Famous Problems of Geometry and How to Solve Them (Dover Books on Mathematics)

Although not reasonable for most high school students, this book does bring to light the background of modern geometry through its treatment of impossible and hard to solve problems.Excellent background reading for a teacher!

The principles of geometry are both elegant and timeless. One cannot help but understand why the Greeks considered it a pinnacle of intellectual achievement. This book sets down several of the classic problems, explaining them in such a clear way that it is easy to forget that it sometimes took centuries of work before the problem was resolved. Of course, those who first toiled on the problems did not have some of the additional machinery that we so take for granted today. The problems covered are trisecting an angle, squaring the circle, constructing regular polygons and constructing a cube whose volume is twice that of a given cube. The background needed to understand the problems and solutions is nothing more than a solid grounding in basic algebra and trigonometry. Calculus is mentioned, but not used. Problem sets are included in all chapters and solutions to all are in the back of the book. They are well-posed, solidly reinforcing the points made in the text. This is a book that covers several thousand years of progress in geometry in a little over one hundred pages. It is done well and it can be used as a supplement in any course in geometry, from high school to college.

Bold has a gem of a book here. It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years.The title describes the book perfectly. These really are "Famous Problems from Geometry" and he does indeed explain how to solve them.The book has four major sections/chapters. He discusses in detail the three problems from antiquity (one section each): squaring a circle, doubling a cube, and trisecting an angle. Furthermore, he spends significant time with constructions of regular polygons (the fourth section) - which ones can be constructed and why. He also discusses which ones cannot be constructed and why.The reader will be expected to understand concepts from Modern Algebra, particularly the concept of a Field. While Bold does spend time explaining what a Field is, his definition is quick and is assumed to be more of a refresher for someone who has already learned about them. Bold also has a section on Complex Numbers where he derives one of the formulas used later in the book. Again - this section is assumed to be a refresher on Complex Numbers. High School Geometry or Algebra students would have significant trouble understanding his explanations and proofs.Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem being studied. The problems are good. As a third year college student majoring in mathematics, I found the explanations/solutions to be sometimes hard to follow. He assumes a great deal about the reader's level of proficiency in math and in geometry. As a result, he liberally skips steps in proofs that are assumed to be "obvious." If you're expecting simple proofs to these problems, you're not going to find them. If they were simple, they wouldn't have taken 2000 years to solve. But they are explained clearly here in terms that anyone with a college degree should be able to understand. Overall, a superb book. A must have for anyone interested in the famous problems from the history of Geometry.