Book Description

Maintaining its hallmark features of carefully detailed explanations and accessible pedagogy, this edition also addresses the AMATYC and NCTM Standards. In addition to the changes incorporated into the text, a new integrated video series and multimedia tutorial program are also available. Designed for a one-semester basic math course, this successful worktext is appropriate for lecture, learning center, laboratory, or self-paced courses. ... Read more

Reviews (1)

try doing the tests on MathZone
The book and the publisher's MathZone show a nice attempt at integrating the power of the Internet with a traditional maths text. The material is for high school readers. You can of course treat the book just as a conventional text, and refrain from accessing MathZone. In this respect, the book is well polished, being in its 6th edition, and very logically internally consistent. As befits Euclidean geometry.

Now if you do want to use MathZone, what to do at the website? Perhaps the most fruitful approach, if you are disciplined enough, is to take those tests offered there. In addition to doing the exercises in the book, of course. The tests are a valuable metric of how well you comprehend the material. The authors and publisher have put a lot of time into MathZone. Go for it! ... Read more

Book Description

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!

The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose.Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist. ... Read more

Reviews (40)

Pursuing the Mysteries of the Ubiquitous Number Phi
Mario Livio, a cosmologist and art aficionado at the Hubble Space Telescope Center and the author of the previous book "The Accelerating Universe," wrote a lot about the irrational (never-ending, never-repeating) number phi, or the Golden Ratio, whose value is 1.6180339877... The story starts from these questions: Who discovered the Golden Ratio? Was phi used in the design of a Babylonian stela and Egyptian pyramids? The author pursues the answers to these questions, writing a series of his thoughts like a detective story.

Then he describes the role of the Greek mathematicians Plato and Euclid, and the Italian mathematician Leonardo Fibonacci in the history of phi, together with the geometrical and arithmetical wonders connected to this number. One example of the wonders is the relation between the Fibonacci sequence and phi. The Fibonacci sequence 1, 1, 2, 3, 5, 8, ... is defined as a series of numbers in which each term is the sum of the two preceding terms. The ratio of successive numbers of this sequence approaches phi as we go farther and farther down the sequence.

Next come the topics of phi found in nature and used in arts. The logarithmic spiral, which goes hand in hand with the Golden Radio, appears in the sunflower, the flight of a falcon, galaxies, etc. The author's study of many historical attempts to disclose the Golden Ratio in various works of art, pieces of music and poetry comes to the conclusion that ... (I have to refrain from writing the ending of the "detective story").

In the final chapter Livio considers the question: What is the reason that mathematics and numerical constants like phi play such a central role in topics ranging from fundamental theories of the universe to the stock market? Noting that the discussion about this question can fill the entire volume, the author gives a brief (but very understandable) description of the modified Platonic view and the natural selection interpretation. He also presents his personal opinion, which adopts complementarity of the above two views. This chapter whets readers' appetite for a possible next book on this topic to be written by Livio.

I strongly recommend "The Golden Ratio" to scientists, artists and laypersons that are interested in the wonders of numbers and mathematics and in their relations to arts and nature.

Golden Indeed!
Following in the steps of his earlier, just as fascinating account linking cosmology and the arts ("The Accelerating Universe"), Mario Livio continues to prove he is one of the most original, exciting and literate writers of popular science today. "The Golden Ratio" is a witty and learned journey generally following the trail of the number Phi, but stopping along the way to take in subjects as diverse as philosophy, history, art, religion, the sciences, architecture, etc.

Writing about science in a way that is both knowledgeable and understandable for the common reader is an infamous hurdle, but Livio leaps over it with the greatest of ease, giving clear explanations of every potentially difficult matter and providing the scientific proofs in the appendices, for those more mathematically inclined. Overall, though, it is the great humanity of Livio's worldview that shines through the book and makes it, at least for me, one of the most memorable reads of the year.

A Difficult Mathematical Concept Revealed
As a non-mathematician I appreciate any help I can get in understanding the more esoteric parts of math. The Golden Ratio is just such a concept. Fortunately, Mario Livio has shown much light on this remarkable corner of geometry in his book "The Golden Ratio."

It is little wonder that such numbers as the Golden Ratio were considered magical. The never ending, never repeating number that cannot ever be expressed as a fraction has an uncanny tendency to show up in the oddest places, not only galactic structure and nautilus shells, but in plant parts and composition of paintings and music. Unfortunately magical numerology can lead to far-fetched relationships, as to the so-called number of the beast (666), and to academicism in art. Just because the Golden Ratio results in a pleasing relationship in a composition we are not tied to always measure art on how well it fits that ratio!

Livio has illuminated the history of the Golden Ratio in such a way that much of the associated themes can be understood by the reasonably educated laymen. While some of the book can be tough sledding for most of us non-mathematicians, the gist is available to all with some effort.

Read this book to learn about the history of interpretation and misinterpretation of mathematical concepts.

A great guide to an amazing number
Livio's book is really an interesting look at a number similar to pi in that's an irrational number which displays itself in various places in nature, from the arrangement of petals on a flower to the logarithmic spirals of galaxies.

