Product Description
Understanding the role of sacred geometry in cosmology and human affairs

• Explains how ancient societies that grasped the timeless principles of sacred geometry were able to create flourishing societies

• Illustrates the social and spiritual values in the natural progression of number

• Contains more than 300 full-color drawings showing the interplay of number and sacred geometry

Galileo described the universe as a large book written in the language of mathematics, which can only be read by those with knowledge of its characters--triangles, circles, and other geometrical figures. The laws of geometry are not human inventions. They are found ready-made in nature and hold a truth that is the same in all times and all places and is older than the world itself.

In How the World Is Made John Michell explains how ancient societies that grasped the timeless principles of sacred geometry were able to create flourishing societies. His more than 300 full-color illustrations reveal the secret code within these geometrical figures and how they express the spiritual meanings in the key numbers of 1 through 12. For example, the number 8 and its octagon are symbols of peace and stability, the holy 7 and its seven-sided figure are connected to the world-soul. He identifies the various regular shapes and shows their constructions; their natural symbolism; their meetings, matings, and ways of breeding; and their functions within the universal order. Some are musical and structural, others relate to life and humanity. In the process of making these discoveries, Michell helps us see the world in a new light. Disparate shapes and their corresponding numbers are woven together, resolving themselves into an all-inclusive world image--that “pattern in the heavens,” as Socrates called it, “which anyone can find and establish within themselves.”
... Read more

Customer Reviews (2)

Sacred Universal Order
Something ancient stirred within me the moment I saw the cover of this book. Not surprising really, since sacred geometry is a nature-made creation story that predates language, homo sapiens, or even the world itself. According to Galileo, "the `grand book' of the universe was written in the language of mathematics and its characters are triangles, circles, and other geometrical figures, without which it is impossible to understand a single word of it."

What makes sacred geometry sacred, is that it connects us with the only world order "in which human nature can happily exist...the cosmological expression of ideal harmony and proportion which constituted the base behind every ancient lasting civilization."

This book is beautifully written and contains over 300 color drawings that illustrate the archetypal patterns that numbers and shapes represent, and how they illuminate social and spiritual development, both in contemporary and historical worlds.

As someone who is mathematically functional, but not sophisticated, there is perhaps more "mathematics" explained in this book than I enjoy or appreciate. But this is a personal bias and in no way reflects the quality of information, knowledge, and wisdom offered in this fascinating and compelling look at sacred universal order.

Beautiful book for alegebra teachers!
My wife teaches algebra and has found this book a treasure for enriching student appreciation of fractals and geometry. ... Read more

Product Description
The book has no illustrations or index. Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Mathematics; Geometry; ... Read more

Product Description
A flexible program with the solid content students need

Glencoe Geometry is the leading geometry program on the market. Algebra and applications are embedded throughout the program and an introduction to geometry proofs begins in Chapter 2. ... Read more

Customer Reviews (2)

Amazon Purchase
Textbook was received in the condition expected based on seller's comments.Shipping occured quickly and textbook was received well before estimated delivery date indicated.Thank you and good job.

geometry book
The book was not in good condition as stated by the seller. It was fair to poor at best ... Read more

Product Description
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. ... Read more

Customer Reviews (16)

let my money back assp
I didn't order this book...

furthermore i don't saw this book.

How it can be happen?

Now I can't believe ordering system of amazon...

Let my money back asap!!!

Concise reference for computational geometry
This book covers the concepts and algorithms concisely and hence forms a very handy reference to Computational Geometry. You could use this as the starting point for any Comp Geom application and build on that. I am pretty happy with this buy!

Good book, not for a primer
The subject is not easy, so the book is surely not for a primer on graphical programming, even more for a primer on computation and algorithms.
But if you need some very advanced algorithms to solve any computational geometry problem, you'll find it here. Maybe the very latest advances on subject are not present here (a new revision of this book is available, not much news on that, look for the difference on the web).
Thanks to the author, whom I asked a clarification on an algorithm present in the book, and responded in less than 3 hours.

