- Tapa blanda: 128 páginas
- Editor: Createspace Independent Pub (1 de agosto de 2011)
- Idioma: Inglés
- ISBN-10: 1463570740
- ISBN-13: 978-1463570743
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº489.359 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
Geometry in Figures (Inglés) Tapa blanda – 1 ago 2011
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This book is a collection of theorems and problems in classical Euclidean geometry formulated in figures. It is intended for advanced high school and undergraduate students, teachers and all who like classical geometry.
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It is also very good to use this book in conjunction with a dynamic geometry program. I prefer Cinderella, but there are plenty of others (Cabri, Geometer's Sketchpad, etc.). Some of these theorems really "come alive" when you first construct them and then you move points and lines around - this is an especially fine way to discover how the theorem works (or doesn't) when you move past "standard" configurations, e.g., what happens when you move the key point from inside the circle to outside the circle - does the theorem still hold?
To see the kinds of theorems this book covers be sure to use the "Look Inside!" feature on this Amazon page. The table of contents is only two pages long, then hit "Surprise Me!" a few times to see a selection of the figures.
The book can be read with pleasure in two ways -- as a textbook by attempting to prove the propositions, or simply as a primer showing the astounding richness and beauty of triangles and the various points related to them. The book also includes results on circles, quadrilaterals and a few other polygons, and conics.
My library of geometry books is large, but whatever size it is, this book will always have a favorite place in it.
The primary intended readers are "all who like classical geometry." To that end, the author challenges the readers to comprehend the meanings of the figures with only the minimal hints. It follows the adage "a picture is worth a thousand words" to the extreme-- 665 times. Not a full sentence is used anywhere to explain any figure, except perhaps for a brief description of the notational convention in the preface. All the necessary information to understand a figure is conveyed by points, lines, segments, angles, and occasionally a result name (e.g., Pythagorean Theorem) and a formula (e.g., c^2 = a^2 + b^2). If you stumble into an "unexplained" label in a figure (e.g., the "M" in 3.1), the chances are it has already been introduced earlier (e.g., the "M" in 2.1). The reader is forced to backtrack to re-learn the definition. This book reads partly like a detective story, and partly like a zen koan. The reader has to immerse his mind into the world constructed by all these little figures. Enlightenment will come only after dissecting everything into analytical pieces and then re-assembling them into an interconnected whole. Only then, the purpose of every single clue that has been provided here and there will be revealed. Readers who know the "Proof without words" column in College Mathematics Journal are certainly already familiar with this format. But constructing and re-constructing a geometrical world 665 times in a row should be a blast to even a seasoned puzzle-solver.
If I have to pick faults on this book, I would recommend more professional proofreading to get rid of the typos and printing defects that should have been obvious given so few words and labels in the main contents. For examples, under "Ceva's Theorem" (4.9.15), segment label q should have been a, and e and f should have been swapped. Also, a directrix of a conic is supposed to be denoted by a bold line, which is unfortunately printed almost indistinguishable from an ordinary line. One may argue that the ability to overcome printing errors is the ultimate test to a student's understanding of the contents. I just think that the author and the publisher should have been more responsible, especially for a book that relies so heavily on labels. Furthermore, while there is nothing wrong for this book to demand a bit of mathematical maturity from the reader, I do wish that the "Elementary theorems" section could have included more fundamental facts. Even something as simple as identical angles between a line and a pair of parallel lines will do. Then more advanced results can be "built" upon the more elementary ones to give a sense of progression as the reader skims through the seemingly unrelated topics.
But all these complaints are really minor comparing to what the author has achieved. I applaud him for giving the readers a nearly spiritual experience by saying so much with only the most rudimentary artifacts (and keeping the price to so low with an independent publisher). This book gets five stars from me.