Livio explains the original formulation of this number by Euclid and proceeds to address the various times in history in which it may have been employed by architects, artists and musicians.

I think this is a really good book if you're interested in reading about the most "irrational of all irrational numbers".

Mathematically Profound
Broad streams of literary, historical, aethsetic and religious thought are pooled together in a concise and well-illustrated review of this powerful proportion, which recurs in the natural world in surprising places both large and small. Clearly presented mathematical proofs give the book a solid backbone. Mathematical ideas are expressed in the book through a combination of prose, appendix proofs, and plentiful illustrations & diagrams. This allows readers of varying mathematical ability and learning styles to appreciate the beautiful ideas that Livio gracefully presents. A must for serious lovers of proportion & geometry, architects, mystics, painters, graphic designers and mathematicians. ... Read more

Book Description

The Third Edition of Elementary Geometry for College Students covers the important principles and real-world applications of plane geometry with additional chapters on solid geometry, analytic geometry, and trigonometry. The text's largely visual approach, strongly influenced by both NCTM and AMATYC standards, begins with the presentation of a concept followed by the examination and development of a theory, verification of the theory through deduction, and finally, application of the principles to the real world. Designed with the appropriate pacing and appearance for college-level students, this text offers a welcome alternative for instructors who, in the past, have had to use secondary-level texts for this course.

• Videotapes, professionally produced for this text and hosted by Dana Mosely, offer a valuable resource for further instruction and review.
• Reminder marginal notes reinforce theorems or formulas from previous chapters to help students progress through the course.
• Enhanced Chapter Openers introduce students to the principle notion of the chapter and provide real-world context.
• Discovery features designed to reinforce the inductive approach of this text include activities that enable students to discover geometry concepts on their own and section tools that provide students with hands-on application of concepts.
• Applications throughout text reinforce the connection of geometry to the real world. A Look Beyond chapter-ending sections provide engaging sketches, sometimes with historical background.
• Summaries of constructions, postulates, and theorems are provided to reinforce learning. In addition, a numbering system for postulates and theorems presents a user-friendly structure.

Reviews (1)

A Wretched and Horrid Book
Entering geometry for the first time ever can be an almost initimidating venture, especially for the first time geometry student. After conquering other mathematical courses successfully (like algebra and statistics), I presumed entering "Elementary Geometry for College Students," based on being given exceptional required texts from previous courses, would be a breeze. Oh how wrong I was!

"Elementary Geometry for College Students," by Daniel C. Alexander (of Parkland College) and Geralyn M. Koeberlein (of Mahomet-Seymour High School), has taught me nothing more than NOT to trust a textbook written by a couple of hack authors from unknown schools with a blatant disregard for meticulously explaining important vital and "elementary" steps as to how to arrive to certain statements, reasoning, deducing, measurements, and so much more NEEDED in successfully acheving full reign over geometry. For example, the origins of postulates and proofing are never explored, but slammed in your face, convoluting both topics along with breaking down statements from deducing a particular shape, its angles and measurements. The book's attempts at explaining triangles, convex polygons, congruent triangles, and properties of parallelograms are all but slandered together (with steps in basic algebraic mathematical equations arrogantly skipped over and presumed upon to you) without any form of thorough reason or explained steps bothered in explaining. Important theorems are disarrayed throughout with quick-step problem examples without helpful or detailed reasoning as to how the answer was ever achieved.

The authors have obviously assumed a college student has had some form of pre-geometry course prepping, and expect both instructor and student to know the advanced fundamentals without considering the beginner geometry student at all (just from judging by example and "solutions" given in each section). As a result, students will fail miserably, along with angering frustration, and discontent wonderment over what purpose geometry may ever serve toward a real-life career. Perhaps trying "Geometry for Dummies" by the infamous IDG publishing company would be a much suitable levelage to this otherwise detrimental book attempting to teach an important equation to the universe of mathematics.

By far, this textbook is the worst and most horrible book in teaching the subject of geometry!!

To professors searching a geometry book for your students: PLEASE avoid this book at all costs! You and your students don't need a textbook that presumes you know it all before diving into shapes, proofing, deducing, theorums, solids, and so forth. Most surely, there are much more superior books to this wretched and horrid title worthy of its decommissioning. ... Read more

Book Description

Following on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals.

Much of the material presented in this book has come to the fore in recent years. This includes methods for studying dimensions and other parameters of fractal sets and measures, as well as more sophisticated techniques such as thermodynamic formalism and tangent measures. In addition to general theory, many examples and applications are described, in areas such as differential equations and harmonic analysis.

This book is mathematically precise, but aims to give an intuitive feel for the subject, with underlying concepts described in a clear and accessible manner. The reader is assumed to be familiar with material from Fractal Geometry, but the main ideas and notation are reviewed in the first two chapters. Each chapter ends with brief notes on the development and current state of the subject. Exercises are included to reinforce the concepts.

The author's clear style and up-to-date coverage of the subject make this book essential reading for all those who with to develop their understanding of fractal geometry. ... Read more

Reviews (2)

Dimension of fractal objects
A suitable book to remove any doubt about calculation of dimension of fractal objects. I enjoyed the chapter about ergodic theorem.

