Product Description

Customer Reviews (18)

Excellent examples
Finally, an understandable upper-level math text! Greenberg walks you step-by-step through the proofs of the foundation ideas for each chapter (with selected exceptions left as examples. However, these proceed predictably from other examples that do have full proofs). There are numerous exercises at the end of each chapter, typically professors will choose a handful that they find interesting or amusing and assign those. No answers are at the back of the book. The problems require proofs and I have yet to see a text that provides answers to proofs problems in the back. Anyhow, many problems have multiple approaches. I actually found this book easier to understand than the professor.

an excellent and really untertaining book
There are already 16 reviews of this excellent and exciting book so i will only add that some people complained about the great number of results of the core text the reader is asked to search proofs as exercises. For a mathematically inclined reader this is not such a big trouble because most of these exercises have extended indications which math-inclined people can easily transform in a complete and sound proof. For myself i had almost no trouble with them (there is one exception with the section on axioms of beetwenness in chapter 3, i took the strategy of admitting the propositions of this section i could not prove as complementary axioms (these propositions are visualy obvious and easy to accept) so i proceeded further for the really interesting matters).
So the difficulty is only for people who did not have a mathematical training as college junior. Even in this casethey can learn a lot about the nature and purpose of pure mathematics and, if they are persistent and enduring, how to read and write mathematical proofs.
As a Frenchman i wonder why such a good book has not been translated in French, it really deserves it because books in French on geometry are so often unexciting and boring.

Quintessential Work on Non-Euclidean Geometry
I had the pleasure of reading and studying the Second Edition of this text while in college.This course with this text was my favorite course during all of my undergraduate math courses.

Being a fan of the subject, I was eager to see the new Fourth Edition of the text.The Fourth Edition is quite expanded from earlier editions, going past the wonderful main story of the Parallel Postulate - told better by Greenberg than any other author, IMHO - and diving into the different non-Euclidean geometries that "open one's eyes" by setting aside the "obvious axiom of a unique parallel". The last chapters are greatly enhanced, with a superb presentation of the issue of straightedge and compass constructions in the Hyperbolic plane.

This presentation of Non-Euclidean geometry is more serious than the "popularized" books on advanced mathematical topics.If you're looking for a "light, fun" reading of this topic, this is not the book for you.

I feel that the real power of the story of the maturing of intellectual thought, so brilliantly portrayed in the story of the Parallel Postulate, must be experienced, through the effort (and often hard work) of actually **doing** geometry, rather than just reading lightly about it. If you want to dive in and actual experience geometry (and the consequent rewards), then this is the book for you.The explanations are magnificent, the problems are wonderful (and, at times, very challenging), all culminating in the "wow!" of modifying the Euclidean way of thinking to a new and beautiful alternate geometrical universe.

As other reviewers have noted, this text reads like a great novel - a drama involving geometry.If PBS/Nova ever make a "What does Parallel mean anyway?" show, this text will be the basis for that show.

I believe this Fourth Edition can be considered the quintessential text on this topic, on which all future discussion of the topics can be based, including both the introductory materials, as well as moving to the forefront of research on many topics in Hyperbolic geometry.

For a university course, weaker students will find this text quite challenging, and possibly too hard.For average students, this text will provide sufficient challenge and interest, and ample areas in the text that will not overwhelm.For advanced students, this text will certainly challenge in many different directions and interests, both in the later chapter discussions, and various problems throughout.

Greenberg's writing is meticulous - you will never find an error, a comma out of place, nor a sentence that is not perfect.

Euclidean and Non-Euclidean Geometries, Fourth Edition, by Marvin Jay Greenberg
The Fourth Edition of M.J. Greenberg's textbook is a wonderful addition to the geometry textbook literature. No praise could be higher than to say that it is even better--indeed, a good deal better--than the highly regarded earlier editions. There are important revisions to each of the chapters and appendices, some of them extensive. As Greenberg aptly notes: "this book is a resource for a wide variety of students, from the naive to the sophisticated, from the non-mathematical-but-educated to the mathematical wizards."In this reviewer's opinion, Greenberg's fourth edition along with the Robin Hartshorne's mathematically more technical Geometry: Euclid and Beyond (2000)--a text to which Greenberg repeatedly makes reference--are far and away the most informed, up-to-date, and historically and philosophically sensitive geometry texts on the market today. No one with an interest in the foundations of geometry can afford to be without copies of these two great works.

A very good book about Geometry
This is a very good book about Euclidean and Non-Euclidean Geometries.
Well written, this book introduces to the lector in the historical context of the development of the Geometry.
I enjoyed very much.

Why is it so cheap, now (April, 2008) ?Because, this is the 3rd edition and exists a new 4th edition since September 28, 2007. ... Read more

Product Description

Customer Reviews (1)

A classic on Euclidean geometry
Thank you Dover!! This is one of the two English books in print that give a fairly complete introduction to advanced Euclidean geometry, the other one being the comparable text by R A Johnson, Advanced Euclidean Geometry (Dover Books on Mathematics). The book contains all the classical theorems with full proofs, including many theorems that belong to the so called triangle geometry that was developed in the last quarter of the nineteenth century. Due to geometry software the subject is becoming popular again. The book also contains a treasure of exercises, but no solutions which could be a nuisance. But what use are the solutions? Problems should be solved and not looked up!. Many problems are about geometric constructions. If you prepare for a mathematical contest or if you are interested in a complete overview of the classical plane geometry (for instance after reading Ross Honsberger's "Episodes"), this is your book.

The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry. ... Read more

Product Description
This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important ares of non-Euclidean goemetry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics and teachers, who need to know how geometry is used in addition to its formal theory. ... Read more

Customer Reviews (2)

Amateurish
Chapter 1 on Euclidean geometry displays the author's poor taste as well as his profound misconception of what it means to prove something. We learn on page 19 that the area of a triangle is (1/2)(base)(height). The only justification for this is that it is "often" clear by cutting and pasting. Fine. We don't have to prove every little thing. But then there follows a "proposition 1.8.1" in which Jennings supposedly "proves", by using this formula, that moving the tip of a triangle along a line parallel to the base doesn't change its area. Jennings is also very fond of isometries and use them to "prove" SAS congruence. Since the discussion of isometries is purely descriptive, with no claims to axiomatic status, this essentially amounts to saying that "the triangles are congruent because I say so", no matter how much it is padded with fancy language (let T be the isometry such that this-and-that, etc.). Although this proof is questionable, at least here Jennings is in the company of Euclid (I.4). But Jennings quickly proves himself unworthy of such dignified company by proving SSS using the cosine theorem, which is certainly not Euclid's proof (I.8). Some other parts of the book are less disastrous, especially when Jennings borrows lots of material from Courant & Robbins and Hilbert & Cohn-Vossen. Still, Jennings almost manages to destroy even these beautiful things through thoroughly tasteless exposition; the proofs typically consist of elaborate justifications of trivial details by mountains of useless symbolism while the key ideas are not addressed at all ("It is important to note that [something completely trivial]: this is because blah, blah, blah, define L(z_4*), blah, blah, blah. It is clear that [important step], so we're done."). It is also ridiculous to claim that "projective geometry blossomed during the eighteenth [century]" (p. 115).

