Product Description
These absorbing essays by a distinguished mathematician provide a compelling demonstration of the charms of mathematics. Stimulating and thought-provoking, this collection is sure to interest students, mathematicians and any math buff with its lucid treatment of geometry and the crucial role geometry plays in a wide range of mathematical applications.
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Customer Reviews (1)

A splendid legacy of 20th century mathematics
This book collects 12 articles by Coxeter, already published in various mathematics technical journal but would be quite tedious to collect for one's pleasure. Each explains fascinating connections between exceptional discrete groups, polyhedra, graphs, sphere packings, projective spaces. All carry the particular favour of HSM Coxeter mathematics with his love of polyhedra and of their geometry. Starting points are often elementary but conclusions and connections are worthwile aven for today mathematics. I recommend it for graduates in mathematics, especially those interested in group theory, discrete/finite geometry, non-euclidean geometry as a very inspiring book giving a sense of unity in those parts of mathematics. ... Read more

Product Description
Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed. ... Read more

Customer Reviews (8)

Fun and hard
If you pass through the Geometry, the book is fun and light.If you study the Geometry again, the book is honest and hard.

An excellent book on elementary Euclidean geometry
This book, which has been available for quite some time, is still a great place to learn about topics in Euclidean geometry which you probably will not cover in a typical middle or high school math class.The level is completely elementary, meaning that anyone with knowledge of pre-calculus will be able to read this book (if they are sufficiently dedicated).The quality of the exposition is superb, and the mathematical content is interesting and varied.

While people who are interested in recreational mathematics will definitely find this book interesting, perhaps the audience for which this book will be most profitable are middle and high school students preparing for mathematics competitions.It is a considerable advantage, especially for the more difficult competitions, to know the techniques and theorems covered in this book.

If you're interested in learning geometry you may not have covered in school, or are preparing for math competitions, buy this book.

The best text on Elementary Geometry in English
This is one of my three favorite texts in Elementary Geometry, and the only one written in English. It's a multipurpose text. You will probably won't cover these material at school, but if you are interested on math contests, or more serious geometry study, this is also a good text to follow to learn, or if you, like me, learned most of this material overa decade ago, but need a good text as a reference, this text is a great to do so. Dearly recommended.

Great book
This is a wonderful book if you want to gain a real understanding of what geometry can be (if you like this book you should buy the biography of Coxeter: "King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry" - it is one of the best biographies of a mathematician on the market and shows that Coxeter was a genius and a hoot).However, if you know a significant amount of geometry, then try "Introduction to Geometry, 2nd Edition" as that is the more complete (and (very) much more rigorous) text.Also, if you like this book, then buy "Visual Complex Analysis".

PS.My son is using this book in his high school geometry course (at my insistence) rather than the 'text' he was issued.He is now assisting the teacher with the proofs and problems.

Incredibly helpful
I just worked through this book & I have to say that it's probably the best for "what's next" after high school geometry. It's got a chapter on each of the following things: triangles (with Ceva's & Steiner-Lehmus' theorems, orthic triangles & Euler lines, etc), circles (like power of a point, etc), collinearity & concurrence, transformations (Yaglom's series of 3 books are better for these though but this is a good introduction), and an intro to inversive geometry and projective geometry. One section that blew my mind is the one about the "3-jugs" problem where you've got a jug that holds 8L, one that holds 5L & one the holds 3L and the goal is to get 4L in each of two jugs. Maybe you've heard of it...? This book gives a general method for solving problems like that using reflections. I liked how each section is very short and typically has just 2-3 theorems, so the book is split into manageable pieces. Maybe it's just a psychological thing, but I like that. Depending on the section, there are 3-10 problems at the end of each section; like any book there are easy ones with fairly obvious solutions and there are hard ounes that take a lot of thought. I think the hard ones might have come from olympiads because Sam Greitzer was a USAMO coach at some point. It doesn't matter though, this book gives you a lot of tools you can use to deal with olympiad-level problems. A couple good ones to work on after this book would be Johnson's "Advanced Euclidean Geometry" and Court's "College Geometry", both out of print unfortunately but maybe a nearby library wold have them? ... Read more

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From the reviews:

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Product Description
Differential geometry is a major field of mathematics that uses tools from calculus, in particular integrals and derivatives, to study problems in geometry. Differential geometry has applications in several fields, including physics, economics, engineering, and computer vision. This book focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems look at how local properties relate to global ones. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena. Each section includes numerous interesting exercises that range from straightforward to challenging. ... Read more

Product Description
This text has been adopted at:

University of Pennsylvania, PhiladelphiaUniversity of Connecticut, StorrsDuke University, Durham, NCCalifornia Institute of Technology, PasadenaUniversity of Washington, SeattleSwarthmore College, Swarthmore, PAUniversity of Chicago, ILUniversity of Michigan, Ann Arbor

"In the reviewer's opinion, this is a superb book which makes learning a real pleasure."