Maybe this book is advanced version of "Fractal Geometry"
I had read "Fractal Geometry" in last year. Then I purchase this book. It seems advanced version of "Fractal Geometry". In this book, some applications of fractal for science and engineering. For example, thermodynamic formalism, ergodic theorem, multifractal analysis, differential equations, and so on. I think that this book will become good textbook for scientist and engineer who apply fractal geometry for their field. ... Read more

Book Description

Geometry & Trigonometry for Calculus By Peter H. Selby If you need geometry and trigonometry as a tool for technical work … as a refresher course … or as a prerequisite for calculus, here’s a quick, efficient way for you to learn it! With this book, you can teach yourself the fundamentals of plane geometry, trigonometry, and analytic geometry … and learn how these topics relate to what you already know about algebra and what you’d like to know about calculus. You’ll work your way through geometry, numerical trigonometry, methods of trigonometric analysis, analytics, and limits—all the way up to the "front door" of calculus. Geometry and Trigonometry for Calculus is one of the Wiley Self-Teaching Guides. It’s been tested, rewritten, and retested until we’re sure you can teach yourself the concepts of geometry and trigonometry. And it’s programmed—so you work at your own pace. No prerequisites are needed. Objectives and self-tests tell you how you’re doing and allow you to skip ahead or find extra help if you need it. Frequent reviews and practice exercises reinforce what you learn. Wiley Self-Teaching Guides Astronomy, Moche Basic Physics, Kuhn Chemistry: Concepts and Problems, Houk How to Succeed in Organic Chemistry, Gordon Basic Electricity, Ryan Electronics, Kybett Ecology, Sutton Energy for Life, Allamong Plant Anatomy, Stevenson Quick Medical Terminology, Smith Human Anatomy, Ashley Dental Anatomy and Terminology, Ashley Math Skills for the Sciences, Pearson Thinking Metric, 2nd ed., Gilbert Using Graphs and Tables, Selby Geometry and Trigonometry for Calculus, Selby Quick Calculus, Kleppner BASIC, 2nd ed., Albrecht BASIC for Home Computers, Albrecht ANS COBOL, 2nd ed., Ashley Structured COBOL, Ashley Fortran IV, Friedmann, Greenberg & Hoffberg ATARI BASIC, Albrecht TRS-80 BASIC, Albrecht Job Control Language, Ashley Flowcharting, Stern Introduction to Data Processing, 2nd ed., Harris Background Math for a Computer World, Ashley Probability, Koosis Statistics, 2nd ed., Koosis Finite Mathematics, Rothenberg Practical Algebra, Selby Quick Arithmetic, Carman Math Shortcuts, Locke Study Skills: A Student’s Guide for Survival, Carman Psychological Research: How to Do It, Quirk Psychology of Learning, Royer Choosing Success: TA on the Job, Jongeward Successful Time Management, Ferner Communication for Problem Solving, Curtis Skills for Effective Communication, Becvar Clear Writing, Gilbert Punctuation, Markgraf Vocabulary for Adults, Romine Spelling for Adults, Ryan Reading Skills, Adams Art: As You See It, Bell Your Library —What’s in It for You? Lolley Quickhand, Grossman Quick Typing, Grossman Consumer Math, Locke ... Read more

Reviews (12)

The Pleasure of Finding Things Out
Like many people, I didn't learn anything in any significant way in high school, so later in life I found out I lacked the necessary mathematical skills to pursue my interests in science.

Looking to fill that void I got this book and its companion introductory volume, Peter Selby and Steve Slavin's "Practical Algebra: A Self-Teaching Guide", and am extremely relieved to find out mathematical illiteracy can be remedied with the right tools.

These books not only taught me the basics of algebra and geometry, but more importantly, gave me a glimpse of how mathematical ideas are developed. Concepts that appeared to me to be mystical elaborations now seem full of reason and purpose, thanks to the self-contained nature of these two books and the step by step construction of ever more complex themes. The authors focus not on mechanical repetition but on understanding, on making sense to the student, so everything fits in in a meaningful way, instead of appearing as a loose aggregation of disjointed bits. I really got a lot of enjoyment out of learning all the material, and finding out what a wonderful world of ideas this knowledge opens up.

Of course, being a great book doesn't mean being a flawless book, and this one indeed has its shortcomings. First, this two volumes do not cover logarithms at all, so you'll have to look for that subject elsewhere. Also, the plain geometry, analytic geometry, and conic sections chapters have insufficient exercises, so you'll probably want to get an additional text to get some more practice in those areas. Finally, even though the books are a very good and well-rounded introduction, they do not go into much depth in any area. On the other hand, the introduction to limits is truly great.

If your knowledge of mathematics has ever held you back professionally or personally, this is a great place to start changing that!!

EXCELLENT! Wish I would have had this author teaching me.
There is no such thing as a student who is "slow" in understanding. There is however a teacher who does not master the art of communicating. A good student memorizes in order to pass a grade. A slow student is normally bugged by the "why" of everything. However I have had the honor of solving engineering problems for students from MIT and other top Universities because my professors were able to explain the "why" to me.

