Product Description
The Geometry Guide illustrates every geometric principle, formula, and problem type tested on the GMAT. Understand and master the intricacies of shapes, planes, lines, angles, and objects.Each chapter builds comprehensive content understanding by providing rules, strategies and in-depth examples of how the GMAT tests a given topic and how you can respond accurately and quickly. The Guide contains a total of 83 'In-Action' problems of increasing difficulty with detailed answer explanations. The content of the book is aligned to the latest Official Guides from GMAC (12th edition).

Special Features:

Purchase of this book includes one year of access to Manhattan GMAT's online Geometry Question Bank (accessible by inputting a unique code in the back of each book). ... Read more

Customer Reviews (3)

A solid review of GMAT geometry
I self studied and scored a 770 on the GMAT. Here are my thoughts on the Manhattan GMAT Geometry guide:

===== OVERVIEW =====

The fifth and final guide in the series of quant guides from Manhattan GMAT deals with the subtleties of geometry. This is another important topic tested on the GMAT, since you'll undoubtedly see quite a few problems on triangles (at least two, I think) and the occasional problem on other shapes (particularly circles, squares and solids made up of these two). The guide is pretty exhaustive with regards to the theory you'll need on test day, but it could have been improved by the addition of some more problems in the circles department and a chapter on overlapping shapes.

The first part of the book concerns polygons, triangles, circles, angles, the coordinate plane and solids, featuring 75 "in action" problems (similar to Problem Solving, but with no answer choices). The second part is fairly small and only has 8 questions. In my opinion, this latter section would have benefited greatly from a few tips and practice items on overlapping shapes, since these tend to be the more difficult of the geometry subset (I actually had to guess on one such problem on my real test).

===== PROS =====

*Pretty much all of the theory you'll need on geometry is explained in this book. Their tips on the maximization of the surface area of polygons were particularly interesting, since I have not seen this discussed in any other strategy book on the market

*Comes with access to 25 online questions and 6 adaptive tests (some of the best in the industry). You'll also find the well-known The Official Guide for GMAT Review, 12th Edition problems list to help you practice with real, retired questions

*The problems they supply in this book do tend to test more than one concept at a time, which is a plus. Their explanations are also pretty detailed

===== CONS =====

*No chapter on overlapping shapes! I find these problems to be some of the more challenging in geometry. Also, no Data Sufficiency practice problems is definitely a minus, since these questions tend to be extremely confusing for most students (they combine this relatively puzzling question type with geometry that you sometimes have to draw on your own)

*More problems on the trapezoid, polygons with more than 4 sides and angles within circles would have been nice. I also couldn't find a review of tangents to circles

*The issues mentioned above also impact the overall difficulty of the problems in this book. If the topics would have been included, the book would also contain more advanced problems than it does right now (only a few, sadly)

===== BOTTOM LINE =====

The Manhattan GMAT Geometry guide earns four stars out of five for its coverage of the concepts you'll need to know to do good on GMAT geometry. Overall, this book still needs a bit of work, but its contents currently contain what most student will need for their test. The elements that are missing are almost all advanced topics, of which you won't see more than one or two problems in the GMAT.

About me: Dana Jinaru, 770 GMAT scorer, expert at Beat The GMAT - a community serving 1.5 million+ MBA applicants each year

Manhattan GMAT is the best prep available!!!
I didn't take a class, but I have alot of friends who have and have used the Kaplan book and practice tests in addition to the Manhattan. Manhattan prep material and tests are head and shoulders above Kaplan. My only wish is that I had started with the Manhattan series and not even worried about Kaplan. Kaplan may have the brand name, but the fact that Manhattan focuses only on the GMAT shines through. The material goes wayyy more in depth, and it really leverages the other best source of practice material you have, the Official Guide (it has a great feature called rephrasing that references the OG problems directly to give data sufficiency help. It almost makes so much sense that it seems obvious but ingenious at the same time. Why not use the actual old test problems provided by the GMAC as much as you can?).

I wasn't going to buy the whole series but was so impressed by the first book I used (Sentence Correction), that I bought a couple of the quantitative prep books. I was so impressed by those, that I ended up buying all the rest of them. I can not stress enough how much more focused and useful this material is than Kaplan. When used in conjunction with the Official Guide, you have everything you need to break 700.

The things these books provide make so much sense as the best way to prepare, that it makes you wonder why everyone else doesn't do it. My guess is that Manhattan benefits from a focused business model of limiting itself to the GMAT. If you're not looking to score that well and only need to practice some and get used to the questions, the Official Guide is enough. But the Manhattan series is also nice in that it allows you to pick and choose the certain topics you need extra help with. Also, by only buying one book, you get access to six practice tests that are very difficult and provide invaluable information in its readouts of your performance (much more detailed and useful than Kaplan's. Hate to keep hating on Kaplan, but it's the only thing I have to compare to. It's not horrible really, it just pales in comparison to Manhattan. I think of the Kaplan material like I think of McDonald's, very well-known but pretty junky. It'll fill you up, but you won't feel great afterward...)

I've never taken the time to review any items on Amazon.com before, but I have been so impressed with this product that I felt compelled to let others know about it.

Don't waste your money on a class, get the Manhattan series instead. You'll save over a thousand dollars and be better prepared as well!

Good luck!