Excellent elementary introduction to modern geometry
I am a Ph.D student in the field of symplectic geometry and topology. This book introduces the foundations of modern geometry in a beautiful and a very clear way,and I am saying this having some experience with geometry and topology books. If you are a skilled high school student or an under graduate student for mathematics or related area,this is a good book to start with in understanding what is modern geometry. The level of the book is about undergraduate level using very elementary notions. The content of the book is: Euclidean geometry and its logical foundations(so one could understand the motivation of the other geometries), Sphirical geometry,conic sections,Projective geometry,and the ending chapter is about the geometrical foundations of special relativity. The approach is not theorem-proof style but rather a more intuitive approch!. This is a recommended book. ... 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

Product Description

This two volume work on ... Read more

Product Description
This charming book introduces us to topics in hyperbolic geometry in a delightfully informal style.

Journey into Geometrics can be read at two levels. It can be studied as an informal introduction to post-Euclidean geometry, or it can serve as background material for university students. The material presented in the text is extended by carefully selected problems. The background required is minimal, standard high school geometry, yet the serious student, aided by problems attached to each chapter, should acquire a deeper understanding of the subject. ... Read more

Customer Reviews (1)

Another magical journey through the wonderland of geometry
One cannot say that Lewis Carroll would be pleased, since he helps with the narration of this account of some additional travels of his darling Alice. Many of the other original Wonderland characters also help Dr. WhatIf and him explain and illustrate a wide variety of geometric problems.
Although the author does an excellent job in presenting difficultconcepts, this is not a textbook, Thinkof it as an excursion into thewonderland of advanced geometry. Experts will frolic, amateurs with grinand eventually understand and beginners will smile right up to the point(pun intended), where they get lost.
Problems are given at the end ofeach chapter and detailed solutions appear in the back of the book. Apartial list of the topics covered includes inversions, reflections, ahyperbolic T-party, hyperbolic geometry, and projections. Verse with adecidedly Carrollean flavor appears throughout the text.
A joy toread and even better the second time through, it is a fitting sequel to theoriginal adventures.

Published in Journal of RecreationalMathematics, reprinted with permission. ... Read more

Product Description
Known for many years as BarronÂ's Easy Way Series, the new editions of these popular self-teaching titles are now BarronÂ's E-Z Series. Brand-new cover designs reflect all new page layouts, which feature extensive two-color treatment, a fresh, modern typeface, and more graphic material than everÂ-- charts, graphs, diagrams, instructive line illustrations, and where appropriate, amusing cartoons. Meanwhile, the quality of the booksÂ' contents remains at least as high as ever. BarronÂ's E-Z books are self-help manuals focused to improve studentsÂ' grades in a wide variety of academic and practical subjects. For most subjects, the level of difficulty ranges between high school and college-101 standards. Although primarily designed as self-teaching manuals, these books are also preferred by many teachers as classroom supplementsÂ--and for some courses, as main textbooks. E-Z books review their subjects in detail, and feature both short quizzes and longer tests with answers to help students gauge their learning progress. Subject heads and key phrases are set in a second color as an easy reference aid. BarronÂ's E-Z Geometry covers the "how" and "why" of geometry, with examples, exercises, and solutions throughout, plus hundreds of drawings, graphs, and tables. ... Read more

Customer Reviews (28)

well organized, easy to follow!
I bought this book as a supplement for my 9 year old who excels in math and loves exploring math in different forms. We just go over a few pages every day. The flow is great. It introduces the essentials of geometry, just the right amount for introduction purpose. It help building good fundamental knowledge. Strongly recommend it!!

Not very good
I got this to help with geometry and to be honest it was not very helpful. I wanted something that could go more in depth then my textbook and this said just about the same exact thing as my textbook. If you are just trying to brush up on your math by yourself it may help you but if you are a student looking for some extra help this will not aid you at all.

Don't judge a book by it's cover...
I was extremely disappointed in this book. Not even halfway through the first chapter I was completely confused. If you're like me, you want to know why something is, and how do you explain it in a way that's understandable. I had a horrible time understanding the way in which they explained how to label an angle etc. On a brighter note, I think this would probably be a useful text to use with another source, such as an actual geometry textbook. I also tried Geometry for Dummies which was not very easy to understand either. Maybe Geometry just isn't! :p I finally decided to purchase the "Geometry Demystified" which of all three books, seems to be the most informative.

A very dry read, definitely not easy
I don't recommend this book for beginners.First it's the kind of book where you have to read the chapters several times before you 'get it'.The exercises are complicated and confusing.For someone who hasn't picked up a geometry book in decades - look elsewhere.

Perfect
This book is exactly what I was looking for it help my daughter with sophomore geometry. Would highly recommend it. ... Read more

Product Description
This textbook demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries. This richly illustrated and clearly written text includes full solutions to over 200 problems and is suitable both for undergraduate courses on geometry and as a resource for self study. ... Read more

Customer Reviews (7)

"Who is who" in geometry
The book presents clearly several geometries in the spirit of Kleinean unifying view of geometry. It begins with a recapitulation of many important facts on conic sections, since conic sections played an extraordinary role in science over two thousand of years, and on the other hand the authors use conic sections as very representative geometric objects to explain transformations that specify affine, projective, inversive, non-Euclidean and spherical geometry. The key ideas, results and techniques that served as corner stone in the discovery and development of geometries are presented clearly and fluently using algebraic methods combined with rich illustrations, which provide the shortest path to the proofs and relationships between geometries.As an excellent example of this approach is the Joachimstal'snotation for plane conics. The book can also serve as `who is who' in geometry. However, the book has no references to the literature, which would have been very useful for further reading.

Avni Pllana

My Favorite Geometry Book.
I have purchased and worked through several geometry books in the past year.This is, by far, the best one I've come across. It is modern, it is fun, and it is enlightening.

I love the clear worked out numerical examples. As I write geometric computer programs it gives me a way to check each function as I go along.It has an abundance of wonderful illustrations that help you understand the theorems and concepts.

I found this Geometry to be clearly and fully presented for an independent reader, and not just a supplement to some lecture course.There is a minimum amount of mathematical history included, but it is well-chosen and well-written.