Mr. Peter H. Selby is an excellent author. You flow through his pages without having to read over paragraphs several times in order to understand the sense of his explanations without stress and fatigue. There is no guessing nor ambiguous wording. It is difficult to put down his book for the day. I look forward to his future books.

Bummer
Content is fine. Binding is not.
The book is falling apart.

good as a companion only
If you want to test your knowledge of geometry and trig after reading another text book, this is good. However, this is not a standalone book. It offers problems and answers, but very little in examples and explanations of why.

Unless you want a refresher, I'd go somwhere else, maybe a dummies or idiots guide instead.

There aren't enough exercises..
The best and most enjoyable way to learn math is through practice, and although Peter H. Selby articulately explains the concepts presented in this book, there just aren't enough exercises for you to "teach yourself" the subject. A given section on plane geometry will give you about 15 abstract principles followed by 5 easy practice exercises. I have learned from this book, but in order to do so, I've had to make flashcards and do lots and lots of rereading to help me memorize the vocabulary and rules. This book would be okay for someone who just needs a quick refresher, but if you really want to learn the material, I would suggest buying separate 350-400 page books for each subject. ... Read more

Reviews (7)

Flat spheres and more
Highly stimulating and extremely hard to read, written for mathematicians in physics. However, the chapter on Riemannian Geometry can be worked through, up to a point, without any knowledge of exterior differential forms, and is notable if for only one fact alone: a simple calculation is provided that explains explicitly that spheres in four and eight dimensions (3-spheres and 7-spheres) are flat with torsion! I don't know another reference that a physicist without special background in math can consult to understand this highly nonintuitive fact.

Just a "better than nothing" book
It's not the best way to learn geometry / topology for physics. It's better than nothing, though, if you are familiar with the topics already. There are many "holes" in Nakahara's book, which you would spend much more time and hard working in a "big" library. than you should to fill in. It's not worth that money and struggle. It's the last one you should consider about owning.

If you are a physics graduate who needs a nice guide to "understand" the aspects and skills of geo / top, I would recommend the following: (1) Milnor's Topology from the Differentiable Viewpoint, and (2) Kreysig's Differential Geometry. The first one was old, and so it does not assume much knowledge about the topic. The latter is a kind-of-Bible for the topic, and all solutions are provided for the problems. These two books will help you a lot if you care about the meaning, not only for those classroom exams or just showing off that you know something about it. Frankel is the next to put on your bookshelf as a detailed and rigorous development for your preparation to be a theoretical physicist.

If you have only a rough idea about topology, Hocking and Steen are the best choices, and they are Dover!!

Anyway, if I could find a cheap used Nakahara, I would get it as a reference.

Best in its genre
I suppose I should preface this by saying that I read this book *after* reading similar books, so my ability to understand this book is probably better than others, but that said, I think that my comparative evaluation is free from this bias...

There seem to be a few books on the market that are very similar to this one: Nash & Sen, Frankel, etc. This one is at the top of its class, in my opinion, for a couple reasons:

(1) It's written like a math text that covers physics-related material, not a book about mathematics for physicists. I prefer this; you may not. As a consequence, this book is more rigorous than its alternatives, it relies less on physical examples, and it cuts out a lot of lengthy explanation that you may not need. Of course, there are drawbacks to all of these "features" -- you need to decide what you need and what's best for you.

(2) It's most comprehensive, with Frankel coming in second, and Nash & Sen least comprehensive (though they have quite a bit on Fibre bundles and related topics). Nakahara has a chapter on complex manifolds, which is absent from the other two. Nakahara also concludes with a nice intro to string theory, which is absent from the other two as well (though nothing you couldn't find in Polchinski or the like). Actually -- I modify this slightly. Frankel covers less subjects than Nakahara, but with more depth (though also more wordiness -- I quit Frankel about 2/3 through because it wasn't succinct enough and I got tired of it).

Depending on your tastes, I would recommend this book before the other two.

It presupposes that you have an understanding of algebra (groups, rings, fields, etc.) but it has an introduction to the necessary components of topology within. Frankel has presupposes both algebra and topology; Nash & Sen presupposes only algebra.

Excellent book
A very nice blending of rigor and physical motivation with well chosen topics. Plenty of examples to illustrate important points. Especially noteworthy is its description of actions of lie algebras on manifolds : the best I have read so far.

Most of the topics are intepreted in terms of their topological/geomtrical structure (and the interplay between those two), but that's what the title of the book says. So you will learn things again in new ways, and gain a powerful new set of tools. If nothing else, it gives you a nice warm fuzzy feeling when you read other field/string theory books that glosses over the mathematics.

One minor rant : the notation of the book can be better. I personally uses indices to keep track of the type of objects (eg. greek index=components of tensors, no index=a geometrical object etc..), but Nakahara drops indices here and there "for simplicity". But that's my personal rant.

Good book. Buy it.