Solid Geometry book but why so few illustrations and no gmat-style questions?
I love most of the MGMAT books but this one just does not feel right. The book is realistically 95 pages and covers all important concepts: from lines to coordinate geometry. Does not go over the top and gives enough material, seems like the writers covered all the bases. However, I have an issue with it - it is not laid out very well. I am a visual learner and felt it would have been a better book if it was spread out more, included more illustrations, and did not have so much verbiage everywhere. Even larger all-in-one books dedicate close to 100 pages for Geometry.

Another issue is that all of the problems in the book are in a non-gmat format (meaning you only get a question, not the 5 answer choices). That is OK for some sections, but not having a single gmat-like question in the entire book is a "no-no". GMAT is heavily about basics and good framework, but there are other ways to solve questions such as backsolving, picking numbers, etc and those skills are honed only when questions are in the GMAT format. Important to point out that the book comes with access to the Geometry quiz bank online, which does have GMAT-style questions, so there is hope.

The big redeeming factors are 6 online tests that are included with every MGMAT book ($39 value), additional online practice materials, and coverage of Coordinate Geometry (a harder topic often omitted in larger textbooks).

***Bottom line: this is a solid geometry book that was crammed in 95 pages but is still a worthy buy for the sake of tests and the coordinate geometry section.

Questions about the book? Post them here - i will respond.
BB, Founder of GMAT Club Community.


P.S. The only other books that cover Coordinate Geometry are: Kaplan GMAT Math Foundations and MGMAT Foundations of GMAT Math, both of which are on the easier side of things but recommended if you need help with math. You can find my reviews for both of them. ... Read more

Customer Reviews (2)

The Best Geometry Book ever!
This geometry book is the best geometry book of all time.It is well written and truly challenges students to understand geometry on a deep level.I wouldn't recommend the book for a lower level of students, but it is outstanding for everyone else.I love it and I am inspired by it.(I am a math teacher.)

Not very acurate but good enough for ninth grade students
I just finished using this book and it was agreat help to me because all the theorems and postulates were listed on the back and it had an answer key. Every lesson only has around 15 questions and there is rarely any examples. If you need to learn geometry really quickly get this book but you wont get every single detail. ... Read more

Product Description
Written for students who need a refresher on Plane Euclidean Geometry, Essentials of Geometry for College Students, Second Edition, incorporates the American Mathematical Association of Two-Year Colleges (AMATYC) and National Council of Teachers of Mathematics (NCTM) Standards on geometry, modeling, reasoning, communication, technology, and deductive proof. To make learning interactive and enjoyable, this new edition includes exciting new features such as Technology Connections and Hands-on Activities. Knowledge of beginning algebra and a scientific calculator are required for this text. ... Read more

Customer Reviews (2)

Essentials of Geometry for College Students
I'm very pleased with this purchase. The book came promptly and was in good condition. I would definitely order from this seller again

Not for serious geometry students
I only own a copy of the first edition (1990), but unless adding a new author (Brown) or drastically changing the text has greatly improved anything, the book doesn't try for much more than its title indicates.Like many other college introductory geometry texts, this isn't much more than high-school-level geometry without all the colorful pictures and stories that are supposed to make the topic fun and show the application of geometry to our lives (making this book about a third the size of most high school texts).
This book is not bad, and is probably fine for the student whojust needs a basic understanding of Euclidean plane geometry (with chapters on solid and analytical geometry, and trig).Many of the theorems are proved (two-column proofs).The exercises are more into reinforcing the chapter contents (solving numerical problems and showing concept understanding) than in exploring new material and applications.
For authors that introduce a more rigorous approach, and show how beautiful geometry can be; try Coxeter and Posamentier. ... Read more

Product Description
You, too, can understand geometry---- just ask Dr. Math ? !

Are things starting to get tougher in geometry class? Don't panic. Dr. Math--the popular online math resource--is here to help you figure out even the trickiest of your geometry problems.

Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Presents More Geometry, you'll learn just what it takes to succeed in this subject. You'll find the answers to dozens of real questions from students in a typical geometry class. You'll also find plenty of hints and shortcuts for using coordinate geometry, finding angle relationships, and working with circles. Pretty soon, everything from the Pythagorean theorem to logic and proofs will make more sense. Plus, you'll get plenty of tips for working with all kinds of real-life problems.

You won't find a better explanation of high school geometry anywhere! ... Read more

Customer Reviews (2)

Dr. Math Presents More Geometry: Learning Geometry is Easy! Just Ask Dr. Math.
Will be using to assist students in HS Geometry as well as passing their state graduation exam.

Four Pentagraphs
This is an interesting book to read through and gives clears information on the logic of proving or using various theorems. Information is separated into chapters on circles, triangles, quadrilaterals, etc. How much you will enjoy this book is probably dependent on how you want to use it. If you have a specific question you need help answering, it may not be of use to you unless you have time to skim through the appropriate chapter, and then you may or may not be lucky and find it. It is not intended to be a text and doesn't necessarily progress in that structured, complete form. It is a fun,math "read" with nice diagrams and clear explanations. ... Read more

Product Description
Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers. ... Read more

Customer Reviews (5)

Excellent for high school teachers and students
I use the ideas in this book in my mathematics teaching in high school. Students learn to think of the world as Euclidean through most of their instruction; Taxicab Geoemetry gives teachers a very straghtforward way to introduce non-Eucliean Geometry. Admittedly, this book is not thorough, and it is very open ended (which I consider to be positive). Nevertheless, for its intended audience it is outstanding.

Disappointing
Very simplistic treatment, with some results left for the reader to work through exercises.The chapters are almost non-existent, with all the book being mainly exercises.