- Revue Romaine de Mathematiques Pures et Appliquees

"This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises."

- Monatshefte F. Mathematik

"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry."

- Publicationes Mathematicae

Contents: Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * Complete Manifolds; Hopf-Rinow and Hadamard Theorems * Spaces of Constant Curvature * Variations of Energy * The Rauch Comparison Theorem * The Morse Index Theorem * The Fundamental Group of Manifolds of Negative Curvature * The Sphere Theorem * Index

Series: Mathematics: Theory and Applications ... Read more

Customer Reviews (8)

Excelent book.
I studied the portuguese version of this book during the master degree program in mathematics at University of Brasilia, 1999. The book is very well written with beautiful results. Manfredo is an excellent mathematician, a great professor, and I had the chance to be present in many colloquiuns where he was the speaker. This is an very good exposition for those interested to learn more about the subject.

Needs a table of symbols
This is another well-written text by Do Carmo. I browsed through it and found I could not understand several passages because I did not know what the special symbols meant and there was no table of symbols. I plead with the publisher to add such a table to the next edition or printing.

Concise and clear
This is really a very good book to start Riemannian Geometry (RG). Exposition of key concepts of RG (affine connection, riemannian connection,geodesics, parallelism and sectional curvature, ...) are well motivated and concisely explained with numerous motivating and not so difficult execises. The book is self contained convenient for self study. It contains an introductory chapter on mathematical background explaining basic concepts as differentiable manifolds, immersion, embedding and so on, which are necessary to deal with RG. I have essentially one basic remark about this book. Formulation of RG as presented in it, is a little bit dated. Now, with the development of geometric algebra and Geometric calculus most, if not all, mathematical concepts needed to study RG like covariant derivative, curvature, and general tensors can be formulated without ressort to coordinates and in a manner to highlight their essential geometric features. Moreover derivation of certain formulae can be much easier and natural. For example the author defines the formula for |x^y| as sqrt(sqr(|x|).sqr(|y|)-sqr(inner product(x,y))). Then explains that it is the area of two dimensional parallelogram determined by the pair of vectors x and y. The reader might be puzzled as to how this formula is obtained. In the context of geometric algebra this is derived very naturally from basic concepts. Anyway, this remark does not diminish the value of this book.

Best 1st semester Riemannian Geometry book after 1 semester DG
This is the best Riemannian Geometry book after students have finished a semester of differential geometry.It gives geometric intuition, has plenty of exercises and
is excellent preparation for more advanced books like Cheeger-Ebin.

Students should already know differential geometry (Spivak "Calculus on manifolds" and Spivak "Differential Geometry Volume I" might be used there)

Warning: the curvature tensor is defined backwards as compared to Cheeger-Ebin.

Definitely a good start
This book is definitely a solid way to start in Riemannian geometry. The topics chosen give a glimpse of more advanced topics that the reader can venture to next, and the order covered leaves little confusion. The book is to the point, with little conversation about the concepts except at the very beginning of each chapter.

I only have two complaints, but neither would cause me to lower the rating to 4 stars.

1. There could be more "deep" exercises that allow the reader to explore more of the subtleties of the subject. And for what exercises there are, the author sometimes gives far too much away in "hints."