A must for any theoretical physicist
With an excellent balance between mathematical rigor and pedagogical simplicity, Nakahara remarkably captures in a single volume much of the mathematics a physicist will ever need. (If he wrote a few chapters on group theory, 'much' might be replaced with 'all'). Containing as much as it does, it is not something to breeze through. Depending on your mathematical background, you may only want to read a few chapters (and if the Homology chapter is tripping you up, just keep moving). But invest the time with it, and you will be rewarded with a solid grasp of the mathematical pictures underlying most modern physics. And once you read it and see physics from this perspective, you'll be amazed you had ever thought you understood the physics it describes. It should be said, though, that some of the latter chapters, in particular 12, are horribly sloppy. There are dozens upon dozens of errors, many at a deep conceptual level. Nonetheless, it is a monumental text, and I recommend it heartily. ... Read more

Book Description

You know that geometry is a math thing, right? You remember that much from school. You also probably remember that it has something to do with circles, squares, diameters, angles, and all those other terms that floated in (and probably right out of ) your head as you were cramming for all those geometry tests way back when. But your math teacher probably never told you that you'd actually use that stuff in real life – if he had, maybe you would have paid more attention!

Well, don't fret. You're in the same boat as almost everyone else. Geometry has about a million (a rough estimate) uses in real life – for example, you may have some home improvement projects you want to tackle; you have to know how to cut the wood at certain angles to make them fit together. ( Bet you didn't realize that carpenters have to be experts at geometry as well!) With a basic knowledge of geometry, building some bookshelves for your kid's room becomes so much easier.

Geometry For Dummies can give you that basic understanding of geometry, and you might actually have a little fun along the way. Written in a breezy, easy-to-understand, non-textbook-like style, this book helps you with all your geometrical dilemmas.

In Geometry For Dummies, you'll find out about the following topics and more:

• Understanding lines and angles
• Working up a geometry proof
• All those funny shapes: circles, rectangles, triangles, and the ever versatile polygon
• Having your Pi and eating it, too
• Taking the next step into trigonometry
• Doing someone a solid: Exploring prisms, pyramids, cylinders, cones, and spheres
• Top Ten list of cool careers that use geometry and tips for making geometry easier
• Appendices with formulas, theorems, and other helpful geometry resources

So whatever your reason for wanting to learn geometry – a home improvement project, helping your kid with his or her homework, or just a fascination with funny shapes – Geometry For Dummies is just what you need to recall what you learned in school and put it to good use. ... Read more

Reviews (5)

...an excellent approach!!!
The title of this book already presents a sort of contradiction, which made me laugh when I first saw it on the shelf. I bought it to solidify and deepen my understaning of this beautiful branch of science and to give me confidence in my ability to teach such beauty to young minds, eager or not. I have found it both entertaining and informative and would recommend it to anyone who has ever felt overwhelmed by the "axiomatic method" which saturates most geometry texts. If you appreciate the power and precision of mathematics and also appreciate the human nature of realistic humor, please buy this book!!!

Book is adequate
This boox is adequate for Honors students...
Try find some other book.
But it's really good for practice

A Textbook, with a tinge of humour
If you want to learn about geometry, but don't want to look through a thick, school like textbook, this is the perfect book!

For every theorem or postulate this book teaches about, right next to it is a short explanation along with a simple diagram used as an example.

This book goes from simple geometry, all the way into a bit of trigonometry.

It is basically like a textbook, but with lots of humour and simple explanations that separates it from the rest of the other geometry books. This book probably covers everything that is taught in 10th Grade, but without all the exercises.

It teaches and explains geometry, but if you are looking for a book full of exercises, this is not the book for you. It should give us more problems or equations to solve, and that is why it lacks 5-stars. That is its only downfall. If you are reading this before you get into geometry, be prepared to know all the material and be bored to death. This is not exactly a bad thing though :) .

Thanks Amazon[.com]
I was surfing the web, beacuase I am a computer programmer of old and know all about webspace and word processing and things. Well, anyway I found this book very helpful, especially for teaching other people, something I find very challenging. I have always been a struggler when it comes to maths and as a general rule didn't understand a word of it. But now I can get up in front of my class with confidence and teach them about squares and triangles and things without having to send people out the room for doing nothing.

Making the DRY drinkable
I recall with anguish over 37 years ago, my 10th grade geometry class, dry as a Wadi in the Sahara. I slept through the first course obtaining a grade worthy of my snoring through an hour a day of irrelevance.
Today some math teachers are asking why math has to be dull or academic. This book is one which revives my faith a math teacher may indeed have real blood pumping in their veins.
This book I'd recommend to some teenagers and more so for adults, those 18 years and up who slept through geometry in high school.
I also recommend the basics of geometry start in school much earlier than grade 10.

I suspect however geomerty and real dummies don't mix well. Read this book and surprise yourself, maybe you're not a dummie after all. ... Read more

Book Description

103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques.

Key features:

• Presentation evolves through gradual progression in problem difficulty to build and strengthen students' mathematical skills and techniques

• Provides in-depth enrichment of problem-solving tactics and strategies, along with practical test-taking techniques, to better prepare students for possible participation in various mathematical competitions

• Topics covered include: trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions

Advanced high school students, undergraduates, and mathematics teachers engaged in competition training will gain both skills and strategies from this cogent problem-solving resource.