Excellent for what it is
Before purchasing this book, realize what it is.This is a book about non-euclidean geometry.Specifically, a specialized form of non-euclidian geometry affectionately referred to as taxi-cab geometry.This is not atable top book, but is a book for mathemeticians and those interested inmathematics.Others need not apply (regardless of how interesting thetopic is).This is an excellent introduction to non-euclidean geometrybecause it strips away common misconceptions about the nature ofnon-euclidean geometries.This text is excellent for grade school childrenand those who would like to branch into more advanced non-euclideangeometries like hyperbolic.

This is a book for a math student only.
I thought that this book would be about geometry of exotic (but real)places in outer space (such as a black hole, for example).Instead, itturned out to be a lethally boring book, full of math problems, that wasLESS interesting than my geometry book in high school!

A simple, real-world example of non-Euclidean geometry
Some years ago, I was employed by a company that built mapping software. One of the projects I worked on was the design of features that allowed for the computation of the shortest path from one position to another followingonly roads. This form of travel is similar to the taxicab geometry in thatmovement is restricted to lines. The only difference is that roads can beplaced at any location or angle whereas the lines in taxicab geometry areequidistant and perpendicular. Think of it as the geometry of graph paper.As I constructed the program, I was struck by how so much of classicalEuclidean geometry does not apply. Yet, the geometry is generally easier tounderstand because it is almost always how we move from place to place.
The phrase non-Euclidean geometry generally conjures up thoughts ofcurved space and Riemannian geometry. However, in this delightfully simplebook, a natural non-Euclidean geometry is developed in great detail. Verylittle mathematics is needed to understand the geometry, if you can markand understand the points on a grid of graph paper, nearly all of thetopics will make sense. A large number of problems are included at the endof each chapter and solutions to many appear in an appendix.
Theproblems cover topics such as finding the point(s) of minimum distancebetween two or more points and what the taxicab analogues of circles andellipses are. Determining the point of minimum distance between three ormore points is a hard problem in standard geometry, but fairly simple inthe taxicab geometry.
Geometry is the godfather of abstractmathematics, being first used to codify the parceling of land and theconstruction of cities. In this book, you will learn how to minimizefunctions based on the restrictions of traveling through cities, a taskwith many applications in the world. ... Read more

Customer Reviews (2)

this book was in good condition when ordered
I have been very pleased with the quality of the books ordered from the marketplace sellers.With very few exceptions, the books are in better condition than listed.It is worth giving it a try!I highly recommend it.I order all the books my son needs for his high school (private) at about 25% of the new book price.I have been able to order most books for less than the book company will pay to buy books back from the student, which is amazing to me.Please check the edition and the ISBN before ordering! The Holt edition of this book comes with a free online tutor that my son swears by.He made an A in this class despite a new teacher and the fact that math is probably not his favorite subject.

Schools beware
My school purchased these books 2 years ago. The content is great.However, after 2 years of use, a quarter of them are almost trashed.The binding does NOT stay on.It is far too heavy of a book for the binding it has.It easily pulls away from the book.One drop to the floor and it has substantial damage. ... Read more

Product Description
A boxed set of cards and book, the sequel to Sacred Geometry Oracle Deck

• Contains 64 full-color cards created from original paintings by artist Francene Hart

• Includes a 160-page guide with wisdom readings for each card and 6 oracle spreads for personal and group readings

• By the creator of Sacred Geometry Oracle Deck

Sacred Geometry Cards for the Visionary Path provides encouragement and guidance to those on the path of conscious evolution. A natural continuation of and complement to the Sacred Geometry Oracle Deck, this divination set by artist Francene Hart contains 64 original full-color images that portray the sacred geometrical proportions in the natural forms of animals, oceans, and celestial bodies. The accompanying guidebook contains detailed interpretations of each card and 6 divination spreads for both personal and group readings.

Integrating math, science, and spirituality, these cards convey the wisdom of ancient cultures in which art, science, and religion were seen not as separate systems but as different facets of the same truth. Working with these cards incorporates this inclusive view into our own lives to bring balance to our energy fields and allow us to access higher levels of consciousness. The wisdom they reveal provides insight into life’s challenges and helps restore us to a state of harmony with the natural rhythms of life.
... Read more

Customer Reviews (4)

A Real One
I was happy to see that The Sacred Geometry Cards for a VisionaryPath was "Real". There was nothing "Tricky"about it. The Designs, pictures, and colors were respectful & In Tune withwhat it represented. The information The Cards held are singing along with Nature's Gifts ( everything around us that we see, use, eat, experience)& Time/History therefore what is given to you is insightful, withsound information.The information allows one to be aware of The Mystical depth to delve into.Thank You

Beautiful illustrations...
While I think the cards are very beautiful, and the descriptions are insightful, I think I was looking for a little more information related to Sacred Geometry.A little more "ummph", I guess as to the meaning behind each illustration and geometric form. Perhaps better used as a spark for meditation, but in terms of "meaning" behind sacred geometrics, I was disappointed.

Sacred Geometry Cards
Beautiful cards, easy to use.If you like cards this is a great deck to have.