Plus, I learned how to draw the tessellations of the Poincare disc, ala M.C. Escher.So that alone made it worth the price and the effort.

Definitely 5 stars.

Geometry
It is a beautiful book to support University course
"Foundations of geometry" for undergraduate students.

A Nice Introduction to Geometrys - Precise and Accurate!
This book is at the level of a freshman mathematics course.

Mainly deals with Affine, Projective, Inversive, Spherical and Non-Euclidean geometrys.The beauty of the book is in its accuracy.Someone has done a good job of technical editing!There is always arisk of getting things wrong when attempting to make mathematics accessible at a lower level.The authors seem to have avoided that pitfall with significant success.The subject matter is focused and to the point. At each point, it precisely explains what is intended and moves on without digressions.

I have had significant interests in geometries, and work in a area that uses some elementary projective geometry.At times I get asked some relatively simple questions such as "why do we need 4x4 matrices in Computer Graphics?"Often I just answer such questions to the minimum (" ... it makes applying translations easier ...").I never proffer a deeper answer because most people I run into either have no background to understand a more technical explanation in terms of the algebra of projective planes or they don't care - they don't need to, for most of their work!.(Many of the computer graphics folks I have met think that the homogeneous coordinates is an ad-hok concept that was invented as a "trick"!)

Occasionally, I do run into some who are interested in knowing the analytical reasoning behind some of the transformations used everyday in computer graphics.This book demonstrated to me how to talk to some of those without having to use very abstract concepts of geometry.I read it first in 1999.I have revisited it since, many times for the nice figures they provide.First time, it took me about three "after work" months to study through the book - not bad at all for a 350+ pages mathematics book!

By looking at the diagrams in the book, I learned how to draw simple diagrams instead of abstract symbols to explain the concepts, theorems and problems.For a book that is as simple, the technical content is remarkably precise and accurate.The book assumes minimal background in mathematics.

Recommended for people interested in computer graphics and want to understand the transformations in there deeper (for whatever reason!), under-graduate students interested in geometry, and for anyone with a casual interest in geometry.

Good and enjoyable for a wide range of readers
A quarter century ago I noticed that some of the graduate physics students in my university were carrying around copies of Scientific American.Armed with that clue, I dug out every article on the newly discovered fundamental particles.Within the space of a week of fairly easy reading I was able to acquire a good sense of what this subject was all about.These articles explained the basic stuff our professors assumed we must know (but most of us surely didn't).

Brannan, Esplen, and Gray's Geometry accomplish for math what those Scientific American articles did for physics: speaking at a level accessible to anyone with a good high school education, they bring the interested reader up to speed in affine, projective, hyperbolic, inversive, and spherical geometry.They provide the simple explanations, diagrams, and computational details you are assumed to know-but probably don't-when you take advanced courses in topology, differential geometry, algebraic geometry, Lie groups, and more.I wish I had had a book like this when I learned those subjects.

Individual chapters of about 50 pages focus on distinct geometries.Each one is written to be studied in the course of five evenings: a week or two of work apiece.Although they build sequentially, just about any of them can be read after mastering the basic ideas of projective geometry (chapter 3) and inversive geometry (chapter 5).This makes the latter part of the book relatively accessible even to the less-committed reader and an effective handbook for someone looking for just an overview and basic formulas.

The approach is surprisingly sophisticated.The authors do not shy away from introducing and using a little bit of group theory, even at the outset.(Scientific American, even in its heyday, never dared do that.)They present all geometries from a relatively modern point of view, as the study of the invariants of a transitive group of transformations on a set.Many explanations and proofs are based on exploiting properties of these transformations.This brings a welcome current of rigor and elegance to a somewhat static subject long relegated to out of date or sloppy authors (with the exception of a few standouts, such as Lang & Murrow's "Geometry").

One nice aspect is the authors' evident awareness of and appreciation for the history of mathematics.Marginal notes begin at Plato and wind up with Felix Klein's Erlangen program some 2300 years later.Although the text does not necessarily follow the historical development of geometry, its references to that development provide a nice context for the ideas.This is an approach that would improve the exposition of many math texts at all levels.

The authors are British and evidently write for students with slightly different backgrounds than American undergraduates.Obvious prerequisites are a mastery of algebra and a good high school course in Euclidean geometry.Synopses of the limited amounts of group theory and linear algebra needed appear in two brief appendices.However, readers had better be intuitively comfortable with matrix operations, including diagonalization and finding eigenspaces, because matrices and complex numbers are used throughout the book for performing computations and developing proofs.A knowledge of calculus is not needed.Indeed, calculus is not used in the first two-thirds of the book, appearing only briefly to derive a distance formula for hyperbolic geometry (a differential equation for the exponential map is derived and solved).During the last third of the book (the chapters on hyperbolic and spherical geometry), some basic familiarity with trigonometric functions and hyperbolic functions is assumed (cosh, sinh, tanh, and their inverses).Definitions of these functions are not routinely provided, but algebraic identities appear in marginal notes where they are needed.

Now for the quibbles.The book has lots of diagrams, but not enough of them.The problems are usually trivial, tending to ask for basic calculations to reinforce points in the text.The text itself does not go very deeply into any one geometry, being generally content with a few illustrative theorems.An opportunity exists here to create a set of gradually more challenging problems that would engage smarter or more sophisticated readers, as well as show the casual reader where the theories are headed.

This book is the work of three authors and it shows, to ill effect, in Chapter 6 ("non-euclidean geometry").Until then, the text is remarkably clean and free of typographical and notational errors.This chapter contains some glaring errors.For example, a function s(z) is defined at the beginning of a proof on page 296, but the proof confusingly proceeds to refer to "s(0,c)", "s(a,b)", and so on.

The written-by-committee syndrome appears in subtler ways.There are few direct cross-references among the chapters on inversive, hyperbolic, and spherical geometry, despite the ample opportunities presented by the material.Techniques used in one chapter that would apply without change to similar situations in another are abandoned and replaced with entirely different techniques.Within the aberrant Chapter 6, some complex derivations could be replaced by much simpler proofs based on material earlier in the chapter.

The last chapter attempts to unify the preceding ones by exhibiting various geometries as sub-geometries of others.It would have been better to make the connections evident as the material was being developed.It is disappointing, too, that nothing in this book really hints at the truly interesting developments in geometry: differentiable manifolds, Lie groups, Cartan connections, complex variable theory, quaternion actions, and much more.Indeed, any possible hint seems willfully suppressed: the matrix groups in evidence, such as SL(2, R), SU(1,1, C), PSL(3, R), O(3), and so on, are always given unconventional names, for instance.Even where a connection is screaming out, it is not made: the function abstractly named "g" on pages 296-97 is the exponential map of differential geometry, for instance.

