a little bit unbalanced. It contains around 200 problems with solutions. The easy problems are just what you would expect in the exercises sections of an introduction to Euclidean geometry like Kiselev's Geometry / Book I. Planimetry. The the harder problems you will find as classical theorems and examples in more advanced texts like Altshiller Courts' College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics). A more balanced text would have contained more intermediate problems and the harder ones would have been more "original".

The methods used are purely synthetic, no analytic geometry. The book is aimed at an advanced high school level audience. Prerequisite is the stuff you find in a book like kiselev I mentioned above.

If you need a book to train your geometric problem solving abilities I think that Altshiller Courts' book is a better choice although there are no solutions to the exercises in that book. But what use are the solutions? Problems should be solved and not looked up!

For many problems, especially the hard ones, several solutions are provided. To me this is what makes the book attractive.

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Rating:
2.5 out of 5 by Book123