2. The book does not take a unified approach to the subject that fits nicely with the full generality of the theory. This is probably what makes the book good to start with, but there is still going to be a somewhat difficult transition from this book to a typical differential/riemannian geometry book. Namely, the basic language of vector bundles, pull backs/push forwards, tensors and tensor fields are either covered in a very specific framework or not at all. ... Read more

Product Description
This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane. The main theorems of non-Euclidean geometry are presented along with their historical development.The author then introduces the methods of differential geometry and develops them toward the goal of constructing models of the hyperbolic plane.While interesting diversions are offered, such as Huygen's pendulum clock and mathematical cartography, the book thoroughly treats the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds. ... Read more

Customer Reviews (5)

An excellent transition for the beginning grad student
I agree that this work is bit to terse for those completely uninitiated with the subject. However, for a first semester graduate student (or anyone with about this level of maturity) who has at least a minimal acquaintance with curves/surfaces this is a wonderful book which fulfills a long standing gap. The divide between undergraduate differential geometry and graduate geometry is too great. A beginning graduate student walk into a course on differentiable manifolds and Riemannian Geometry with no undergraduate diff geometry and be fine (as I did). There simply doesn't seem to be anymore that a superficial connection (no pun intended) between the two. This may not trouble the student at first, but as Spivak notes in his tome: "this ignorance of the roots of the subject has its price." Eventually one needs to assimilate the intuition of classical geometry with the technical language of manifolds. This book very elegantly leads the student from his undergraduate education to the doorstep of modern global geometry. As an added bonus, the author also endeavors to bridge the gap between Euclid and differential geometry.

The only other successful attempt at this is in Spivak, but unfortunatelyhe goes backwards. Volume 1 is entirely devoted to manifolds. Then in volume 2 he explains the classical point of view and then builds the bridge. While these are beautiful books, this is not efficient for the beginning student. The prospective geometer should read this before a class on manifold theory.

I give 4 stars only because the author advertises this as a "first exposure", and this book is simply not suited for this purpose.

great history of geometry book, terrible introductory differential geometry book
Do not buy this inappropriately titled book if you are seeking an introductory text to learn differential geometry. It's not that the concepts in the book are so advanced, so much as not that much space is actually devoted to the subject. The author's real objective is to trace the development of geometry from Euclid to the (relatively) modern formulation of differential geometry, and as a book on that topic it succeeds admirably.

The core theme of the book is that efforts to prove the parallel postulate, or, equivalently, show that non-Euclidean geometries are impossible, inadvertently, through their failure, led to the discovery of many fascinating areas of mathematics, such as hyperbolic and Riemannian geometries, and to the development of philosophical ideas about what actually constitutes mathematics and how it is independent from physical reality. The book culminates with the results of Beltrami and Poincare that showed that hyperbolic and Euclidean geometries are logically equivalent, in the sense that if there is a self-contradiction in one then the other is also impossible, thus putting an end to all attempts to disprove hyperbolic geometry. (Unfortunately, Marilyn vos Savant is unaware of this, or at least she was when she wrote an article some years back criticising Andrew Wiles's proof of Fermat's last theorem because it used hyperbolic geometry.)

As an appendix, McCleary adds a translation of Riemann's lecture "On the hypothesis which lie at the foundations of geometry," perhaps the most influential single lecture in the history of mathematics (and physics), in which, in the mid-1860s, he presented to a general faculty a talk (involving only a single equation) on the foundations of geometry that anticipated the concepts of a manifold and Riemannian geometry as well as general relativity and even hinted at quantum mechanics.

I used this text as a primary reference when conducting an undergraduate seminar on the history of hyperbolic geometry 12 years ago. For this purpose it was suited perfectly, but if you want to learn differential geometry by all means buy one of do Carmo's books or Gallot, Hulin, and LaFontaine.

not for the uninitiated
I'm a master's student in math. I bought the book thinking I'd use it for an independent study. I was wrong.

The book has interesting historical tidbits and some classical proofs, including material I hadn't seen elsewhere. However, it takes little time to explain to the novice exactly what's going on. It comes off more as a set of lecture notes than as a text for self-study.

For instance, in ch. 8 McCleary breezes through the basics of regular surfaces--coordinate charts, differentiability, implicit/inverse function theorem, the tangent space, orientability, the first fundamental form in about 19 pages. This is the same foundational material that folk like do Carmo or O'Neill rightfully spend 60-70 pages to cover.

His treatment of the Gauss map and the second fundamental form is even more schematic.

If I hadn't already worked the other books, when I got to McCleary's treatment of surfaces I would've been completely lost.

This book is best for people who know basic differential geometry already but are curious about certain historical aspects of it, not for people who are trying to learn differential geometry.

a great book!
This is a great book.The author develops the differential geometry of curves and surfaces.The endpoint is the vindication of Euclid's parallel postulate.I thoroughly enjoyed reading this book.Very readable.