The definitive guide to computational geometry.
When studying computer science, one will encounter a number of books."The Dinosaur Book", Operating System Concepts (7th Edition), "The White Book", Introduction to Algorithms, "The Green Book", Artificial Intelligence: A Modern Approach (2nd Edition) (Prentice Hall Series in Artificial Intelligence), and a select few more.The best way to articulate my satisfaction with this material is to refer to it as "The Blue and Yellow Book."

Each chapter is introduced with a problem.For example, "How would one install cameras on the inside of an art gallery (represented by a polygon) such that each wall can be observed with as few cameras as possible."The chapter then presents the material in a clear, concise fashion, and applies this newfound information to solve said problem.

It could be argued that the book is math heavy; certainly those with a strong grip on linear algebra and geometry will have an easier time, but those without can still grasp the material enough to benefit.For those interested in proofs, there's no shortage in the book, either.

Strongly recommended and a great deal of fun to read.

Excellent Background
This book is extremely well written, easy to understand, and actually is the standard text for Computational Geometry classes, as far as I know.The only thing I didn't like about it was that there seemed to be a few errors in some of the pseudocode.But, it's to be expected when publishing a textbook, and I think it'll probably be cleared up in future editions.

Overall, great book.I'd recommend it to anyone taking graphics or a computational geometry class. ... Read more

Product 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

Customer Reviews (13)

A Great Investment of Your Money
I purchased this book for my 15 yr., and he told me that it was very helpful. It explains things in a way that makes it easier to understand.

I Love Math - Great Help for kids to learn how to apply them selves
Added to Library with other books to help communicate ideas and thoughts to kids.Variety in communicating is a great way to see other angles to help kids figure out how things work.

Now Very Helpful
We purchased this book along with the workbook to give my son an extra reference for his geometry class.With few examples in the book to illustrate the concept and no worked out answers in the workbook to see where you may have made a mistake, it was a waste of money for us.

Quick review but it might just confuse you
Easy read/review of geometry, but so many mistakes in the proofs that it doesn't seem like anyone edited the thing.

Simple yet Effective
This is a book written in simple terms and explanations about Geometry. It is not a deep venture into the subject but is meant to be a thought provoking tool to stimulate detuctive reasoning and apply logic to material presnted in this book. This is a starting point for the person who knows very little about Geometry but is going to delve into it. ... Read more

Product Description
Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery. ... Read more

Customer Reviews (15)

Very useful book.
The child I bought this book for is very very happy :) It arrived in 1 day.

Like New
This textbook was in very good condition. It was just like new; no tears, wrinkles, or anything. Very satisfied :) Thanks!

Geometry
The price was affordable it cost almost half the price from my schools bookstore. The book came in timely manner. As soon as I needed it I had it ready for school.

Elementary Goemetry for College Students
I still have not received this book.I am very disappointed with the service

Worst possible approach to Geometry in existance.
I do not recommend this book to anyone. I have taken both Geometry and Trig in High School and they were the easiest thing ever. This book complicates everything ten fold and wants you explain your reason for absolutely everything you do no matter how painfully simple it is. In the first few chapters, most of the questions are open ended. Instead of the focus of teaching you Geometry, the focus is more along the lines of teaching you Philosophy and how to go about proving things in massive detail. It even goes on to create it's own definitions of words that already exist but giving them different meanings. The actual Geometry is subtle and rushed, and you don't end up learning it unless you have an amazing teacher that steers away from the book and hopefully skips half the sections.

I really don't understand why any College in the world would use this book. But Riverside Community College only offers Geometry classes that use this book. It is absolutely the worst possible approach to Geometry.

Edit:

@Fishmael
That's great and all if you're an English major and know every single word in the English language like the back of your hand, but English majors don't have to take Geometry to get their degree. Us Engineers are good at math and problem solving. We couldn't properly structure a sentence if our life depended on it.

