Geometrical Kaleidoscope (Dover Books on Mathematics) by Boris Pritsker (PDF)

Description

A high school course in geometry and some curiosity and enthusiasm for the subject are the only prerequisites for tackling this original exploration into the field, long a favorite for readers whose interest in math is not only practical and educational, but also recreational. The book centers on geometric thinking—what it means, how to develop it, and how to recognize it. Readers will discover fascinating insights into many aspects of geometry and geometrical properties and theorems, including such classic examples as Archimedes’ law of the lever, Euler’s line and circle properties, Fagnano’s problem, and Napoleon’s theorem.The volume is divided into sections on individual topics such as “Medians of a Triangle,” and “Area of a Quadrilateral.” Chapters typically begin with some interesting geometrical history, some relevant theorems, and some worked examples of problems followed by problems for readers to figure out for themselves (solutions are provided at the end of the book). The result is a many-faceted exploration, rather like a kaleidoscope, focusing on the mysteries and the pleasures of geometry.

User’s Reviews

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

⭐One of the best geometry books I’ve seen in a long time. It’s a great assortment of interesting topics and problems with detailed analysis of methods and techniques for their solutions. I like the idea of making connections and links from one theorem to another, from simple topics and issues to medium and more complicated ones. The author explains not only how to solve a problem, but shows why it is done in a specific way, compares the different approaches. It helps to solve difficult problems in the most efficient way and makes solutions look nonthreatening and relevant. I also like the author’s approach in utilizing classic theorems and formulas in simplifying problem’s solutions. One such an impressive example is the application of Bretschneider’s formula for the area of a quadrilateral and its variations, the Brahmagupta’s formula being one of them. The author not just introduced these not very often encountered formulas and aquatinted readers with them, but showed how useful and efficient they are in practical matters. There are many other similar instances throughout the book.Good selection of problems for readers’ own exercises with well written solutions at the end of the book for self-review.It’s a great buy, I highly recommend it.

⭐The book justifies its name and really is a kaleidoscope of bright and flashy geometrical topics, gems, and puzzles. Proofs, problems solutions, and explanations are clear and well presented with the respective references to the applied concepts. Author displays not just interesting theoretical facts but mostly concentrates on their practical applications.One of my favorite Russian math magazines is “Kvant”, which used to have the American sister-version in “Quantum”. I consider “Quantum” the best math popular publication I’ve ever read. Unfortunately, it is not available anymore as it went bankrupt around a decade ago. It was a pleasant surprise to find the new high quality geometrical book reminding me the style and techniques displayed in the favorite magazine. The topics covered in “Geometrical Kaleidoscope” are of the “Quantum’s” material level and quality. I would highly recommend the book to help the reader build problem-solving techniques. It is a good resource for math teams; the book is also useful for teachers of regular geometry classes.To summarize – it is great geometry book at very affordable price, definitely it is worth owning in your library.

⭐I enjoy reading the book and highly recommend it. It is a great selection of interesting geometrical topics providing multiple techniques for tackling difficult problems. All the proofs, constructions, and problems solutions are well thought, organized and well presented. I like the selection of exercises for the reader’s own practice as well.The book is a source with excellent supplementary material for college professors and school teachers, math teams. At the same time it provides great pleasure for the general reader who loves mathematics as well.

⭐It’s been a joy reading this book, and not just because it reminded me of my youth when I spend countless hours solving math and geometry problems. Through college, graduate school, and years as a professional mathematician, one skill has been the most helpful to me – the ability to look at the problem from a different perspective. This book is a wonderful tutorial on how to do it. Right from the first chapter, the book shows how switching from a geometrical to a mechanical viewpoint transforms a seemingly impenetrable problem into a trivial fact. There are many examples of that throughout the book. If you want to be a professional mathematician or just enjoy the beauty of geometry, the Geometrical Kaleidoscope is a worthy buy and a worthy read.

⭐Great math book. It features material that I haven’t seen elsewhere, and it’s written with humor (extra plus for a problem solving book) and an interesting background. Some suggested techniques are un-orthodox and very efficient in simplifying solutions. Author’s search for problems-siblings, so-called family related problems reveals the keys and insight how to distinguish specific common attributes in getting elegant and efficient solutions. The concept is well demonstrated in vector algebra techniques, line and point symmetry, rotation applications. Interesting was the auxiliary elements introduction technique. It is always good to see different approaches to math topics. The author’s style is logical, well organized, and easy to follow. I would love to see more books of this author.

⭐Great book, walks you through each problem step by step and offers many opportunities to practice. A lot of exercises. One of the reason I like the book, it is because it teaches you how to identify the problem and then reach for the right solution. The book offers a lot of different geometry concepts, hence the name – Geometrical Kaleidoscope. Very useful for young, studious minds who wants to learn and grow. Very affordable price. Highly recommend it.

⭐Some people think that math is boring, but it is not, and this book proves it 100%. This is real brain teaser and source for very useful knowledge. It makes you want to continue working on your math skills and find interesting non-standard solutions to the problems.Definitely recommend to all who like math!TK

⭐Great book, helped to my son a lot, very clear and greatly explained … it was even interesting for me!!Highly recommend!

⭐Das Buch hat mir sehr gefallen. Es machte einen starken Eindruck.Das Material wird klar und deutlich präsentiert. Logische und folgerichtige Begründung für die Zusammenhänge zwischen den Problemen und Theoremen heben das Buch hervor. Besonders hat mir die Themenauswahl und die Methoden zur Aufgabenlösungen, der im Buch vorgeschlagenen Problemen gefallen. Der Autor schenkt auch den historischen Fakten viel Aufmerksamkeit, was zu einer besseren Wahrnehmung des Materials als Ganzes beiträgt. Ich möchte insbesondere einen unkonventionellen Ansatz für viele Beweise und Lösungen von Aufgaben herausgreifen.Ausgezeichnetes Buch zu einem erschwinglichen Preis. Auf jeden Fall verdient 5 Sterne.

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