Despite these limitations, Brannan et al. is a good and enjoyable book for anyone from high school through first-year graduate level in mathematics. ... Read more

Product Description
Each chapter devoted to single type of problem with accompanying commentary and set of practice problems. Amateur puzzlists, students of mathematics and geometry will enjoy this rare opportunity to match wits with civilization’s great mathematicians and witness the invention of modern mathematics.
... Read more

Customer Reviews (3)

Very Good for the interested reader
Although not reasonable for most high school students, this book does bring to light the background of modern geometry through its treatment of impossible and hard to solve problems.

Excellent background reading for a teacher!

Classic problems of geometry made simple
The principles of geometry are both elegant and timeless. One cannot help but understand why the Greeks considered it a pinnacle of intellectual achievement. This book sets down several of the classic problems, explaining them in such a clear way that it is easy to forget that it sometimes took centuries of work before the problem was resolved. Of course, those who first toiled on the problems did not have some of the additional machinery that we so take for granted today.
The problems covered are trisecting an angle, squaring the circle, constructing regular polygons and constructing a cube whose volume is twice that of a given cube. The background needed to understand the problems and solutions is nothing more than a solid grounding in basic algebra and trigonometry. Calculus is mentioned, but not used. Problem sets are included in all chapters and solutions to all are in the back of the book. They are well-posed, solidly reinforcing the points made in the text.
This is a book that covers several thousand years of progress in geometry in a little over one hundred pages. It is done well and it can be used as a supplement in any course in geometry, from high school to college.

Well done..
Bold has a gem of a book here.It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years.

Thetitle describes the book perfectly.These really are "Famous Problemsfrom Geometry" and he does indeed explain how to solve them.

Thebook has four major sections/chapters.He discusses in detail the threeproblems from antiquity (one section each):squaring a circle, doubling acube, and trisecting an angle.Furthermore, he spends significant timewith constructions of regular polygons (the fourth section) - which onescan be constructed and why. He also discusses which ones cannot beconstructed and why.

The reader will be expected to understand conceptsfrom Modern Algebra, particularly the concept of a Field.While Bold doesspend time explaining what a Field is, his definition is quick and isassumed to be more of a refresher for someone who has already learned aboutthem.Bold also has a section on Complex Numbers where he derives one ofthe formulas used later in the book.Again - this section is assumed to bea refresher on Complex Numbers.High School Geometry or Algebra studentswould have significant trouble understanding his explanations andproofs.

Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem beingstudied.The problems are good.As a third year college student majoringin mathematics, I found the explanations/solutions to be sometimes hard tofollow.He assumes a great deal about the reader's level of proficiency inmath and in geometry.As a result, he liberally skips steps in proofs thatare assumed to be "obvious."

If you're expecting simple proofsto these problems, you're not going to find them.If they were simple,they wouldn't have taken 2000 years to solve.But they are explainedclearly here in terms that anyone with a college degree should be able tounderstand.

Overall, a superb book.A must have for anyone interestedin the famous problems from the history of Geometry. ... Read more

Product Description

Schaum's has Satisfied Students for 50 Years.

Now Schaum's Biggest Sellers are in New Editions!

For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates its 50th birthday with a brand-new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study.

Schaum's Outlines-Problem Solved

More than 400,000 sold!

This review of standard college courses in geometry has been updated to reflect the latest course scope and sequences. The new edition includes an added chapter on Solid Geometry and a chapter on Transformation, plus expanded explanations of particularly difficult topics, as well as many new worked-out and supplementary problems.

Customer Reviews (3)

Abysmal typesetting
The content seems okay.Free versions of Euclid Elements are available, though, as PDFs.

The typesetting is terrible, though!Every single image and math font and mathematical character is done with the following problems:
1.Blurry.
2.Faint.
3.Differently sized than the line it is in.
4.Heavily pixellated and blocky.

For example, there is one line that contains "... OA, OB, and OC ..." -- and these three items are in 8-point, 16-point, and 28-point type.There are dozens of typesetting problems like this on every single page.

Every single geometric line is heavily pixelated, instead of crisp.

This book saved my bacon!
This book condenses out the fluff from a typical textbook, and details solution methods for almost every conceivable problem.The price is a STEAL compared to hundred-dollar textbooks.If you are struggling, or if you want a great book to use before that big test, you have to get this book.I'm getting all A's on my Geometry tests now, and their concise explanations helped solidify new concepts.

not for kids
The thing I like about the Schaum's series is that they don't try to be your friend.If you're going to try to sit down to learn something intricate like geometry, you've got some serious work to do, and the sooner you get to it the better.To this end, there are no pictures in the book (other than geometric diagrams, of course), no blurbs on famous geometers or famous applications of geometry.No, this sucker's as dry as a bone.

But that's good.This is a book for motivated, adult learners.You've got your explanations, your worked examples, and then tons of exercises with answers to all of them in the back of the book - not just the odd.The thing I like about this book, now in its fourth edition (white cover), is that it takes an example-exercise approach to geometry, rather than forcing you to memorize postulates.

Even if your teacher is the most entertaining guy in the world, you're still going to have a lot of tedious work to do if you plan on mastering geometry.The way this book is laid out is an accurate reflection of that.

They say that many of these Schaum's outlines, while they might be helpful supplementary material for a course, do not go deep enough to replace the course itself.I would disagree if that charge were leveled against this one:Schaum's Geometry easily provides everything you'd get in a high school geometry course and more.

The only criticism of this book that I can muster is the following:of all the major branches of math, geometry is one you kinda need a live teacher for.For this reason, the Schaum's approach -- in parts -- is unsatisfying.The whole Schaum m.o. of humorless exercises, dry explanations, no pictures, etc. can work very well for algebra, calculus, trig, etc.

But geometry is a different beast.In particular I'm thinking of proofs.Since the Greeks, teachers have laid out postulates for their students, then given them a statement and asked them to prove it.This supernal art is really why I love geometry so much:it's like practice in thinking, and it's why I recommend it to people who want to improve the caliber of their minds even if you don't need math for anything.To quote Greg Mankiw, "Math is good training for the mind. It makes you a more rigorous thinker. . . . Your math courses are one long IQ test. [Colleges and companies] use math courses to figure out who is really smart."To which I add that math -- viewed this way -- properly begins with geometry.

Of course, Schaum's does ask you to do proofs.The problem is, it should not be the student himself who judges if the steps of his proof were fully articulated or not:for that, you need a real live human.If, alone in your garret, you write "Segment AB is congruent to CD" for one step of the proof, but then find that the answer key has it "Segment AB is congruent to CD by the definition of congruent segments," do you give yourself the point?