I am now going to Butte Community College and have advanced quite a bit since my review of this book. Luckily we have an amazing Math teacher here, Trish Cabral, that wrote her own math books for the school to use. This includes Geometry, Trigonometry, Calc, etc as she also knows how bad some of the books out there are. I tutor students in Geometry and Trigonometry now and her books make math incredibly easy to learn without a bunch of pointless fluff!

So if you are failing in a class that is using this book, it just might be the book and not you! ... Read more

Product Description
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles. ... Read more

Customer Reviews (8)

this is a wonderful book by a master
Robin Hartshorne is a master of Grothendieck's general machinery for generalizing the tools of classical algebraic geometry to apply to families of varieties, and more broadly to number theory.A fundamental difficulty is to grapple with algebro geometric objects such as doubled lines, or surfaces with embedded curves and points in them,that arise as "limits" of simpler varieties.Here the algebra is essential as the naive set of points does not reveal the antecedents of the limiting object.Even more in number theory, when the rings of coefficients used may not admit solutions, the structure of the rings themselves is all you have to go on.For the most basic invariants, when we leave the complex numbers and Riemann's topological and integration techniques are not available, sheaf cohomology is the abstract substitute.

These esoteric developments did not arise spontaneously, but out of classical problems that should be approached first in order to motivate and appreciate the power of the tools in chapters 2,3 of this book.Professor Hartshorne says himself that he taught the chapters out of order when he first was writing the book.The average reader should probably read the chapters in the order he taught them in, not the order they appear in this book.Thus first read chapters 4 and 5 on curves and surfaces, or possibly read 1,4,5, to get first a general introduction, then study curves and surfaces.Only then delve into chapters 2 and 3 for the sophisticated stuff.

If you really want to start with the classical roots, begin instead with Rick Miranda's book on Algebraic curves and Riemann surfaces.Of course there are hardy souls who can wade right through Hartshorne's book in order, but for many that is a prescription for losing heart and losing interest in the subject.When all is said and done, there are very valuable ideas and tools in this book that are not available as easily anywhere else.You just have to learn how to get at them.You might want to read in whatever order appeals to you.But do not feel obligated to just plow from page 1 on.Or try the first volume of Shafarevich and then this, or bounce back and forth as the spirit moves you.Kempf also has a book on Algebraic varieties with sheaf cohomology but not schemes, which may ease the abstraction level, and there is also Serre's original paper FAC in that vein.

A Necessary and Useful Pain
Algebraic Geometry is the first textbook on scheme-theoretic algebraic geometry. Scheme theory was created in the 1960's by Alexander Grothendieck. Grothendieck also co-authored an extremely well-written, 1800-page reference manuscript on scheme theory called "Éléments de Géométrie Algébrique" (EGA). However, EGA is unsuitable as a textbook because it had no examples or motivation and proved every theorem in great detail and maximal generality.

Algebraic Geometry has 5 chapters. The first chapter summarizes algebraic geometry before schemes. The next two chapters compress EGA to 230 pages(!). The last two chapters show how well scheme theory can solve classical problems from algebraic geometry.

That should be a hint that Algebraic Geometry is one of the most dense and difficult math textbooks ever written.

To achieve that kind of compression, Hartshorne's writing is extremely terse. He assumes a solid understanding of commutative algebra and point-set topology. He often gives one or two-sentence proofs and explanations that, when fleshed out and made complete, would need both many pages and new techniques that are never mentioned in the text. He also gives almost no motivation throughout Chapters II and III, because Chapters IV and V fill this role. When he does give motivation, it is usually relegated to the exercises, many of which, again, require techniques that are never mentioned in the text. Finally, he assigns the proofs of many essential and extremely difficult theorems as exercises.

There are other, much more user-friendly introductions to scheme theory than Algebraic Geometry---For example, The Red Book of Varieties and Schemes, The Geometry of Schemes, and Algebraic Geometry and Arithmetic Curves. These books, along with EGA, can also serve as complements to Algebraic Geometry when Hartshorne's writing becomes too dense to learn from.