Reviews (4)

A clear, friendly introduction to topology
Is space finite or infinite? Does it have borders? What shape does it have? These are among the most pressing and interesting questions in astrophysics and cosmology today. To answer (or at least understand) these questions, one must possess an understanding of topology, a branch of mathematics dealing with properties of shapes that are not changed upon deformation.

This book is an ideal introduction to topology for beginners with little or no mathematical background. It introduces topological manifolds (especially 2- and 3-manifolds) and their applications to cosmology and the shape of space. It is filled with diagrams, examples and exercises with full solutions at the end of the book.

The book assumes almost no knowledge of mathematics or physics, and is thus suitable for high-school and beginning college students. It is a must read for students contemplating a career in pure mathematics or theoretical physics, and who want to get a taste of the applications of pure mathematics to the physical world.

For those wishing to go a step further on the subject of the shape of space, the author published a paper (Nature 425, 593 - 595, 09 October 2003) claiming that the universe is a dodecahedral 3-manifold, based on cosmic microwave background measurements. This book may be a nice introduction for this paper and for subsequent papers that will surely ensue, trying to describe the shape of space.

Topology for everyone
Jeffrey wrote this book with the high school student in mind, but even as a second year student in Mathematics I found this book quite informative. Most textbooks in Analysis or Topology do not give you an intuitive feel for the subject. I recommend this book for anyone taking a course in Topology, even Graduate students.
This book is well written with many illustrations and exercises to help you get an intuitive understanding of 3 Dimensional manifolds. This helped me a lot in my second year Analysis class as I had an intuitive notion of manifolds taught in class.
At the same time the book is easy enough for high school students who always wondered what a Mobius strip or a Klein bottle was but did not find any books on it. This book would make Topology interesting for everyone. I give it a five star rating.

Loads of fun
But this book can also be quite serious, although it may take someone with an extensive math background to see this. The book seems aimed primarily at high-schoolers, but graduate students in topology can definitely benefit from reading it.

Weeks starts out by explaining surfaces and the quotient space descriptions of the torus and klein bottle. Later chapters describe 3-manifolds, fibre bundles(!), and the 8 geometries relevant to Thurston's geometrization conjecture. The focus of the book is on applying these concepts to investigating the shape of our spatial universe. This is a particularly apt goal, given that many times in the book the reader is asked to imagine living in various kinds of spaces.

He has a very good set of exercises designed to increase one's visualization powers. For example, in the chapter on 3-manifolds, he has the reader color various covering space pictures of 3-manifolds like the 3-torus, according to some specifications; this really helps one understand how covering maps work.

As someone who was familiar with topology before reading the book, I can say that the book has definitely increased my understand of 3-manifolds, which is more than I can say for most topology books. In particular, I found the material on fibre bundles very enlightening.

Straight talk about curved space
What is the universe as a whole shaped like? Does it curve back on itself? Does it meet itself at the other side without curving? Is its Flatland analogy a plane, or a sphere, or a doughnut, or a Klein bottle? What other, stranger geometries become possible with the added dimension? And if the universe has one of these exotic shapes, how could astronomers ever know for sure?

Jeffrey Weeks, a MacArthur ("genius grant") fellow and a consultant to NASA on cosmological observations, believes that there's no reason why a liberal arts student or a high schooler shouldn't be able to have a solid understanding of the answers to these questions, even though some of them are at the edge of research in cosmology and three-manifolds, and others have traditionally not been part of the math curriculum before graduate school.

The math is presented at an elementary level, but it is genuine mathematics. Readers in the intended audience must be prepared to roll up their sleeves; there are exercises, and there are formulas, and their minds will be stretched. But there are no prerequisites other than a little first-year algebra, and the discussion stays at a vividly concrete level, with a plethora of diagrams to aid the swelling imagination. High schoolers will benefit from some guidance getting through it; it's appropriate for undergraduate self-study.

More mathematically sophisticated readers, even those who've taken a course in algebraic topology or differentiable manifolds, will find the book a lively read, but will still probably learn a thing or two. I, for one, was startled to be shown a Moebius strip that was two-sided! (The trick is to embed it in a non-orientable three-space.)

The payoff is in the final two chapters, which detail programs of astronomical observation that could well tell us the precise topology and geometry of the universe, and explain just how they would do it. One chapter is devoted to a technique based on correlating distances between galactic clusters, and the other to a statistical search for correlated arcs of great circles in the cosmic microwave background. Both observations will probably be completed within the next decade. It's an exciting prospect.

Buyers note: I believe the Amazon characterization of this as a paperback is in error. I bought the second edition in hardcover at the same list price. In its (successful) attempt to avoid intimidation, it uses a large typeface, so it would fill out some 200 pages in a more typical math format. ... Read more

Book Description

A practical, accessible introduction to advanced geometry

Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An excellent introduction to advanced concepts as well as a reference to techniques for use in independent study and research, Methods of Geometry also features:

• Ample exercises designed to promote effective problem-solving strategies
• Insight into novel uses of Euclidean geometry
• More than 300 figures accompanying definitions and proofs
• A comprehensive and annotated bibliography
• Appendices reviewing vector and matrix algebra, least upper bound principle, and equivalence relations

Book Description

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises. ... Read more

Reviews (3)

Lots of illustrations and exercises-with answers at the back
This is a wonderful book. It isn't for mathematical beginners, but it isn't opaque either. It requires a student to think, experiment and to learn by puzzling things out in one's mind rather than simple memorization and regurgitation. Nor does it follow the all too common modern method of over simplifying things to allow people to pretend they have learned math while only dabbling in a few basic topics.