In other words, being an autodidact might be okay in other math areas, but the whole power of geometry hinges largely, I submit, on some unpleasant Other forcing you to articulate a proof without getting sloppy.

But I don't see how there's much that Schaum's can do about that.Still a fantastic text.

NOTE:The first two chapters of this workhorse used to be a review of basic algebra, but not anymore as of the 4th edition.This was unfortunate.Why did they delete them?Schaum's owns the material:what was the harm in letting them stay in?These chapters have been replaced by a one-page "warning" enumerating all the algebra you will probably need to negotiate this book.But here's the problem:if you don't feel comfortable with some of it, you are referred to Schaum's Outline of College Algebra.The problem with THAT is that the latter book more or less circularly assumes you're familiar with basic geometry, the point of this book!So Dr. Thomas, if you're still at the reins, please put those two chapters back if you put out a 5th edition. ... Read more

Product Description
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry’s correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
... Read more

Customer Reviews (7)

Geometric Overview of Core Math and Physics +++
This book presents a wonderful geometric overview of core math and physics. It is equally great for a preview or review of core math and physics. This work is done with attention to learning such core topics via a unifying and clarifying approach. Via this approach someone learns about a vector space approach to geometry via great cross-magnification of the illustrative sub-topics. I finally feel I clearly see the various sub-topics via the illumination of vector space geometry. But there is more -- physics methods, such as center-of-mass, are used directly [as primary mathematics] to magnify vector space geometry from the start. The notation is also clear and sharp as well as the mathematics presentation and the order of the chapters and topics. This is quite a unique timeless work +++

A bit longwinded
I didn't find this book to read like a novel.I got it hoping to learn about projective transformations for computer graphics, but was disappointed because of the method of presentation was too long to get through.I believe the text would appeal to those whose interest was strongly in geometry and had a college level background in math. I gave it three stars for the seemingly interminable proofs of geometric theorems that I had little use for.

Must have if on the road to Linear Algebra
This is one beautiful book. The whole book is one long thread about geometry and vectors. To make this review short, I'll say you absolutely *must* have this book if you want to set yourself on the proper track to Linear Algebra. In fact, this book could almost be considered an Analytic Geometry book 'done right.' But be careful: I said almost. By that I mean that some staple AG stuff is missing. For instance, no long discussions about a plane intersecting a sphere, no quadric surfaces. So it does lack the sort of drill exercises you need to succeed in an AG class - but such stuff is not its purported goal, anyway -but then again, your 'vector 6th sense' will increase tremendously with this book. I wish I had discovered this book while I was having my Analytic Geometry. Now I'm taking a Linear Algebra class and I'm glad I found this book.
It also is full of other interesting insights and relations to other topics, including some applications to Calculus (motion) and some topology.

A useful High School Geometry book for Computer Graphics
This is essentially a high school geometry book; but with a difference - its fully linear algebra based approach.If you are a beginner in computer graphics, and want to review elements of geometry and linear algebra, you will benefit from studying through this book.

The almost four hundred pages book is remarkably readable and is very consistent at that.There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision.

If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book.But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that.

Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc.I rarely have seen any of these topics mentioned in a book aimed at this level.

Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes.Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written bookthat is a quick read helps at that!

Perfect for first and second year, or physicists
The basics of the very deep connection between geometry and vector spaces. If you do undergrad math you will see everything in this book during first and second year. But what this book does is fit those bits together. He does this very nicely at an introductory level. If you are not in math, but need to learn some geometryfor a physics course, this will be a useful book.

It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples.

Keywords: tangent spaces, determinants, barycentric, linear transformations. ... Read more

Product Description
Analytic Geometry By Gordon Fuller. ... Read more

Customer Reviews (1)

Last of A Dying Breed
This is a classic textbook which introduces students to the fundamentalsof analytic geometry.In order to understand calculus, one must have athorough background in analytic geometry.Unfortunately, the current trendin math publishing is to forgo this great subject and present students withan motley mix of topics in a course called PreCalculus. Trigonometry andanalytic geometry end up getting the short shrift, with greater emphasisbeing placed on algebraic manipulation.This is a tragic loss for studentson a number of levels.Theyneed analytic geometry in order to succeed ineven first semester calculus, and yet for many analytic geometry isrelegated to the second or third semester of a calculus class in college,or in one chapter (or less) in a precalculus book!Also, the analyticgeometry allows the high school student a glimpse of mathematical beauty,of how things in mathematics work together: that mathematics holds up as asubject and is not just an assortment of tricks for various situations.Hopefully, the trend will turn around and this will not be the last of adying breed: that others will continue to offer and write expository workson this subject for the benefit ofstudents who wish to continue on tohigher mathematics. ... Read more

Product Description
Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michèle Audin, professor at the university of Strasbourg has written a book allowing them to remedy this situation and, and starting from linear algebra extend their knowledge of affine, euclidian and projective geometry, conic and quadric sections, curves and surfaces. It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for each exercise are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding. ... Read more

Customer Reviews (1)

Math
Un libro con un contenido propicio para lo que buscaba, el lenguaje se entiende claramente y no deja espacio a dudas ... Read more

Product Description
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day is an invaluable resource for both students and adults. ... Read more

Customer Reviews (4)

A MUST!
Okay, first of all, most geometry books for high school and college cost around $150, weigh more than a brick, and are filled with so much fluff that its impossible for students to remember it all and any teacher to effectively cover every aspect of every chapter unless he/she goes through the book very fast which will leave the student behind.

This book on the other hand is basic and to the point. It cuts out all the unesseccary fluff and covers the basics for geometry in a fashion that will leave the reader comprehending everything. Its written to the point that anyone could grasp the fundamentals of geometry. One of the best things I like about this book is that each page is very open with a lot of white space and is not crammed with a bunch of visual garbage which makes it easier for the eyes to follow.

The examples are very clear and shows the reader step-by-step how to work through each problem so they will be prepared to take the quiz at the end of the each chapter.

As for my personal opinion, I highly recommend this book for people who need a quick and easy refresher in order to prepare themselves for the harder more in-depth geometry courses in college. It also serves great as a reference. This book will build the basic foundation of your geometry studies. Also, I think that this book, combined with the Practical Math, Algebra, and Trigonometry versions are the best 4 books you can buy to prepare yourself for the ASVAB test. The books are small, to the point, and are all you really need to know to succeed.

Simple and easy, overall very good--would like more of it!
I bought this book for my teen daughter who is having trouble in her h/s Geometry class. My daughter is a gifted student, but put her in a classroom with a caring yet inaccurate teacher and watch those grades sink!This is especially troublesome when the teacher is giving incorrect information and mis-grading papers.My daughter's head was spinning--the teacher said one thing, the school textbook said another.End result: disenchanted, frustrated, and failing student (in a class full of failing students)!