Excellent text connecting classical to differential geometry
This book is ideal for those with a long time interest in mathematics or the student just becoming interested in advanced topics.It successfully takes the concepts of classic geometry (Euclidean), clearly explains how the parallel postulate interacts with the other postulates and then introduces differential geometry as a natural outgrowth of hyperbolic geometry.McLeary's book succeeds by demonstrating the connection of modern differential geometry to the concepts in which we were educated.This is not a book for the casual reader, but includes many problems and solutions to the more interesting of them ... Read more

Product Description
Ideal for users who may have little previous experiencewith abstraction and proof, this book provides a rigorous and unified—yetstraightforward and accessible—exposition of the foundationsof Euclidean, hyperbolic, and spherical geometry. Unique in approach,it combines an extended theme—the study of a generalized absoluteplane from axioms through classification into the three fundamentalclassical planes—with a leisurely development that allows ampletime for mathematical growth. It is purposefully structuredto facilitate the development of analytic and reasoning skills andto promote an awareness of the depth, power, and subtlety of the axiomaticmethod in general, and of Euclidean and non-Euclidean plane geometryin particular.Focus on one main topic—The axiomatic developmentof the absolute plane—which is pursued through a classificationinto Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the “gap” plane. Gradually presents axioms for absolute plane geometry. ... Read more

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Product Description
This book draws on geometric ideas from cultural activities from Subsaharan Africa, and demonstrates how they may be explored to develop mathematical reasoning from school level through to university standard. Paulus Gerdes provides a thoroughly illustrated and researched exploration of mathematical ideas, motifs and patterns. Many important mathematical points are brought to the fore, not via the formal 'theorem-proof' method, but in a more schematic and diagrammatic manner. African artifacts, oral traditions, sand drawing and other forms of artwork with a geometric basis, all provide mathematical ideas for discussion in this unique book. Mathematicians and teachers of mathematics at all levels will be fascinated, as will anybody with an interest in African cultures. ... Read more

Customer Reviews (2)

2000 CHOICE Magazine Outstanding Academic Book
CHOICE Magazine selected "Geometry from Africa" as one of the Outstanding Academic Books of 2000.

"The author expertly blends art, mathematics and lore, thereby giving the reader a greater appreciation of African culture...Gerdes' volume is a significant contribution to the literature of non-european centric mathematics.All of the mathematical ideas are accessible to undergraduates" CHOICE

"Are you a mathematics teacher seeking new sources for ideas?This book may be just what you are looking for....With copious illustrations, the author shows how geometrical ideas are manifested in the work of African artisans... One does not have to be a mathematician to appreciate the illustrations in this book"

AAAS Science Books and Films

Art as mathematical achievement
The combination of mathematics and art is one that has not been explored to the depths that it should have been. It is true that the explosion of fractals in the 1980's led to some examination of how mathematics can be used to create and explain art, but that is a specialized field. While most of the mathematical background of fractals was decades old, it was necessary for computing powerto evolve before it could be completely developed. Lost in all of this was the simple beauty and underlying mathematics offolk art in non-industrial cultures. The word ethnomathematics has been coined to describe the study of this art form and as the title suggests, this book is an ethnomathematical study of the art of Africa.
The beauty of the designs in simple items such as pots, hats and the walls of huts made from dung is often striking and always beautiful. It is sad to learn that much of the art that was handed down for generations has been lost due to disruptions of the African cultures as a consequence of the clash with Western culture. It is also simultaneously gratifying thatmost of the remaining forms of this folk art are being archived, cataloged, and studied. It makes one proud to be a member of an organization that is actively supporting this movement by publishing books like this one.
While the bulk of the book consists of pictures of the artwork, there are sections where the images are analyzed for the mathematical basis behind the design. As those who have studied the golden section have repeatedly noted, the human eye has a natural affinity for patterns possessing certain mathematical characteristics. It is even argued that some geometric theorems could have been suggested by looking at the artwork. There are also several places where suggestions are made for craft work that could be done by children of all ages.
It is generally conceded that geometry as we know it originated in Egypt. Reading this book, it is clear that we can expand our common mathematical heritage if we do not restrict our study to the Northeast corner of the African continent.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Product Description
The learn-by-doing way to master Geometry

Why CliffsStudySolver™ Guides?