However, Algebraic Geometry is unique in that no other textbook on scheme theory covers nearly as much material as it does. Also, for all of its density, Algebraic Geometry is very well-written and an excellent reference, especially considering how much it covers and the length and complexity of its source material. Because of this, I cannot foresee any significantly better replacement for it being written in the near future. Algebraic Geometry will probably continue to be a necessary and useful pain to learners of scheme theory, just as it has been for the past 30 years.

Unfortunately a better book on the subject doesn't exist.
The motivation is nonexistent, and the examples are trivial. If you want to learn anything you have to trudge through exercises which require techniques that are not addressed in the text. I don't mind working to learn a subject, but spending two hours trying to understand what a question is asking is a bit much.

The best, and most concise review I have ever heard was, "Hartshorne is the worst book on Algebraic Geometry, except for all the others".

Nice selection of exercises
Here's my impression after doing the first 30 pages: What makes this a really good book is the exercises. Not too hard, always interesting. If you are new to the subject you need to look up results from commutative algebra somewhere else. It can be a little strange getting used to working with the Zariski topology. All open sets are dense, so you don't have the notion of a small neighborhood of a point. For instance any bijection between two curves is a homeomorphism.

THE book for the Grothendieck approach
This is THE book to use if you're interested in learning algebraic geometry via the language of schemes.Certainly, this is a difficult book; even more so because many important results are left as exercises.But reading through this book and completing all the exercises will give you most of the background you need to get into the cutting edge of AG.This is exactly how my advisor prepares his students, and how his advisor prepared him, and it seems to work.

Some helpful suggestions from my experience with this book:
1) if you want more concrete examples of schemes, take a look at Eisenbud and Harris, The Geometry of Schemes;
2) if you prefer a more analytic approach (via Riemann surfaces), Griffiths and Harris is worth checking out, though it lacks exercises. ... Read more

Product Description
Basic Mathematical Skills with Geometry, 7/e by Baratto/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics.The seventh edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage onmastering math through practice.This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce basic mathematical skills and put the content in context.The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student’s skills in relating to mathematics. The book is designed for a one-semester basic math course and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill’s online homework management system, MathZone. ... Read more

Customer Reviews (9)

Great price!!
This is exactly the book I needed for college and I received it in good condition. Fast shipping and great price!!!I've ordered in the past from Amazon and have always received excellent service. No problems here.

Basic Mathematical Skills with Geometry
This was the frist time that I have order a book from this site. I was afraid at frist but when the book came I was very pleased.The description was very clear and true to what it said about the book. I will be ordering more books in the future.I am going to college and I will need more books. The price was excellent and the book was in excellent condition.

Thank you
Sharon D

GREAT SERVICE A++++
Fast Shipping and book was is great condition when it arrived. Exactly what I ordered. A++++

expensive school books
I am not sure how this person ended up with a book still in plastic, but I am a person that cannot do my online classed with online books (gives me a headache to stare at the screen that long). So getting my books online for a very good price has really helped my budget and my eyestrain. The book showed up in plenty of time for my class, thank you.

Basic Math Skills with Geometry
This is the book I need for my other class. Although it is the basic math, it refreshes my math skills as far as going back to elementay school. ... Read more

Product Description
Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space.First Edition Hb (1997): 0-521-38334-XFirst Edition Pb (1999): 0-521-38753-1 ... Read more

Customer Reviews (18)

could have been so much better
this is a damn hard book to understand. i am a theoretical physicist who already knows the stuff here and i find the explanations sometimes very confusing.it's not a simple book to read. you have to pay close attention to every line, and this is a major pain since the book is so big. also some sentences are very bloated. i know the author spent a lot of time on this book. but he should have gotten a better copy editor.

it has a lot going for it.the emphasis on physics is nice.but unless you have a lot of patience and haven't read any other books (so you don't confused about the unorthodox notation), this book may drive you crazy.

its really too bad, because this is the only book that i know of which tries to really "explain" bundles in a non-pedantic way.unfortunately, it is not that successful. (the part on bundles is perhaps the most transparent and easiest part of the book though).