Anyway, this book starts at grade 5 math (just as a very brief refresher) and quickly but easily glides into high school math. By page 28 my daughter was helped immensely with some of the concepts that were poorly explained or completely overlooked by her teacher. It has bolstered daughter's courage to know that she is not a complete math dummy (she is straight A's in Algebra 2). Armed with a new sense of mastery, she is going to have a conference with the teacher and review each and every incorrectly graded question on her prior exams.

The only "con" I have---and it is not a "con" at all but rather a plea to the author--is that there are only *SOME postulates and SOME examples given--none very agebraic, as far as I could determine.I wish the book had continued in its format and gone into the slightly deeper and more complicated "stuff".The book would be a real winner and it would sell many more copies if the author done so.An ideal format would have been to leave each chapter as it is, but add another 2 or 3 pages onto each chapter as optional--going into a TAD more detail with a couple of basic algebra equations for each.The author would pick up a bunch more readers because there is a HUGE market of students who need SAT/ACT
prep but not at the really complicated (translation: scarey) level of those big, fat, heavy Barron's/Peterson's/Kaplan's guides.

Hopefully the author is reading this post and will revise the book--it's very worthy of doing so!

*Rest assured, there is an ENTIRE list of postulates and theorems at the end of the book.

Great for GED prep, but not enough for SAT prep
Can you explain the difference between a ray and a line segment? What's the formula for calculating the volume of a pyramid?Does the phrase "distance = the square root of the square of X2 - X1 plus the square root of Y2 - Y1" mean anything to you?If not, you need this book - NOW.Here's why...

This book teaches you not only the theorems of geometry, but also its vocabulary.The 20 lessons are presented in a logical order, building on each concept in a sequential way.The lessons really only take about 20 minutes to complete and they are structured to give you enough chance to practice each concept so that you get it without getting bored.

When it comes to SAT prep, however, it falls short and here's why...

SAT problems are complex, involving at least two geometrical theorems to solve one problem.This book does an excellent job of presenting the theorems one at a time so that you can practice them, but it never gives you the opportunity to practice multiple theorems at once.For example, a typical question on the SAT might show a figure of a circle with a square overlapping part of it.You are told that the perimeter of the square is 24.The question asks you to give the area of the circle.Where do you begin to answer a question like this?To solve it you must first find the radius by finding the length of each side of the square.To do that, you must know the basic theorem that the perimeter of a square is 4x the length of each side (p=4s), then you have to solve for the unknown length of each side of the square, thus giving the radius of the circle.From there you must use the radius to find the circumference to solve for the area... you get the idea.

If you couldn't answer the questions at the beginning of my review, PLEASE get this book to use as a solid starting point for your geometry studies, but you'll do yourself a disservice if you rely on it as your only learning tool.

Bottom line: this book is hands-down the best tool for gaining a solid learning of the basics of Euclidian geometry. Completing the lessons in this book will give you a foundation solid enough to pass your a G.E.D., but this book alone won't prepare you enough for the SAT.

Geometry-success in 20 minutes a day
I am a homeschooling mother of 2 high school students.I have been teaching geometry but with great difficulty.It has been 30 years since I have taken geometry and it was not a happy experience then and a strugglenow.We do use a regular textbook but they are not always as clear a Iwould like them to be.I have been using this book as a back up inteaching the basics.They are clearly presented and easy to grasp.Eachchapter presents a concept with self tests to make sure you understandbefore you go on the the next idea.It is a great suppliment to ourtextbook and a good review for the GED test. ... Read more

Product Description
Covers topics in plane and solid (space) geometry.Pictorial diagrams with thorough explanations on solving problems incongruence, parallelism, inequalities, similarities, triangles, circles,polygons, constructions, and coordinate/analytic geometry. Aninvaluable aid for students. ... Read more

Customer Reviews (3)

Enough review and you get it
I wanted to get better at organizing my mind.You knew they taught Chess at West Point.Right?Well, Geometry makes you think.It makes you think in logical steps for problem solving.This book just gives example after example and exhaustively ingrains how to solve Geometry problems.Along the way it coincidentally builds your endurance for solving other problems.This may not be the best book or the most cutting edge but it has such a huge mass of answers and ways to arrive at them that you will absorb the methods.I like it.You might say that if you stare at these pages long enough that you learn by osmosis.I think there should be a book like this in every field of endeavor.Call it canned experience. Oh, a better typeset would be nice.

Excellent resource, really does the trick.
I bought this book right after I started a class in Linear Algebra where the first chapter had us working some geometric proofs using the rules for vector addition, subtraction, and scalar multiplication.

Although this book strictly focuses on geometry and does not use vectors in its proofs, it did clearly illustrate proofs that were easy enough to think through in terms of vectors.

The book is well-written and begins with a review of Methods of Proof, Lines & Angles, Perpendicularity, and Triangles before getting into specific geometric forms.

900+ pages and 900+ problems with a summary of theorems and properties at the end of the book.Some reviews at Amazon contain complaints about REA Problems Solvers, but I have always liked them and I really like this one.They are not intended to replace a textbook, but to give lots of examples over-and-above what a textbook would include.

For example, a few years ago I was studying College Algebra and I was having trouble understanding logarithms.So I reviewed the examples in the REA Problem Solver for Algebra and Trigonometry and worked some problems along with the REA book and then I saw how simple they really were.I have purchased REA Problem Solvers for Calculus, Differential Equations, and Linear Algebra as well and have found all of them to be helpful with some being more useful or better-written than others.

One of the complaints about these books is that they are all written using a Courier-style font.This is true, but there are still Greek symbols, integral signs, exponents, etc (e.g. you do not see 10-squared written as 10^2 - they use a superscript for the exponent).Another complaint that I have seen is that they contain errors.I have not noticed any, but that does not mean there are none present.I do not review these books cover-to-cover, but take a look at those topics that I need to review, so I may not have encountered any errors but they could still be present.

Purchased new, the books may seem a bit pricey if you are on a budget (nowadays the books have a list price of $30.95 for some subjects and $25.95 for others, with discounted prices ranging between $17.95 and $30.25).I always buy them from the affiliated 3rd-party booksellers on Amazon.I got my Geometry Problem Solver extremely cheap $3.15 plus $3.99 for S&H - total of $7.14 and the book arrived in a couple of weeks and was in excellent condition (like new!).