Go with the name you know and trust
Get the information you need--fast!
Written by teachers and educational specialists

Inside you’ll get the practice you need to learn Geometry, including:

Basic Geometric Concepts

• Points, lines, and planes
• Postulates and theorems
• Line segments, midpoints, and rays
• Angles and angle pairs
• Parallel lines

Shapes and Measurement

• Measuring angle sums
• Triangles, polygons, and circles
• Determining perimeter and area
• Ratio and proportion
• Similar figures
• Solid figures and measurement
• Coordinate geometry

Problem-Solving Tools

• Clear, concise reviews of every topic
• Practice problems in every chapter--with explanations and solutions
• Diagnostic pretest to assess your current skills
• Full-length exam--with answers--that adapts to your skill level

We take great notes--and make learning a snap ... Read more

Customer Reviews (4)

Great book for learning and reviewing concepts - Some errors
I used this book to prepare for a ACT Compass Geometry test, to fulfill a graduation requirement. I am a 28 yr old returning student, and I'd been away from math in general for about 10 years. This was a great book for learning and reviewing the geometry concepts. I went through it quickly, in about 3-4 weeks. I just took the compass test and scored a 99 out of 100! Very nice. My one complaint is that there are a few random editing errors in the book. This definitely caused me some confusion as to why my answer was off, or how to do a problem. I've read the same complaint for other math books in their series. I am onto Algebra I next. Hopefully, I will be as succesful with that book as this one. Overall, a very good book.

Better than a teacher.
I'm a high school freshman-going-on-sophomore and I bought this to help prep myself for a get-ahead summer course I'm taking. So far, I've learned faster and better than I have with any of my previous math teachers.
Essentially a learning-by-example book, the description of new theories and postulates can be sketchy at first, but the multitudes of examples help to cement the ideas, and end of chapter tests ensure you don't forget.
If I had any gripes, they would be about the elusive problem 20, which I was instructed by the book to refer to a few times. Also annoying was the fact that the answers to the problems were often on the same page, making it hard to answer of your own skill, due to a wandering eye. Other than those minor issues, however, this book was a lifesaver.
I would definitely recommend this to anyone looking for prep, review, or even to help you pass a class if ever you're stuck with a truly horrible teacher.

Great for reviewing
I used this book to study for Middle School Math Praxis (20069) and was very pleased. I also used Cliff's Algebra I and II, which were also great

Excellent
This is a excellent guide in learning the fundamentals of geometry. The theorems and concepts are easy to grasp and the problems at the end of each theorem(s) make it easier to memorize. The only problem i have with this book is that some problems are easier than what can be expected on SAT II Math Level IIC or SAT I.I would suggest to buy Schaum's Outline Geometry to further your knowledge in geometry. Cliffnotes for easy explantations and Schaum's for the problems and extra concepts that are not discussed in cliffnotes. Overall, I was very satisfied to find a book that made geometry easier than I expected ... Read more

Product Description
The learn-by-doing way to master Geometry

Why CliffsStudySolver™ Guides?

Go with the name you know and trust
Get the information you need--fast!
Written by teachers and educational specialists

Inside you’ll get the practice you need to learn Geometry, including:

Basic Geometric Concepts

• Points, lines, and planes
• Postulates and theorems
• Line segments, midpoints, and rays
• Angles and angle pairs
• Parallel lines

Shapes and Measurement

• Measuring angle sums
• Triangles, polygons, and circles
• Determining perimeter and area
• Ratio and proportion
• Similar figures
• Solid figures and measurement
• Coordinate geometry

Problem-Solving Tools

• Clear, concise reviews of every topic
• Practice problems in every chapter--with explanations and solutions
• Diagnostic pretest to assess your current skills
• Full-length exam--with answers--that adapts to your skill level

We take great notes--and make learning a snap ... Read more

Customer Reviews (4)

Great book for learning and reviewing concepts - Some errors
I used this book to prepare for a ACT Compass Geometry test, to fulfill a graduation requirement. I am a 28 yr old returning student, and I'd been away from math in general for about 10 years. This was a great book for learning and reviewing the geometry concepts. I went through it quickly, in about 3-4 weeks. I just took the compass test and scored a 99 out of 100! Very nice. My one complaint is that there are a few random editing errors in the book. This definitely caused me some confusion as to why my answer was off, or how to do a problem. I've read the same complaint for other math books in their series. I am onto Algebra I next. Hopefully, I will be as succesful with that book as this one. Overall, a very good book.