Powerful
This new deck by Ms. Hart is magical.The images are simply gorgeous and the accompanying descriptions for each card insightful.Each time I've chosen a card, for myself or for others, the result has been amazingly synchronistic. ... Read more

Product Description
Get ready to master the concepts and principles of geometry! Master Math: Geometry is a comprehensive reference guide that explains and clarifies the principles of geometry in a simple, easy-to-follow style and format. You?ll begin with the language of geometry, deductive reasoning and proofs, and key axioms and postulates. And as you understand the most basic fundamental topics you?ll progress through to the more advanced topics, with step-by-step procedures and solutions, along with examples and applications, to help you as you go. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up, Master Math: Geometry will help you master everything from deductive reasoning and proofs to constructions and analytic geometry. ... Read more

Customer Reviews (5)

Master Math: Geometry
Master Math: Geometry (Master Math Series)I was impressed with the orginization of the text for this book. Topics were well-covered in an easy to read format.
Martin

Warning:A Texbook with no exercises
I am so amazed that anyone would write a textbook with no exercises.There is very little chance of anyone developing a good grasp of any kind of math subject without practice.I bought this book because of the good reviews-I can't believe that no one mentioned that there is not one single exercise in all 406 pages!Now I am left with the choice of not using the book at all or purchasing another book with exercises.

Recommended for high school collections on up
Any high school to college-level student wishing to master the basics of math needs these comprehensive references that clarifies and explain basic math principles. Two new math studies titles by Debra Anne Ross are particularly to be recommended for math students, as well as non-specialist general readers seeking to develop a basic understanding of algebra. Master Math: Geometry moves from basic topics, examples and applications to building upon basics, Master Math: Algebra surveys algebra by itself and moves from simple algebraic equations to graphing, and her Master Math: Basic Math & Pre-Algebra surveys basic arithmetic subjects and formulas. These are perfect for study, review, or supplemental learning and are recommended for high school collections on up.

Perfect Choice!
My 14 year old daughter is homeschooled and she needed some guided help with her Geometry class.This book was the perfect choice!It's well written, easy to comprehend and easy to find what you are looking for.

The best basic geometry book written!
The best presentation of geometry I have ever seen.The topics are presented in a logical manner so that they build, are in context, and make sense.It explains logic and proofs in a way students can really understand.Definitions are provided in the beginning so you can orient yourself and understand the jargon of geometry from the start.It presents concepts three ways: a description, a picture, and a description of the picture.It makes learning so easy!There are plenty of real-world and fun examples and tidbits of information that makes learning fun.It is clear, concise, and the topics have a flow and context that makes is easier to learn the material whether you are taking geometry for the first time, are older and need a review, or are taking higher level math, science or engineering classes and need to quickly look something up and understand it.Learning geometry does not need to be a frustrating experience!Everything you need for basic geometry is in this book!Master Math: Basic Math and Pre-Algebra, Master Math: Algebra, Master Math: Trigonometry, Master Math: Pre-Calculus, Master Math: Calculus (and the novel, Arrows Through Time: A Time Travel Tale of Adventure, Courage, and Faith) are also fantastic!

... Read more

Product Description

Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity.

Aimed at a general readership, the text makes accessible complex subjects such as Chaos and Fractals. It includes a wealth of the author's own illustrations and features appendices on related topics.

Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment.

Customer Reviews (1)

Gems is right word for this book
Gems of Geometry, eh?I tried the Search Inside feature here, and everything seemed pretty good, so I finally went and purchased a copy.

There is an astounding amount of great material in this book, all visually enticing, and mathematically deep.Well written explanations, and lots of good facts.

Looking through this, I get the idea that a much longer book was outlined first, and then the duller sections were pared away again and again, until a cohesive, exciting mathematical narrative remained, featuring all the best material of modern mathematics.

Try out the "Surprise Me" option in Search Inside.If you like those random pages, you'll like the whole book. ... Read more

Product Description
The latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with users alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, CLASSIC EDITION, 12E, effectively prepares users for further courses in mathematics through its excellent, time-tested problem sets. ... Read more

Customer Reviews (7)

Avoid at all cost!

The text only introduces the basics of a concept before introducing much more complicated problems in the chapter practices. Very little detailed information to help understand concepts. I had to use other texts and online resources to supplement this POS testbook.

A really bad math book
Precalculus is hard enough without having to use a book like this. I thought that the prose was unreadable, the graphics confusing, and many of the exercises supercomplicated (our professor thought so too). In my opinion *Algebra and Trignometry* is a triumph of marketing over pedagogical competence. My advice? Not only should you not buy this book; you should avoid a class in which it is assigned.

Awful!
I teach a high school class for advanced mathematics in preparation for college maths, and I honestly have to say that this is the worst book from which to teach.Yes, I can understand it perfectly, but a student will be lost the moment he or she lays eyes on the first page.The only good thing about this book is the number of exercises it has in each section.

For mathematicians, by mathmematicians
Frankly, I found this text way too brief in its coverage of topics prior to being bombarded with questions. There isn't much good to say about this book other than providing lots of problems to work. Save yourself the money and buy a "10000 problem" text instead.

Solid math textbook
I'm a little torn on what to say about this book. On one hand, I have a huge amount of respect for this book. On the other hand, it's not an easy book to learn from.

I have no doubt that if people work through this book, they will be very knowledgable and skilled in the areas covered. It is, however, a slow, tedious, sometimes frustrating process. The authors are clearly proficient at math, but their style is pretty dry. It's a "just the facts, ma'am" approach to instruction. It would be nice to have perspective, interpretation, and helpful guidance in addition to straight math. It's kind of like reading a technical manual.I prefer a more engaging presentation. ... Read more

Product Description
Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant problems and solutions. Bibliography.
... Read more

Customer Reviews (5)

The most consistent reliableand readable so far
With this book, I hope I have finally broken the code and reached a critical mass in advanced mathematical understanding. These Dover Series books allow "it all to hang out." It is "old school" in the best sense of that phrase: that is, in the sense that they do no "sugar coat" their explanations. They do not "dumb it down" or "fancy it up to" ease the pain. One knows what one is up against when one picks up a book from the "Dover Series." They are always clean and sparse in their explanations.