This book is amply illustrated with many exercises (answers are provided at the back for all the exercises). The book also has some humor and wit with the quotes it distributes throughout the book to help liven things up.

There is also a list of helpful references and an index. When reading the book, don't be afraid of going to a dictionary or the web or some other math books for clarification of some terms or more basic concepts. It is essential to have everything clear in your mind before moving on or you will stumble. As in all math, it is like a building with the next stage being built on the present one which is built on the previous one. You can't skip steps very successfully very often.

This is a great volume to have in your library, but even better to work through.

this is not an introduction
A better title for this book would be "Advanced Topics in Geometry". The chapters are pretty much self-contained.

This book presumes a thorough, rigorous knowledge of high school geometry such as you might get in a college geometry course designed for future teachers along with considerable mathematical maturity.

Best survey of geometry.
This is Coxeter best book. Introduction to Geometry covers a wide range of topics and is the first book that I will look at for any geometry topic. It is now a little dated but only in the topics that it does not cover. Like all of Coxeter works each topic is clear and to the point. If you only buy one book on geometry this is it. ... Read more

Reviews (5)

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

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

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

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

A Very Good Geometry Book
A good geometry book for high school students. It teaches everything one needs to know about basic euclidean geometry with intuitive lessons and clear explinations of all the content. One thing to note though is that you need a strong understanding of the algerbraic principals of equality, and the fact that the teachers edition is very hard to come by.

Jacobs sugar-coats the process of rigorous proof!
I really enjoyed reading this text. This book is very sensitive to students who are encountering proof for the first time. Jacobs does a great job in building the subject. His motivations and also the humor in text is what makes this book so enjoyable to read. What's more amazing is that he still maintains all the rigor that is critical for advance studies in mathematics.

My favorite high school geometry text
Jacobs is a great teacher and he has written a book that contains much of the essence of that teaching. He presents the material well, with entertaining hooks and careful exposition. There's a good mix of approaches (transformational, intuitive, and rigorous) and a good mix of problems (easy, medium, hard, a few really hard). It's the best balanced of all the geometry texts I've seen. The one drawback is that it doesn't respond to modern trends of using more discovery-based inductive approaches, or using tools like Geometer's Sketchpad or Cabri. Michael Serra's _Discovering Geometry_ is a good source of problems and activities if you wish to supplement your course with this sort of thing. ... Read more

Book Description

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

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

Reviews (3)

Very handy little summary
After several years in a corporate engineering job, I started moonlighting as a math tutor. The Cliff's Quick Review Guides are wonderful to have in my "back pocket" when I need to quickly look something up that is covered in dust in the "archives of my brain."

A Good Start for Geometry Review
This is a helpful tool for practicing concepts of geometry, and stimulation of memory. However, it may not be helpful if you never had any experience with geometry.

A Great Review of Geometry
This review of geometry is exceptional. It is quick, simple, and easy to use. It provides access to all the common postulates and theorems of geometry. This book is designed to be read straight through as a review. In fact, it does not even have an index. Because of this, I found myself searching through the book hunting for small pieces of information. But through the use of the table of contents, I could find the desired information.
Reading this book is an excellent way to prep for any geometry midterm/final or any standardized test (ACT, PSAT, SAT I, SAT II, etc.). It helped me greatly for the SAT, and in a lot less time than studing a text book or reading SAT prep books. If you need to review geometry in a short amount of time, this is the book to get. ... Read more

Book Description

Featuring rich applications and integrated coverage of graphing utilities, this hands-on trigonometry text guides students step by step, from the right triangle to the unit-circle definitions of the trigonometric functions. Examples with matched problems illustrate almost every concept and encourage students to be actively involved in the learning process. Key pedagogical elements, such as annotated examples, think boxes, caution warnings, and reviews help students comprehend and retain the material. ... Read more

Reviews (1)

Excellent book for all levels
It provides wide range of practical applications, with plain English, colorful pages, step by step from basic to advanced approach. It has got answers at the back. I recommend it`s Instructor`s solutions manual as well... ... Read more

Book Description

The second edition of the Handbook of Discrete and Computational Geometry is a thoroughly revised version of the bestselling first edition. With the addition of 500 pages and 14 new chapters covering topics such as geometric graphs, collision detection, clustering, applications of computational geometry, and statistical applications, this is a significant update. This edition includes expanded coverage on the topics of mesh generation in two and three dimensions, aspect graphs, center points, and probabilistic roadmap algorithms. It also features new results on solutions of the Kepler conjecture, and honeycomb conjecture, new bounds on K sets, and new results on face numbers of polytopes. ... Read more

Reviews (1)

Very comprehensive overview of computational geometry
This book, written by many well-known experts in the field, is a fine compendium of articles on the most active areas of computational geometry. Each article is supplemented with a glossary of terms needed for understanding the relevant concepts and frequently contains a list of open problems. An overview of the convex hull of a collection of random points in Euclidean n-space is given in one of the articles on discrete aspects of stochastic geometry, where also a very interesting discussion of generalizations of the Buffon needle problem is given.