Better than a teacher.
I'm a high school freshman-going-on-sophomore and I bought this to help prep myself for a get-ahead summer course I'm taking. So far, I've learned faster and better than I have with any of my previous math teachers.
Essentially a learning-by-example book, the description of new theories and postulates can be sketchy at first, but the multitudes of examples help to cement the ideas, and end of chapter tests ensure you don't forget.
If I had any gripes, they would be about the elusive problem 20, which I was instructed by the book to refer to a few times. Also annoying was the fact that the answers to the problems were often on the same page, making it hard to answer of your own skill, due to a wandering eye. Other than those minor issues, however, this book was a lifesaver.
I would definitely recommend this to anyone looking for prep, review, or even to help you pass a class if ever you're stuck with a truly horrible teacher.

Great for reviewing
I used this book to study for Middle School Math Praxis (20069) and was very pleased. I also used Cliff's Algebra I and II, which were also great

Excellent
This is a excellent guide in learning the fundamentals of geometry. The theorems and concepts are easy to grasp and the problems at the end of each theorem(s) make it easier to memorize. The only problem i have with this book is that some problems are easier than what can be expected on SAT II Math Level IIC or SAT I.I would suggest to buy Schaum's Outline Geometry to further your knowledge in geometry. Cliffnotes for easy explantations and Schaum's for the problems and extra concepts that are not discussed in cliffnotes. Overall, I was very satisfied to find a book that made geometry easier than I expected ... Read more

Product Description
Jacobs' highly successful, distinctive text was revised on the basis of users' comments and ten years of classroom experience - perfecting an already acclaimed approach to teaching geometry. "...the book concentrates on making the formal treatment of geometry both attractive and accessible..." The Mathematical Gazette Supplements: Teacher's Guide/Test Masters/Transparency Masters ... Read more

Customer Reviews (8)

Geometry by Harold R Jacobs
Very good book for high school level geometry. Concepts are broken down into well organized and small lessons, that way not too much is introduced at one time.
Easy to read, easy to follow, and even entertaining at times.

Taught Classes With it Several Times, Fabulous for Home-Schoolers
As the other reviews show...this book is not only lucid and brilliant, but quite accessible. I've taught classes with it starting in Jr. High with gifted youngsters and with homeschoolers starting in the 6th grade.
I regularly recommend this book to homeschool moms because it is not intimidating, and they invariably enjoy it.
Also, this is PURE geometry, untainted by algebra. Probably the first and only time most students have to learn logic and the structure of argument.
A no brainer. This is the best geometry book I've ever seen, hands down.

Excellent user friendly geometry text
This is the second book on geometry which I have read almost cover to cover. The first was Geometry by Ray Jurgensen and Richard G Brown written in 2000.Each of these texts seem to me to provide a good introduction to the basics of geometry. I suspect, even someone at the college level, can learn some items which could be quite useful for math, science, or engineering courses.The author has a wonderful sense of humor, which he springles over the text.I have not read the most recent edition of this book, but I hope to one day.This last edition is 17 years younger, having been published in 2004, instead of 1987.

The best geometry textbook in existence, bar none.
A very clear, very entertaining textbook for a high-school course on geometry.

This book introduces logical proofs right at the beginning; you may have some difficulty convincing your kids or yourself that you need to work out all these silly logic puzzles in order to begin studying geometry, but you do.

From there on, the book is a sheer joy to read, full of interesting and tricky problems, clear explanations, and of course those famous B.C. and Peanuts clips.

Worked every problem
I have no experience with other geometry books--although I did use the Schaum book and other "outline" help books early in the school year as a reference. Actually Jacobs was easier to use than the "outline" help books. Many problems skate close to calculus (limits are introduced) and analytic geometry. Some problems are quite nearly elegant. Highly recommended. ... Read more

Product Description

Activities in Geometry provides a set of versatile enrichment exercises designed to motivate students interest in a broad range of topics. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for teachers.

First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to students and show them that there is much more to geometry that proving theorems. To demonstrate this aspect of geometry, it is necessary for the investigation to be quite different from what students encounter in their basal texts-different in both substance and form. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any.