In this regard, this book is no exception. Professor Struik begins at the beginning and goes straight through to the end without skipping any steps and without passing go to collect his $200. He gives the fundamental conceptions of the theory of curves and surfaces, introducing all of the machinery necessary to understand them in a graduated fashion suitable only to the requirements of the topic itself. Elementary calculus will serve the reader well, especially with a smattering of Linear Algebra thrown in. The author wastes no time with sexy side issues or superfluous explanations: Just the basic facts of the fundamental elements here. Those looking for more advanced topics, should consult those books that use this one as their background.

Explanations are sparse, but never deficient; the same is true of the equations. Notation is straightforward and always clear and economical. It is easy to see that(and why) other books on the same topic have used this one as background, but oddly, those other books have been unable to improve upon this one. Other than the fact that the graphics need updating, and more modern topics are missing, this is a splendid effort. Just what I needed.

Five Stars.

Very Readable Work on Classical Differential Geometry
While it is quite true Dirk Struik's work is on classical differential geometry, the older methods and treatment do not necesarily imply obsolescence or mediocrity as some readers or reviewers suggest in their evaluations.Classical Analysis is still an important branch of Mathematical Analysis.So classical approaches and topics should not be dismissed as a waste of time, useless, outdated or even invalid.Remember Andrew Wiles' recent attack on Fermat's Last Theorem and his ultimate proof of its validity, an event that made headline news.That is a quintessential classical problem in mathematics (i.e., in number theory), only recently resolved.So remember: CLASSICAL Differential Geometry is part of the title.

First of all, this book is very readable, being that it requires no more than 2 years of calculus (with analytic geometry and vector analysis) and linear algebra as prerequisites.Exposure to elementary ordinary and partial differential equations and calculus of variations are highly desirable, but not absolutely necessary.There are numerous carefully drawn diagrams of geometric figures incorporated throughout the book for illustration and, of course, better understanding.Topological methods are not used in the book, and the concept of manifolds not mentioned, much less treated.So this is an older work that bridges the very foundational and applied aspects of differential geometry with vector analysis, a field and body of knowledge widely used nowadays in the sciences and engineering and exploited in applications such as geodesy.For those insisting on modern approaches and want to omit studying foundations and historical development, please read up on other books such as O'Neill and Spivak.(Also, there are tons of other newer works, i.e., on "modern differential geometry", I am unfamiliar with.They are probably availble for browsing in college bookstores.)

The author begins by leading the reader from analytic geometry in 3-dimensions into theory of surfaces, done the old fashion or classical way, i.e., utilizing vector calculus and not much more.Along the way, he takes the reader through subjects such as Euler's theorem, Dupin's indicatrix and various methods for surfaces.Then he continues with developing important fundamental equations underlying surfaces, e.g., Gauss-Weingarten equations, looks at Gauss and Codazzi equations, and proceeds to geodesics and variational methods.He includes a somewhat detailed treatment of the Gauss-Bonnet theorem as he progresses.He ends up with introducing concepts in conformal mapping, which plays an important role in differential geometry, minimal surfaces and various applications, one of which is geodesic mapping useful in geodesy, surveys and map-making.He does all of it with clarity and focus, including problems or "exercises" as he calls it, in under 240 pages - brevity that is rare in many mathematical books and works these days.

For those with a mind for or bent on applications, e.g., applied physics (geophysics), applied mathematics, astronomy, geodesy and aerospace engineering, this book would be an excellent introduction to differential geometry and the classical theories of surfaces - being that one need not worry about abstract analysis and topological aspects of mathematics.Perhaps the title should be "Topics in Classical Differential Geometry" or "Introduction to the Theory of Surfaces in Classical Differential Geometry".But one must keep in mind that Dirk Struik is an old MIT hand and contemporary of Norbert Wiener, also at MIT, and Richard Courant (and many great German-educated mathematicians) who lived and worked in the early to mid-20th century, a long time ago and before computers became commonplace, an era in which total abstraction in mathematics and physics was not quite widely emphasized, but clear concrete thinking was important.A good friend of mine and co-worker who studied at the University of California, Berkeley, told me he had great respect for the classical geometers such as Struik and Eisenhart, understanding that they built ideas from a scatch and wrote in such a way that readers can discern the physical origins of geometry, in particular of differential geometry, a subject that supposedly started with Gauss during the early or mid-19th century when he performed survey work for his government in Germany.(The term "torsion" introduced and sed by Struik in the first few chapters of the book comes from classical mechanics, and is commonly employed in mechanical structures/structural engineering nowadays.)

I for one am an aerospace engineer.There were one or more occasions where I consulted the book for formulas and expressions of curved surfaces and spheroids in my work of flight navigation (flying over the ellipsoidal Earth, as one example).I am sure that are other areas, e.g., space engineering, where classical methods of differential geometry embodied in Struik's book can come in handy.

The only problem I have with the book is that the "exercises" do not come with solutions, but I do not think that is a major drawback unless one uses it as a textbook for a course that requires assignments and drill exercises.

Judge for yourself by borrowing this book to read, i.e., if you are interested, can tell whether you like or dislike it on the first pass, and for what reasons one way or another.Find out for yourself.

classical
This is a survey of classical i.e. early 20th century differential geometry and not a more "modern" abstract treatment.

