Most Helpful Customer Reviews
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137 of 143 people found the following review helpful:
5.0 out of 5 stars
Better than the Best?, June 30, 2003
Amazon reviews let you know what teachers and students think about texts. Type in the following ISBNs to see the reviews of the second edition (ISBN 071671745X) of this text or of the author's Mathematics: A Human Endeavor (ISBN 071672426X). These comments on the third edition are based on close reading, not classroom experience. With an initial review up, I hope to see what others have to say.I taught at Reed, Wellesley, and Bard Colleges and watched the reform mathematics program develop when I was associate director of the Mathematical Association of America, in Washington, DC. Geometry is my research area. I worked in publishing as an editor for more than 20 years. I have read every word of this book and worked all of the exercises because I was its freelance editor. I am a knowledgeable, interested party. The third edition towers over the second edition, which is described by its most recent Amazon reviewer, Edward Lee, as "the best geometry text in existence, bar none" (January 25, 2003). Begin by noticing the use color throughout, then notice how color has been used to make key material in the text and diagrams stand out more clearly. Detailed comparisons will show you that every part of the book has been scrutinized and reworked, adding a host of new examples and exercises, fine-tuning the concepts and wording. Coordinates are used throughout, so that analytic methods are now another tool rather than the subject of a special chapter, late in the book. Chapter 1, An Introduction to Geometry is completely new and shows the reader how geometry has been used from the dawn of history, in the East and the West, to design cities, measure the earth's circumference, design pyramids, and figure land taxes. This last brings us to the final lesson of this chapter, "We Can't Go on Like This." Here the student discovers that the Egyptian tax assessor's formula, though plausible, does not work. Something may look sensible and even be used, but we need to be careful and check things. Not everything that is plausible is true. And so we are off to Chapter 2 on deductive reasoning, and then on to all of geometry, including solid geometry (Chapter 15) and non-Euclidean geometry (Chapter 16) --- optional in most first courses. Jacobs put all of his art into this revision. It is his best effort. Donald J. Albers begins his foreword "This is one of the great geometry books of all time. ... It is the finest example of instructional artistry I have ever encountered." Geometry is a wild and beautiful subject. Think of it as a continent you might visit and explore. The lessons in this book are station stops on your tour. At each stop, Jacobs gives you a sense of what there is to see and explore. The exercise sequences are side trips for individuals or groups. It is these jaunts that give you a real feel for the place, they build the muscle you need for further exploration and show you small wonders or glimpses of distant peaks. Albers calls these exercises "the beating heart of the book." Here is a side trip you can explore now: Take a lopsided quadrilateral and erect equilateral triangles on its sides so that their third vertices point alternatingly into and out of the quadrilateral. Connect these four new vertices in the order of the sides of the quadrilateral they are derived from. You will see that no matter what your original quadrilateral was, the new quadrilateral is of a very special sort. The exercise is straightforward, and the result is surprising. Some readers may want to understand the geometry that lies behind this observation. That goal is like the wish to scale a distant peak. Many may feel the call, but only some will set out and reach the summit. Geometric proofs, sometimes so mysterious, are our search for an answer to the question "Why?" A Teacher's Guide with solutions to all the exercises, lesson plans, reduced size images of the transparency masters, and commentaries on the subject is available. There is also a separate Test Bank. The Transparency Masters, for teachers who use an overhead projector, are available on a CDROM. In 10 years, I expect to see a crop of geometers who cut their teeth on this book. In the meantime, I expect to see many reviews from students and teachers on this site. Let this be the beginning.
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61 of 61 people found the following review helpful:
5.0 out of 5 stars
Book and guide provide a thorough geometry course, February 25, 2005
There is some criticism that this textbook has lost the rigor of the 2nd edition. Having used that for 5 years and this for two years, I would argue that the current edition demonstrates far more care toward the reluctant student and causes the math nerds to stop and think about who is interested in knowing or needing geometry.
There are good reasons for every change. One is simply that there are only 180 days in the school year. I use this text with homeschoolers. We meet 72 days per year, and we do every chapter, every problem, plus a fair bit of other supplements.
I do not understand the criticism that the book is disorganized and chaotic. In the last 8 years I have taught math from more than 10 different texts, from pre-algebra to pre-calculus. Harold Jacobs sense of organization is a relief. I suspect that since the 2nd edition has been around since 1987 and has stood the test of time, that the criticism stems from the fact that even mathematicians dislike change. (What in the world is wrong with geometry students using a protractor?) I do not believe the book is a nod to political correctness defined by the NCTM. I think it rather corrects the course taken by other publishers in their interpretation of the NCTM standards.
Proofs from the 2nd edition are available online from the Freeman publisher website, so you can add that back in, as I do. The teacher guide that accompanies the text, written by Peter Renz (above reviewer), adds several more levels of richness and complexity. Use as much or as little as you want. You now have the flexibility to use this text with those enthralled by math as well as those resistant to math.
In my first review, since withdrawn, I was critical of the tests provided by the publisher as being for weenies. They are being replaced by a set that Harold Jacobs wrote himself. I have been given the opportunity to test drive some of them, and I am satisfied that this completes a first-year presentation of geometry.
Harold Jacobs is a master mathematician, and a master teacher. He clearly loves doing both. (Confessional:) I do not own a degree in mathematics, and I my greatest growth in math has been a result from working with texts by Harold Jacobs. This is not a text generated by a publisher to fill a hole in a lineup of texts. This is a successful presentation of a difficult subject.
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42 of 43 people found the following review helpful:
4.0 out of 5 stars
A good source for high school geometry problems., August 23, 2005
The third edition of Harold Jacobs' geometry text is an engaging, clearly written, and carefully developed introduction to high school geometry that contains many fascinating problems. As is the case in his excellent algebra text Elementary Algebra, Jacobs finds intriguing ways to introduce and explain each concept. The problems, many of which Jacobs culled from the numerous sources that he cites in his footnotes, are well-chosen. They reinforce the concepts taught in the text by placing the ideas in interesting real-life contexts or puzzles, and they also introduce new ideas. What the book lacks are problems in which the reader gets to practice writing proofs. Instead, almost all the proofs in the exercises are ones in which Jacobs provides the statements and asks the reader to provide the reasons. Consequently, this text is not useful if you want to learn how to write your own proofs.
Jacobs begins the text with a discussion of inductive reasoning and its limitations. He uses this discussion to stress the importance of deductive reasoning and proof before introducing Euclid's postulates. Jacobs covers lines and angles, congruence, inequalities, parallel lines, quadrilaterals, and transformations of the plane before a midterm review. Then he covers area, similarity, right triangle trigonometry, circles, concurrence theorems, regular polygons in relation to the circle, geometric solids, and non-Euclidean geometries before concluding with a final review. Each chapter contains a summary and a chapter review in addition to the problem sets at the end of each section.
Jacobs carefully develops the material, proving each result except in the more intuitive discussions in the chapters on transformations, solids, and non-Euclidean geometries. I found the chapter on concurrence theorems particularly fascinating.
The book contains a glossary, a list of formulas, and a list of postulates and theorems, making it useful as a reference. However, concepts discussed only in the problems are not included in these lists. There are answers to a few of the problems in the back of the text, but not enough of them to be useful if you want to check your answers systematically.
I recommend this book as a supplement rather than a text because it contains many intriguing problems but does not teach the reader how to write proofs. Those students who want to learn how to write proofs should consult the rigorous text Geometry by Edwin E. Moise and Floyd L. Downs, Jr.
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