Customer Reviews (1)

Great source of interesting problems
I'm teaching a ninth grade geometry class and this book is a fantastic source of interesting problems that we can tackle at various points during the year.All the problems are difficult enough to be interesting while still being approachable when taken step by step. ... Read more

Product Description
This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry". ... Read more

Customer Reviews (1)

Interesting material, perhaps a bit loosely held together
The book begins gently with some background labelled "forming intuition" (although defining a geometry as a point set with a metric feels more like forming formalism to me). Then we get to the main theme of the book: isometry groups. They help us classify locally Euclidean geometries in two dimensions. The presentation is very elementary and explicit with details, and therefore quite tedious (we are already by page 120). Next we do the same thing in 3 dimensions, which is especially interesting, the authors argue, since the universe in which we live is three-dimensional. But it is hard to imagine these potential universes, except to say that there are 18 types and decide which of them are bounded or orientable. Perhaps sensing our dissapointment, the authors seem to say: well, yes, but at least these ideas pay off in physics as you can see here in our next chapter on the marvelously interesting theory of crystallography. We are not too impressed: Crystals?! Who cares about ****ing crystals? Anyway, after that the authors decide that it is interesting to study different locally Euclidean geometries on the torus. This leads to the modular group, and now we should be convinced that it is interesting to look for a geometry to accommodate the modular group as a group of motions. Lo and behold, hyperbolic geometry falls out, and the book ends triumphantly since we only wanted hyperbolic geometry in order to understand the modular group and torus geometries. Apparently, our previous interest in the true geometry of the universe, repeatedly appealed to in the discussion of locally Euclidean geometries, is gone without a trace. ... Read more

Product Description
This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design.The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron.A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues.The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels.The code in this new edition is significantly improved from the first edition, and four new routines are included.Java versions for this new edition are also available. ... Read more

Customer Reviews (7)

Excellent text, obfuscated code
I bought this book to learn about convex hulls, voronoi diagrams and delaunay triangluations, and line arrangements.So far I have made it through the chapter on 2D convex hulls, and I must say that it is an excellently written book for learning about the covered topics in computational geometry.The text is clear easy to understand; algorithms are sufficiently detailed and illustrated to allow full implementation without needing other resources.Corner cases are meticulously covered.I also like the text because it is straight to the point, i.e., it does not spoon-feed the reader. So, although relatively short book, it contains a lot of densely packed, but still enjoyably readable, information. Illustrations are simple but excellent: they are carefully designed and very helpful for understanding the described algorithms.

I give the book four stars for two reasons.

First, the coverage of floating-poing precision issues is almost non-existant: most of the algorithms are integer-only.A survey chapter over techniques for handling FP precision issues would be *VERY* welcome.(After all, geometric algorithms are most often applied to floating-point data in the real world.)Judging by the quality of existing bibliography, I think the author would make an outstanding job on this topic.(Hint for the 3rd edition :-))

Second, I have strong objections against the coding style used in this book: the presented code is an excellent demonstration of how to obfuscate C programs by using typedefs and hungarian notation (inconsistently!) applied in postfix. (NOTE: I have 10+ years of experience in C and C++ coding, so I'm not just a "little bit confused").

collates useful computational geometric algorithms
If you are perhaps a graphics or robotics programmer, then you will often have need for computing various geometric forms. And the intersections of these forms. Rather than derive algorithms from scratch, you might want to first look here. O'Rourke has collated several useful sets of methods. Germane to two and three dimenions.

Convex hulls are important enough that he devotes 2 chapters to these. While the somewhat related idea of Voronoi diagrams gets its own chapter.

The C code is a nice bonus to some readers. Though if you are experienced enough in another language, you should be able to readily code an algorithm in the book from scratch.

Nice balance of theory with code
This book was pleasantly surprising:I had expected to see code presented with minimal motivation or discussion of the underlying ideas -- something of a "Computational Geometry for Dummies" sort of book.That's not the case at all.This is a bona fide textbook on the subject, suitable for an undergraduate course.
It covers all of the the "classical" topics: convex hulls, line segment intersection, polygon triangulation, Voronoi diagrams, motion planning.

The mode of presentation -- supporting a discussion of the theories with implementable code -- is actually a bit refreshing.For comparison:Other books, when discussing the line segment intersection problem (ie: Given a set of line segments, find all of their intersection points) simply assume that computing the intersection of a pair of segments can be done in constant time.This is not an especially difficult problem, but the discussion seems more complete with a brief description of how this might be done.The same can be said about other primitive tests and operations in other algorithms.

Overall, this book can stand alone as an excellent introduction to computational geometry, but a serious student in the subject will want more: perhaps Preparata and Shamos or de Berg et. al.