Good treatment of classical differential geometry
Struik's book provides solid coverage of curve and surface theory from the classical point of view, i.e. the kind of stuff Monge, Serret, Frenet and Gauss did. I agree that the book should be on the shelves of mathematicians. A number of classical topics are simply not in vogue these days, and one can find them discussed at length in Struik, or in the exercises. In this sense the book certainly has a more geometric flavor than a number of contemporary texts.

However, Struik can't be used to understand what is happening today. For these purposes,books by O'Neill and do Carmo would be more appropriate. The discussion of manifolds and coordinate charts, the discussion of connection forms, differential forms, covariant derivatives, exterior derivatives, pullbacks and pushforwards can be found in these texts. This is the language of modern geometry.It leads on naturally to tensors, fibre bundles, de Rham cohomology and so on and so forth.The emphasis in modern geometry is on global phenomena, the interaction between local and global (e.g. Morse theory or De Rham cohomology), and the attempt to do everything in an algebraic setting (projective modules, spectral sequences, categories etc.) For this purpose, Struik is useless, though he does have some coverage of forms (he calls them by their earlier name of 'pfaffians').

The price of the book makes it an attractive purchase.

Struik's book - a classic on classical differential geometry
I simply cannot believe I am the first reviewer of this book!This book should be on the shelf of every mathematician interested in geometry, every computer graphics specialist, everyone interested in solid modelling.Forten bucks, you get a great summary of a wide range of topics in"classical differential geometry" -- the stuff geometers wereinterested in one hundred years ago.Today it's gauge and string theory --but the topics discussed in this book are timeless, and many have seenremarkable renaissances in recent years. It is a wonderful little book ...I am using it to teach a basic differential geometry course next year. ... Read more

Product Description
Teacher's Edition. This book has been written so that all students can understand geometry. The course focuses on the key topics that provide a strong foundation in the essentials of geometry. Lesson concepts are presented in a clear, straightforward manner, supported by frequent worked-out examples. The page format makes it easy for students to follow the flow of a lesson, and the vocabulary and visual tips in the margins help students learn how to read the text and diagrams. Checkpoint questions within lessons give students a way to check their understanding as they go along. The exercises for each lesson provide many opportunities to practice and maintain skills, as well as to apply concepts to real-world problems. ... Read more

Product Description

This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry. Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities.

Customer Reviews (3)

the most geometric, user friendly book on algebraic geometry
In the 1950's algebraic geometry was tedious and hard to grasp because it was mostly commutative algebra, developed by Zariski and Weil andtheir schools to fill logical gaps in the Italian arguments of the previous half century.The rich geometric texture of the italian school was lost.In the 1960's Serre and Grothendieck introduced homological algebra to the subject and greatly expanded and enhanced it to embrace also arithmetic, but the abstraction level went WAY up, so again it was hard to grasp and relate to geometry.Hartshorne is a member of both Zariski and Grothendieck's schools and appreciates down to earth objects like space curves, but his book has a long beginning section on schemes and cohomology that can definitely throw a beginner off the horse.

Pardon the delay in getting here, but the point is that Shafarevich's book has none of the tediousness of the previous generation, yet benefits from the rigorous foundations via commutative algebra of Zariski's works.I would say Shafarevich's book, is a geometrically oriented explanation of the material that can be explained using Zariski's methods.I.e., it has a rich geometric feel, is very well explained, includes many easy examples, and is rigorous in its use of commutative algebra.This book allowed many of us who were stymied by the huge amount of algebra needed for 1960's Grothendieck style AG, to finally gain admission to the subject.I love this book.

There are three themes one can mention in algebraic geometry, 1) projective varieties, 2) schemes 3) cohomology.The first topic concerns the objects most geometers are interested in.The second one is of more interest to number theorists, but also has value for geometers in understanding limits of varieties.The third is a powerful and abstract technical tool which is valuable to both schools.

So here is the difference between Shafarevich and Hartshorne:Shafarevich focuses mainly on varieties, as the title reveals, has nothing at all in volume I on schemes, and neither volume treats cohomology.Hartshorne quickly reviews varieties then goes straight to schemes and cohomology, presenting schemes before cohomology.Thus Shafarevich is much more elementary than Hartshorne, and is a good introduction to that book.For a book treating cohomology before schemes, try George Kempf's algebraic varieties, but hartshorne will eventually be essential.

A few negative aspects to Shafarevich:it has a large number of typos and outright errors, in spite of numerous editions and reprints.One of the worst mathematical mistakes is the false assertion in the section I.6.3 of the first edition, that for any regular map f:X-->Y the set of points of Y over which the fibers of f have dimension at least r, is closed in Y. One needsthe map f to be closed, e.g. proper, for this to hold, and unfortunately this false result is used in the treatment of the tangent bundle of a variety.The proof of thenormalization for curves seems also flawed to me.All these mistakes can be fixed, and even in the present flawed form, this book still has no peer in readability and geometric richness with the same scope (although the undergraduate book by Miles Reid, Shafarevich's translator, is excellent for what it covers).I recommend it highly.

I would give it 4 stars for the errors, to leave room for a higher score for a book not only well conceived and well written but also well edited, but there is no other book that approaches this one in its strengths so how can one give it only 4 stars?But how can this book go through so many printings and not repair the most egregious mistakes?(There are other famous books out there with more and worse errors, but we who do not write books should not be too harsh in this regard.What if no one had the courage to attempt to explain this difficult stuff to others?)