Most of the time I have spent in the $12-$15 range (incl S&H) for these guides.Even if I only were to find help on a single topic within the book, that, to me, is still a bargain.Especially so if you consider the price relative to the cost of tuition and textbooks.If you are really price conscious, most college libraries have copies that are rarely checked out.Until my copy was shipped, I used the one in our library and saw that it had last been checked out in 2004!

p.s. I am 54 years old and went back to night school and started studying math 3 years ago with College Algebra, Trig, PreCalc, Calc 1,2,3, Diff Eq, and now Linear Alg.I have had REA guides for all of the classes and have found them useful in every case.

GREAT BOOK
A great book loaded with proofs for geometry (SAS, CPCTC, etc) and geometic problems (Pythagorean Therom). ... Read more

Product Description
Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on how to solve challenging problems.The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next, through numerous problem solving techniques.A large collection of problems, varying in level of difficulty, are integrated throughout the text, and suggested hints for the more challenging problems appear in the instructor's solutions manual for use at instructor's discretion. ... Read more

Customer Reviews (4)

Euclidean and Transformational Geometry
"Euclidean and Transformational Geometry: A Deductive Inquiry" is a text that every mathematics teacher should have a copy of.Not only does it provide a comprehensive coverage of geometry, but it reads like a historical journey through the development of mathematics. The order of the topics is so logical that the reader cannot help but leap from theorem to theorem and take wonderful vacations along the way into islands of interesting problems.

This book's major strength is its clever combination of challenge, clarity, and instruction to teach ideas. The concepts are so clearly presented that students can easily learn them and the skillfully done illustrations augment the book's clarity. Each step of instruction is included and labeled so that the student will not miss some crucial step in their thinking. Multiple paths to the solution of a problem are presented so that the student learns alternative ways of thinking about that concept. This variation and the easy to understand style of writing makes this book interesting and an intellectually stimulating read.

As a high school teacher I find this book to be the richest single resource I have. Most of my students are directed to its well-worn pages multiple times throughout their time with me. I send them to read further about something that interests them, or to read an alternate explanation of a concept that they are struggling with, or simply to find some interesting and challenging problems to work on at home. I believe it is my duty to provide each student with problems that challenge them and are attainable at their level. Dr. Libeskind's book provides me with enough material for all of them, even the brightest of my students, from basic Algebra to Calculus. The problems are not necessarily hard, though some are, but more importantly they're interesting. Many students come early to my class or stay after simply to talk with me, or each other about problems they are working on from this book.

I highly recommend "Euclidean and Transformational Geometry" to all math instructors at the middle school, high school and college levels. Not only has reading it and doing the problems myself greatly enhanced my own understanding of geometry, it has made the subject become beautifully alive for me and the students I share it with. It is a book I cannot imagine being without.

Memorable Geometry
Fifteen years ago I was fortunate to be a student in Professor Libeskind's geometry course at the University of Oregon.The problems that he presented to us, and the way that he emphasized multiple approaches and deep understandings, helped shape my career as a high school mathematics teacher more than any other singular experience.I have now been teaching for thirteen years, and geometry is one of my favorite courses to teach.

My experience in Professor Libeskind's class was unforgettable.I wanted to share some of the problems with my honors students, and was overjoyed to discover that the wonderful collection of problems from that course have now been published as a book!I have yet to find a person who has opened this book and is not immediately interested in finding a solution to the famous Treasure Island Problem.The presentation, clarified through ample diagrams, immediately draws one into the world of exploring.Professor Libeskind writes in a style that invites students of all levels, encourages success, and provides support and assistance to those who need it.He patiently allows the student to make the connections first, but his clear explanations that reveal multiple connections between topics ensure that the student will fully understand the depth of the content.

The development of proof is one of the greatest strengths of this book.High school geometry texts typically begin with a list of theorems and then expect students to construct proofs.As a result, many students look at a proof and have no idea how to proceed.In this book, Professor Libeskind guides students through the process of constructing a proof as an extension of an investigation.I strive to teach my students proof through a similar process, and I am eagerly anticipating Professor Libeskind's high school geometry text.

The wide range of topics introduced and the connections developed between them help to foster a passion for mathematics.One of my favorite aspects of the book is the experience of using Geometer's Sketchpad to investigate problems that formerly led me to use reams of paper.Although the same exercises can be completed without Geometer's Sketchpad, it definitely adds to the experience and helps to keep students motivated.I have not found another geometry book that covers as much material and involves the student in learning as much as this one.

Fantastic Resource
As a middle school math teacher, I am constantly struggling to find textbooks that I can use with my advanced students.There is a dearth of high-quality math textbooks aimed at advanced middle school and high school students, and I usually have to create my own lesson plans using bits and pieces from a number of sources.Though Dr. Libeskind's Euclidean and Transformational Geometry is intended to be a college-level text, I have found it a gold mine for for my advanced middle school classes.The format of the text very closely matches the way I present concepts to my students: each section begins with an introduction to new concepts and vocabulary, followed by simple diagrams and illustrations, and then a theorem and its proof.The exercises are designed to tie back into the main text discussion, and each section builds upon concepts that earlier sections have introduced.

Textbooks that I have worked with in the past have rarely given the same level of focus to writing and understanding proofs that this one does.My experience suggests that while many students find thinking about theorems in terms of proofs foreign at first, they quickly acclimate to the process if proofs are readily available for every property that they encounter.Dr. Libeskind's book is fantastic in this respect because he provides proofs for every mathematical relationship that the text proposes.The book is written to actively encourage students to get into the proof mindset so that they can deconstruct problems, and it is the only textbook that I have come across that does this effectively.

I am also impressed with Dr. Libeskind's ability to collect the diverse topics that his book covers and arrange them in a simple and logical way.This book is straightforward and to the point; no time is wasted on extraneous diagrams, pictures, or problems.The content is clear and concise, but unlike many other textbooks it also encourages the reader to think through problems himself rather than simply providing statements.Even the page layout, which separates ancillary discussions and exercises from the main text using color-coded side-bars and subsections, has been designed with simplicity and ease-of-use in mind.

Though my school district mandates the use of particular textbooks for middle school and high school math, I would like to have several copies of this book in my classroom for students to use as a resource.I have found it vastly superior to many other textbooks that cover the same subject, and though it is aimed at college-level courses, it has been very useful in my lesson planning.

Review from Karen
I highly recommend this book by Professor Libeskind, because it has many outstanding features which make it is vastly superior to the typical college geometry textbook.This geometry textbook is a unique and extraordinary resource for students.It is an elegant book, beautifully written and illustrated, that will introduce students to the process of mathematics - that is to say, to explore interesting problems, discover for themselves possible solutions, and to verify a solution through the process of writing a proof.This book will be treasured by students long after they have completed their coursework and will surely be a continuing resource for students who enter the teaching profession.As a high school math teacher, I can also recommend this book for advanced high school geometry students.