Very hepful
Anyone who is involved in areas such as computer graphics, computational radiology, robot vision, or visualization software should have a copy of this book. The author has done a fine job of introducing the most important algorithms in computational geometry, choosing the C language for their implementation. The choice of C might be somewhat dated now, since C++ is now beginning to dominate computational geometry, but readers who are actually programming these algorithms using C++ can easily extend the ones in the book to C++. Not all of the algorithms in the book are implemented into C, unfortunately, but the clarity of presentation is done well enough to make this implementation a fairly straightforward task. My interest in the book came from a need to design and implement algorithms for polyhedra in VRML and toric varieties in algebraic geometry. This book, along with others, was a great help in that regard. The running time of these algorithms was not really an issue with me, so the detail the author spends on discussing the complexity of the algorithms was not a concern. Readers who need to pay attention to running-time issues will appreciate his discussion of them for the algorithms that are presented.

The ability to visualize objects in an abstract subject like algebraic geometry boils down to, in the case of toric varieties, to a consideration of how to manipulate polytopes geometrically. A major portion of the book, if not all of it, is devoted to the computational geometry of polyhedra. Because it is an introductory book, some more advanced topics, such as Bayesian methods to find similarities between polyhedra, and neural network approaches to classifying polyhedral objects are not treated. Readers who need to do such things will be well-prepared for them after a study of this book. In addition, there are good exercises assigned at the end of each chapter, so the book could be used in the classroom. Some readers will however choose to use it as a reference source, and it would be a good one, for the author gives references to topics that he only touched upon in the book.

Some particular areas that were treated especially well were: 1. The discussion on data structures for surfaces of polyhedra. Although not very general, since he choose to deal with only triangulated polytopes, readers who need to be more general will have a good start in this discussion. 2. The discussion on volume overflow and how to deal with it using robust computation. 3. The discussion, albeit short, of the randomized incremental algorithm. 4. The treatment on the minimum spanning tree and Kruskal's algorithm. Communication network performance optimization is now a major application of this algorithm and others in graph theory, including the author's later discussion of Dijkstra's algorithm.

my rewiew
i think that these website is very.it has everything that i need. all of my books are from amazan. ... Read more

Product Description
Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry. ... Read more

Customer Reviews (1)

Excellent comprehension
I will not say this book is an introduction but that its a confusion remover for a serious student of algebraic geometry. This book I consider a part of the much needed revolution happening in algebraic geometry which means that if you browse or spend time reading a book you must learn something. Excellent coverage of a fascinating subject. Enjoy! ... Read more

Product Description
When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.

At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase -- and zero in on the essential information you need to succeed. ... Read more

Customer Reviews (8)

To the Point
This book is stripped down and to the point, which is exactly what I needed to do a thorough review.I would have rated it a "5" if it had more "Test Yourself" questions...but that's a personal preference (don't let it stop you from ordering this book).

Geometry ebook
Geometry Quick Study Guide - FREE Geometry Background and Triangles chapters in the trial version

This is a great ebook. The author provides us with simple yet understandable and memorable explanations of what is what and why.

great for reviewing
I am involved with tutoring and haven't looked at geometry for MANY years. I am using Cliff's for review and to supplement more in-depth material.I am finding it great for bringing back the material.

caution
Overall this isn't bad for a rapid summmary
but there are some subtle errors which may
undermine the reader's confidence in the
material (e.g.note altitudes and areas
of the triangles on page 76).

A compact, yet complete review of basic geometry
As a long-time teacher of mathematics at the college level, I am always trolling for additional/better materials to help students learn mathematics. Since I am not a fan of the Cliffs Notes series, I hesitated before purchasing this book in a used book store. However, once I started looking through it, I realized that it is a very good review of basic geometry.
It begins with the fundamental postulates and immediately goes to some basic theorems, although no proofs are offered. The chapters are:

*) Fundamental ideas
*) Parallel lines
*) Triangles
*) Polygons
*) Perimeter and area
*) Similarity
*) Right triangles
*) Circles
*) Geometric solids
*) Coordinate geometry

There are a small number of exercises at the end of each chapter and a summary exam at the end of the book. Solutions to all exercises are included. If you need a fast, complete review of geometry, then this is an excellent selection. However, it has little value if you are trying to learn geometry.
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Product Description
This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. ... Read more

Customer Reviews (1)

excellent product and service
hi,
i'd like to thank you for excellent product and service.
i got the book very shortly after ordering it, and much time(!) before your commitment.
i found this book very helpful for my studies.

thanks again,
shai
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