if you have patience and are willing to decipher some of the prose which is ambiguous, or difficult to understand because there are like 5 commas in a single sentence, then this is absolutely a 5 STAR book.the material is wonderful, and there is an enormous amount of insight shared.

otherwise, if you are a typical math guy (like me) you are probably better off going with a thinner and more mathematical book like Darling's differential geometry book or Morita's book or the new book on differential geometry by Tu.

it is of course an alternative to Nakahara.but Nakahara isn't a proper textbook.it's a collection of examples. in summary, despite the book's flaws, i have not seen anyone write a better story in a single volume of how to combine math and physics at an "elementary" level than Frankel.

Fantastic - for the scientist
A very good book: buy it. But only if you are a scientist or student of physics/mathematics. This is not popular-science-common-public level.

a book worth keeping
This book can be quite confusing if you start without any background on the idea of manifold or knows nothing about general relativity. However, it does have strong points:

1. The notation is very up-to-date, and is entirely coordinate-independant approach.

2. The author explains in great details of formulation of modern differential geometry, and the details are comparatively lacking in other reference books.

3. The author never hesitate to use graphs and diagrams to illustrate points, and stroke nice balance in between mathematics rigor and physical insight.

Although it appears quite verbose at some point, it is mainly because differential geometry is such a heavy subject. Another book nice to have as companion reading is Goldburg's "Tensor analysis on Manifold", a terse, well-written text book.

Phenomenal
I just finished reading this book and I found it phenomenal. The physical ideas are made very clear in a natural mathematical framework.

You should buy this, despite its flaws
The other reviews on this page give this book anywhere from 1 to 5 stars, and they are all correct in their own way. The book is inspired, deep and full of physics applications and insights. On the other hand, it skims over mathematical rigor to a large degree and focuses more on defining things, getting a feel for them and moving on to application.

My advice: buy the book for its strengths, and read other books in parallel if you need more rigor. But still, buy it.

Also, things can be confusing on the first two or three reads, but keep at it and you will be glad you did. ... Read more

Product Description

Product Description
Starting in June 2009, the New York State Board of Regents is reinstituting the high school geometry exam. This brand-new Regents Exams and Answers: Geometry joins BarronÂ's famous series of Regents Â"Redbooks,Â" presenting an in-depth subject review, plus hundreds of practice problems with answers. Topics reviewedinclude the language of geometry; parallel lines and quadrilaterals and coordinates; similarity; right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and an introduction to solid geometry. Also presented is a full-length practice geometry exam that accurately reflects New York State Regents standards in subject matter and degree of difficulty. ... Read more

Product Description
Lucid, well-written introduction to elementary geometry usually included in undergraduate and first-year graduate courses in mathematics. Topics include vector algebra in the plane, circles and coaxal systems, mappings of the Euclidean plane, similitudes, isometries, mappings of the intensive plane, much more. Over 500 exercises. "...lucid and masterly survey."—Math. Gazette.
... Read more

Customer Reviews (5)

Book Review
This is a good geometry book far anyone looking to expand on their typical introduction geometry class in college or a college graduate in Mathematics. It does not read like a textbook, it appears the author already assumes you are a Math major or have already taken other geometry courses. The only downside is that it reads like an encyclopedia and does less "teaching" that a regular textbook would do. Makes a great reference though!

Goodto augment a textbook
I purchased this book to provide a second source of information for a college senior/ graduate level geometry class.It was quite helpful at times in giving second explanations of topics covered in class at a price significantly less than the class textbook.The book is comprehensive, and reasonably well written for a math book. One drawback was that it does not discuss Poincare's upper half plane model of hyperbolic geometry, only Poincare's disc model is covered.Inversions are well covered, and one could use this information to map from the disc model to the upper half plane model, so this was not a serious omission. I have no regrets about buying this book.