There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject.

The article on shortest paths and networks is somewhat disappointing since there is no in-depth discussion on network routing algorithms.

The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of Mayer-Vietoris sequences to design efficient divide-and-conquer schemes for computing the homology of higher-dimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.

The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraic-geometric codes, which is good considering their importance in applications.

The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed.

A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area. ... Read more

Book Description

CliffsQuickReview™ Trigonometry mirrors the curriculum for a typical trigonometry course, which includes trigonometric functions, trigonometry of triangles, trigonometric identities, vectors, polar coordinates, and complex numbers. And, like all CliffsQuickReview books, it includes concise, focused review on introductory-level courses, tear-out pocket guide that highlights fundamental concepts, easy-to-navigate design, self-tests and exercises, resource center for recommendations for more books and more! In short, this is the ultimate supplement for studying Trigonometry – compact, portable, and crammed with everything you need to succeed. ... Read more

Reviews (2)

Handy Little Summary
After several years in a corporate engineering job, I started moonlighting as a math tutor. The Cliff's Quick Review Guides are wonderful to have in my "back pocket" when I need to quickly look something up that is covered in dust in the "archives of my brain."

Great series... Great book.
I'm a (returning :P) university Freshman preparing for the College Board CLEP tests. I was already familiar with the material covered in this book, but needed to refresh my memory. This review turned out to be *exactly* what I needed.

The author's ability to explain the material to the student are just shy of enlightening. The discussions & theorem proofs are written in a very concise, clear style.

I'm a big advocate of the Cliff's QuickReview series. Intended as a course supplement, these books are also *GREAT* for students wanting to refine their skills. Most of them are also very accessible to students with less familiarity on the subject; trying to learn it for the first time.

After reading this, I bought the Calculus & Differential Equations QuickReviews & I'm looking forward to reading them! ... Read more

Book Description

Three million high school students and 172, 000 college students enroll in geometry classes every year. Schaum's Outline of Geometry, Third Edition, is fully updated to reflect the many changes in geometry curriculum, including new terminology and notation and a new chapter on how to use the graphing calculator.

Reviews (3)

NOT AS GOOD AS 2nd Edition!
I think this updated version is not as clear and accurate as the 2nd. Though efforts can be seen trying to improve it and make it more attractive but, simply not as good as the 2nd edition.

Helpful in some cases, but . . .
This is definitely a great review book, but the review problems are very, very easy and not at all like the ones on the actual test. That is definiely my biggest gripe about the book.

However there are many pluses to this book as well. Each theoreom comes with examples, pictures, and definitions so you can easily understand them.

Also, every concept is well defined and in a way that is helpful and concise.

Schaum's Outline of Geometry
This is not only the best elementary geometry (and related subjects) outline, but also the best text in its field, in my opinion. The student will find as many theorems and definitions as in very long and detailed texts, presented much more concisely and in a much more organized fashion here in categories that are easily understood. As with my review of Schaum's algebra, I recommend strongly that the student make flash cards from Schaum's theorems and definitions before trying to work out or even read the numerous solved problems by themselves. Close to 95% of students, in my opinion, make the mistake of doing massive amounts of geometry problems and homework before learning what the theorems and definitions say. This is like trying to learn to play the violin by playing symphonies before one knows how to move the bow and fingers, and is probably the main cause of middle school, high school, and college elementary geometry failure. ... Read more

Book Description

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

Reviews (4)

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

THE BEST SOURCE FOR GEOMETRY
I am a high school student who competes in extracurricular mathematics contests. I've found many great books for trigonometry, algebra, precalculus, calculus, and any other field of math except geometry, i.e. until I found this book. A thorough knowledge of geometry beyond what you learn in high school in necessary needed to be competitive, and the place to get it is Geometry Revisited. This book covers any geometry you could need and is by far the best, if not the only, book out there with what you need to know. This book was also very interesting and thought provoking. The selection and arrangement of topics couldn't be any better. Each lesson even contains exercises (with answers and hints) to show you how to apply what the book teaches you. I would recommend this book to any high school student competing in any contests, to any person interested in extending their knowledge of geometry, or to anyone who with any interest in math. I can tell you that you will learn multitudes and enjoy the book too.

FOR ALL THOSE INTERESTED IN MATHEMATICS
This is 'the book' the typical high school student in America needs to read in order to see what Geometry is really all about. Geometry can be fun and engaging. Unfortunately it has taken a back seat in the high school curriculum. This is unfortunate considering the beauty that the subject has to offer. Many topics are covered in this book: The extended law of cosines, Ptolemy's theorem, transformational geometry, conics, and many, many, many more. This is also a book that is essential for mathematical problem solvers-- particularly for those interested in competing. All that is needed to follow along is the basic geometry learned at the high school level. This book is a must have for any mathematical library.

A++ Highly recommended.