Geometric Constructions (Undergraduate Texts in Mathematics). Dieser Artikel ist nicht verfügbar.Geometric Constructions (Undergraduate Texts in Mathematics)

Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations. As specified by Plato, the game is played with a ruler and compass. The first chapter is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never seen. The second chapter formalizes Plato's game and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, using only a compass, using toothpicks, using a ruler and dividers, using a marked rule, using a tomahawk, and ending with a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics. He hopes that readers will learn a little geometry and a little algebra while enjoying the effort. This is as much an algebra book as it is a geometry book. Since all the algebra and all the geometry that are needed is developed within the text, very little mathematical background is required to read this book. This text has been class tested for several semesters with a master's level class for secondary teachers.

From the reviews: "Much of Martin's charming and accessible text could be used with bright school students. ... The book is rounded off by a section called 'The back of the book' which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended." (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004) "This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! ... If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book." (W. Moser, Mathematical Reviews, Issue 2002 g) "This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas ... . A lot of 'easy' applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems." (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001) "The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. ... The author uses non-worked discovery-type examples to lead into observations about the material. ... There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains a'Back of the Book' section rather than an Answers section." (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)