Someone hasn't read the first page of the index!!!!!!
I have been a student of AG for the past six years and I have come to the conclusion that Shafarevich is a great place to start.Having said this, one must have the necessary background in algebra and topology.I disagree with the other reviewer about doing this after Hartshorne--start here then do Hartshorne!!!Oh ya, the index refers to both volumes 1 and 2; read the first page of the index!!!

After Hartshorne!!!
This book is very good for the secondary course after learning with Harshorne's Algebraic geometry. ... Read more

Product Description
How do you fold a sheet of paper into the shape of a whale? How do you measure the area of a pizza pie? How can you draw a circle within a circle without lifting your pencil from the paper?

Now you can discover the answers to these and other fascinating questions about elementary geometry—the study of shapes. Packed with illustrations, Geometry for Every Kid uses simple problems and activities to teach about acute and obtuse angles, parallel and perpendicular lines, plane and space figures, and much more! By arranging the pieces of an intriguing Chinese puzzle called a tangram, you'll explore all the different shapes you can form. You'll also learn how to create a colorful 3-D drawing that seems to rise right off the page! And, by building a geoboard, you'll discover a quick, fun way to compare the area of different geometric figures.

Each of the activities is broken down into its purpose, a list of materials, step-by-step instructions, expected results, and an easy to understand explanation. Every project has been pretested and can be performed safely and inexpensively in the classroom or at home.

Also available in this series from Janice VanCleave:

• ASTRONOMY FOR EVERY KID
• BIOLOGY FOR EVERY KID
• CHEMISTRY FOR EVERY KID
• DINOSAURS FOR EVERY KID
• EARTH SCIENCE FOR EVERY KID
• GEOGRAPHY FOR EVERY KID
• THE HUMAN BODY FOR EVERY KID
• MATH FOR EVERY KID
• PHYSICS FOR EVERY KID

Customer Reviews (4)

Janice VanCleave's Geometry for Every KId
I just love this book. It's not only Geometry for every kid, it's really helpful for adults as well.

Janice VanCleave's Geometry for Every Kid
This is a great book. It is offers a variety of activities that not only teach geometric concepts, but are also fun!

Great fun with my eight year old!
I bought this for my son who loves math and building things. We've only gone through four chapters so far, but we've had great fun identifying how many right angles there are in his room and folding a oragami whale. This book was a real treat for him. Parents of gifted children should dive into this whole series with their kids, and I think they're great for teaching any kid that math is fun!

Janice VanCleave has done a great job as usual !!!!!
Her books teaches geometry using hand-on activities for all grade levels which children love.It teaches form the basics of geometry to the advancements. Teachers and students will both find this book interesting ... Read more

Customer Reviews (1)

Great for homeschoolers
This is a wonderful geometry text and very reasonable. We are a homeschool family and this is perfect for us. ... Read more

Product Description
Contains detailed solutions for all odd-numbered exercises in Chapters 8-14. ... Read more

Customer Reviews (5)

Back of the Book
Decent review but only covers odd numbers. Bought it via Amazon and came a little earlier than the estimation.

Should be minus stars Rubbish!!!!!!!!!!!!!!!!!!
I cannot disagree anymore with one the reviewer that this book is rubbish. Why: 1) the solution manual is just covering half of the questions. 2) Only the odd answers given and so why I need to buy it. 3) no answers for even nunmber questions. Tha author is just want to make money!!! It is a pity that Thomas' Classic is ruined by that Guy!! Shame on you the author of this book!!!!

Useless
I bought a Student Solution Manual in the hopes that it would contain solutions that supplement the text. However, this book only contains the same solutions that are in the text, the only difference being explanation is provided on a few of the problems for each chapter (usually the more involved ones). If you are looking for solutions to check your work for the even problems, this will not help you.

Calculus and Analytic Geometry:Student Solution Manual, Part
The examples worked in this manual are a great help when used along side of the text book.A must have for everyone purchasing the test book.

Well done solution manual
It was very helpful and useful.This solution manual is a great way for students to check their work and learn from their mistakes.I found some (minor) typo errors that needed to be fix. ... Read more

Product Description
ENGAGING MATHEMATICS, SUPPORTING ALL LEARNERS, DELIVERING THE CONTENT NEEDED TO MEET TODAY’S STANDARDS

Glencoe Geometry delivers the depth of content required to meet the new changes in your state’s standards; provides relevant applications for teens; unique instructional resources for teachers; and is available in print, online, and on CD-ROM or DVD formats. ... Read more

Customer Reviews (1)

I ordered the wrong book
Thank you for taking it back and crediting my acct so promptly. You did right by me. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Customer Reviews (7)

The Foundations of Geometry - Forgotten Books edition

The FORGOTTEN BOOKS edition of Hilbert's Foundations of Geometry isn't Hilbert's Geometry. Notice the number of pages (which I didn't when ordering it). This publication contains ONLY the diagrams in large format (with a very few absent) from the text of Hilbert's Geometry. There is no title page or author listed, but this is in fact what the content is from. It is clearly a scan from an old book, so there must be some historical context for it. Maybe someone can clarify the mystery. I give it 5 stars because these comments will probably show up among the reviews of Hilbert's full text and I don't want to skew the star rating of the book, but this particular reprint I don't find of any actual value, except that it's from Hilbert and there may be some interesting reason why it occurs as an independent publication.

Along with this reprint, I also ordered the FB Classic Reprint of Elements of Geometry and Trigonometry by Charles Davies. These two books are the first reprints I've purchased from any of the reprint publishers selling on amazon. For more on the quality of Forgotten Books reprints, see my review of Davies' book. The mysterious Hilbert-diagrams text they sell under the title of Hilbert's Foundations of Geometry is, I suspect, an anomaly. Besides, their honest page-count should raise questions about the content. Now you know what that content is.