With its beautiful illustrations, uncluttered diagrams, and clear writing style, this book will pique interest by offering students intriguing problems to consider.The book incorporates several features that will develop student appreciation for mathematics, including historical notes about mathematicians that give thoughtful glimpses into the personal lives of those who have contributed to the development of mathematics.The multicultural nature of the discipline of mathematics is clearly described in these notes, and in reading these notes, students will gain a deep respect for the contributions other times and cultures to present-day mathematics.

The book contains a wide range of problems designed to challenge students at every level of understanding.The author's clear belief is that all college students can engage in mathematics at a meaningful level, even beginning students.This textbook is written to develop an in-depth understanding of geometry, and also contains material that will challenge advanced students.Traditional geometric constructions with compass and straight-edge are approached as the outcome of exploration and discovery, rather than as mere techniques.Computer geometry software activities are also included in the text (i.e., Geometer Sketchpad).Sections on recursive formulas for evaluating ð, trigonometric functions, isometries, extremal problems, and complex numbers provide options for providing more complex material for advanced students.
... Read more

Product Description

This two volume work on ... Read more

Product Description
Bob Miller's Geometry for the Clueless tackles a subject more than three million students must face every year. Upbeat and always enthusiastic, Professor Miller acts as a private tutor to his readers, painstakingly covering the current high school curriculum as well as post-secondary courses in geometry. His failsafe methodology makes geometry easy to comprehend, giving the student quick techniques for working through problems in an energetic tone that helps students not only learn the material, but also learn how to think about the discipline. Perfect as a supplemental guide for all geometry courses, Geometry for the Clueless includes:

• Expert tips and techniques for solving difficult problems
• Non-technical language
• A unique way of explaining complex concepts to make learning geometry less daunting

Customer Reviews (4)

Geometry For The Clueless
Received as new in excellent condition.Bob Miller's Geometry for the Clueless, 2nd edition (Bob Miller's Clueless)

This Book Needs A New Title!
This geometry book is very nice for those wanting to brush up on their definitions! It does have a few typos in the examples which shouldn't cause you a problem if you actually get what he explains!
If you are clueless however I do not think you would like this book.
It's because it does assume you went through at least pre-algebra(or my pre-algebra book.) You don't have to understand geometric concepts to begin with! And by that I mean alot of them! *perhaps the reason for the title*
The only problem with this book is it's title. I am a complete math lover so I was ashamed to show anyone else who loved math the title. I did though and they thought it was a bit funny that I would be reading a book named Bob Miller's Geometry for the Clueless!

Embarrassing...
I picked this up at a local book store, flipped through it quickly, and purchased it on a whim, intending to review my basic geometry skills as I work my way up to more advanced college level mathematics

While reviewing the first 2 chapters, I immediately noticed a few typos, a perfectly obvious mistake in an equation, and a missing diagram to explain the definition of an angle bisector.(I am not a math whiz-- if I can find these mistakes, there's a problem.)I also noticed that the author had a tendency to rage over the evilness of new math and how poorly written student textbooks are these days (This is funny considering how poorly written/edited this book is).

Since I'd already written in the book, I ignored these problems and continued on my quest to understand geometry.I didn't get far.

Throughout the first several chapters the author tends to get sidetracked with poorly written paragraphs devoted to showing the student whether or not their school textbook/instructor is worthless or not.Fine, but what does that have to do with helping a student understand basic concepts so that he/she can pass their exams?

Often, the author's written explanations are so convoluted, they're impossible to understand without re-writing them yourself.

McGraw Hill should be ashamed for printing this.On careful review, say for example, if one was attempting to learn from the book, the book comes off like unedited notes.Also, the layout is appalling.The author is constantly referring to diagrams that either flat out don't exist, or they're found several pages earlier in the text and are not labeled.

I can't get my money back, but you can make sure not to waste yours...
If I could rate this item with negative stars I would.

Does not teach understanding, only Rules.Poorly Edited.
This is the worst geometry book I have ever seen.Being an educator, I thought that this book may provide some useful information for students with misconceptions about geometry.However, the author mostly just rants about the difference between "old/traditional" and "new" math methods.He spends more time trying to convince the reader that his "method" is better than others, when in reality, he is teaching the exact same thing in the exact same way that it is taught in a typical high school classroom.The only difference in his "method" is that he provides a number of geometry "rules".For example, he lists a number of "rules" used to determine if a triangle is equilataral, isosceles, or scalene.Instead of rules, one should learn WHY and WHAT makes a triange fall in one of these catagories (i.e. - understanding, not rules).He seems to want to establish a bunch of rules for things that are not necessary if one can understand conceptually why something is true.Also, the book is poorly edited.There are frequent errors (typos) in his proofs which can cause quite a lot of confusion if you do not know how to do proofs or do not know geometry well enough to discover these errors.How can someone learn when the textbook is wrong?Finally, his material presentation is confusing.Figures are not properly labeled and are often hard find. Once, he talks about "angle A in Figure 2", but I could not find the figure, since it was not labeled.After searching for it, I found the figure 4 pages BEFORE.Why present a figure if you are not going to talk about it on that page?In summary... poorly organized, poorly edited, and not concerned with teaching understanding - it is OK if you are looking for a simple geometry "rule book" but not if you are trying to actually understand geometry. ... Read more

Product Description

About the Contents:

Pretest

Helps you pinpoint where you need the most help and directs you to the corresponding sections of the book

Topic Area Reviews

• Basic geometry ideas

• Parallel lines

• Triangles

• Polygons

• Perimeter and area

• Similar figures

• Right angles

• Circles

• Solid geometry

• Coordinate geometry

Customized Full-Length Exam

Covers all subject areas

Appendix

Postulates and theorems ... Read more

Product Description
Readers now have the perfect tool for when there’s no time to read a lengthy textbook : the quick and accurate lessons and focused practice exercises in Just in Time Geometry. In ten streamlined chapters, this book teaches the fundamentals of geometry that are essential for a solid score on any standardized test, from high school to adult level. ... Read more

Customer Reviews (1)

Exceptionally clear and relevant. Thank YOU,just in time!
This looks like the work of a talented and experienced pedagogue, with a tremenduously organized mind.

Crystal clear short introductory explanations, proper sequence of approaching different geometry chapters,relevant exercises,in short a geometry bible for a student and a welcome refresher for anybody.

I am an enginner, and I always loved geometry , but I found myself at loss of words when to explain my grade-8 kid parts of it.
But this is the life-saving book that makes geometry very, very easy to understand. It had a huge positive impact on my kid's geometry knowledge.I cannot believe my luck in finding it.

I would recommend it to any school as grade 7 & 8 textbook.
Thank you.
... Read more