Buy the Open Court edition - a better translation into English
For the best translation into English (not Townshend's translation) see Hilbert's "Foundations of Geometry" as extended by Paul Bernays, Open Court Publishing Co, second edition in English, 1971.(This should be a translation of the 10th and final edition in German by Bernays, which dates from 1968.)Bernays was Hilbert's assistant at Göttingen beginning in 1917 and his co-author of "Grundlagen der Mathematik" (1934-39).
Hardcover ISBN: 0875481639
Paperback ISBN: 0875481647

Incomplete
This is the first book ever to present the axiomatic foundations of euclidean geometry. The first edition appeared in the nineties of the nineteenth century.

Most of the book can be read and appreciated by someone who is mature in elementary euclidean geometry (in fact the material was originally conceived to be used in a summer school for mathematics teachers in Germany). If you expect to find a treatment that will fill up all the gaps in the elementary books you will be disappointed, it does not. If you are looking for a text that does fill all the gaps try to get a copy Forders' book The foundations of Euclidean geometry,.

This edition is not based on the last German edition that is available and does not contain the appendices by Hilbert and thesupplements by Paul Bernays, so as a text on the foundations of euclidean geometry it is not useless but it is surely crippled.

I do not dare to give a book with Hilberts name on it less than five stars.

Enjoyable
Hilbert gives his new system of axioms and studies their consistency, independence and necessity. Consider for example the theorem that the angle sum in any triangle cannot be greater than two right angles. We can prove it as follows. Consider a triangle ABC with the angles labelled so that ABC<=ACB. Let D be the midpoint of BC. Draw AD and extend it to E so that AD=DE. By SAS, ACD=BDE, so that angle CAD=angle BAE and angle DBE=angle ACB. Thus ABC has the same angle sum as ABE. ABC<=ACB means that AC=BE<=AB, so angle BAE<=angle AEB, so angle BAE<=angle BAC/2. In other words: for any angle A in any triangle we can construct a new triangle with equal angle sum that has as one of its angles A/2. By repeating this process we can make the angle A as small as we like. Thus, if the angle sum of some triangle was greater than two right angles, and we applied this procedure, we would get a new triangle where two of the angles are greater than two right angles, which is impossible. The "as small as we like" part gives away the fact that we are relying on Archimedes' axiom, which is necessary. "The investigation of this matter which [Max] Dehn has undertaken at my urging led to a complete clarification of this problem. ... If Archimedes' axiom is dropped then from the assumption of infinitely many parallels through a point it does not follow that the sum of the angles in a triangle is less than two right angles. Moreover, there exists a geometry (the non-Legendrian geometry) in which it is possible to draw through a point infinitely many parallels to a line and in which nevertheless the theorems of Riemannian (elliptic) geometry hold. On the other hand there exists a geometry (the semi-Euclidean geometry) in which there exists infinitely many parallels toline through a point and in which the theorems of Euclidean geometry still hold. From the assumption that there exist no parallels it always follows that the sum of the angles in a triangle is greater than two right angles." Another interesting topic is the connection between laws of algebra and the theorems of Pappus (which Hilbert calls Pascal's) and Desargues. Geometrically, we can multiply two numbers a and b using only the axioms of projective geometry as follows. We choose a line to be the "x-axis" and call one of its points the origin O and another of its points the unit 1. Mark Oa and Ob on this line. Draw another line, the "y-axis", through O. Pick some point i on the y-axis. Connect 1 and i, and draw the parallel to this line through b, meeting the y-axis at b' (as usual, "parallel to l" means: meets l at an arbitrarily designated line called the line at infinity). Connect a and 1 and draw the parallel to this line through b'. In Euclidean geometry this line cuts the x-axis at ab. In general, then, we may define multiplication in this way. The algebraic identity ab=ba now becomes a geometric theorem. This is the beautiful part: ab=ba is not just any old geometric theorem, it is in fact equivalent to Pappus's theorem: the construction of ab consisted of the line connecting 1 and i and three more lines, the construction of ba consists of the line connecting 1 and i and three more lines, each of which is parallel to one of the lines from the ab construction. Therefore, deleting the line connecting 1 and i, Pappus applies and says ab=ba. Similarly, Desargues is equivalent to a(bc)=(ab)c.

Available for Free
This historic book is available for free from Project Gutenberg http://www.gutenberg.org. Search for Geometry. This book is one of a few books available. This is the complete Open Court text. It is available both as a pdf file and a TeX file. ... Read more

Product Description
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition and trigonometrical formulae. However, the book not only provides students with facts about and an understanding of the structure of the classical geometries, but also with an arsenal of computational techniques for geometrical investigations. The aim is to link classical and modern geometry to prepare students for further study and research in group theory, Lie groups, differential geometry, topology, and mathematical physics. The book is intended primarily for undergraduate mathematics students who have acquired the ability to formulate mathematical propositions precisely and to construct and understand mathematical arguments. Some familiarity with linear algebra and basic mathematical functions is assumed, though all the necessary background material is included in the appendices. ... Read more

Customer Reviews (2)

Too Advanced for most
This is so rigorous it is only for the advanced mathematician. I was looking for something much more accessible. I'll have to keep looking.

Great math book
This book about euclidean and non-euclidean geometry is great! A must for researh or math class! ... Read more