Clarity and Simplicity
This text - comprised of detailed accounts of Euclidean, Affine, and Projective geometries, a thorough discussion of the Poincare model of hyperbolic geometry, and a motivating chapter on Algebraic geometry - is remarkable for its clarity and simplicity. Very little is initially expected of the reader - a sound knowledege of linear algebra, complex arithmetic and trigonometry - and the proof style is not too formal. Considering the level of detail of its treatment (it's a little more than twice the length of Coxeter's Geometry Revisited, which shares a similar selection of topics) it is ideal for undergraduates or those looking for a good, inexpensive text for self study.

Throughout the text the author emphasizes the use of basic algebraic techniques as an aid to finding clear and simple proofs. In more than one case a result is proved several times, each proof illustrating a different technique. In the first chapter, the utility of the vector approach is highlighted by using vector arithmetic, inner-products and exterior algebra to prove several classic theorems of plane geometry. In later chapters elementary group theory, Moebius transformations and linear algebra are used extensively in the discussions of the mappings of the Euclidean plane, of the mappings of the inversive plane, and of projective geometry respectively.

Basically, this is a good, detailed undergraduate introduction to geometry. It's perhaps a little less entertaining than Coxeter's introductory geometry books but it has a much friendlier price-tag.

Definitely a comprehensive course
Be aware that the preface of this book explains that it is based on a course for junior and senior college students and first-year graduate students.This book is much more than the average person will ever need.A simpler approach for people like me who just want to prepare for calculus is Geometry and Trigonometry for Calculus by Peter H. Selby.

a complete and succinct book!
A wonderful book, value for money! If you are learning geometry for interest or to prepare for competitions such as IMO, then this book is for you! The theorems and diagrams are complete and straight to the point. Theauthor presents the informations in a succinct manner; thus it is easy forone to follow and comprehend. I guess it may be one of the most completebook on geometry in the market! ... Read more

Customer Reviews (1)

Good for some, challenging for others
I give this textbook 3.5 stars. I have been teaching out of this book for three years now. The textbook is structured very nicely with example problems in each section, very short video tutors that are accessible online, a dictionary in the back, orange and green boxes to highlight the most important concepts, and a "what you need to know" section before starting each section. Also, quite importantly, there are exams at the end of each section that can be taken online that are actually graded*. In this regard this could be a good text for homeschool students.

On the flip side, many of my students have had trouble with this text. In the second half, trigonometry is introduced, but then in subsequent chapters such as finding area, there are many problems that are unmarked that are unsolvable without a full understanding of the trig. My students who struggled with trigonometry then struggled with area. I like that the trig is included in the area section, but it's not in many geometry texts, and the problems that require trig should be marked in someway. Similarly, coordinate geometry is not explored in detail, but spread throughout, and many of my students were confused on how to solve these problems.

In summary, I think this is a solid text for students who are mathematically capable. I think that the text is too challenging for students who are just looking to survive math by taking the minimum requirements.

PROS:
Spanish-English dictionary in back
A few challenge problems at the end of each section
Proof problems are labeled (not a proof-oriented text)
Good supplementary materials come with full curriculum
Example problems are listed next to problems in a given section (eg. see example 2)

CONS:
*Online tests can be retaken by hitting the back browser and students can then change all the answers to the correct ones
Chapter 1 is an introductory chapter that covers too many topics
Chapter 2 is entirely on logic but three of the five sections are primarily about English language words - it's a little overkill
After the build-up to proofs in chapter 4, they are more or less ignored for the rest of the text
Circles are not introduced until the final chapter, 12, and therefore an important concept could be missed

NEUTRAL:
Answers to most odd problems in the back, but sometimes many are left out; it's inconsistent
Problem Set B is called application problems, but sometimes this means solving for diagrams with Xs; the important problems are usually in part A, but not always ... Read more

Product Description
Passport to Algebra and Geometry0618374221 ... Read more

Customer Reviews (4)

All you need to know
I am currently homeschooling my daughter and forgot all the basics to math. This was a great book to show problems and how to analyze the answers.

Passport to Algebra
The condition was listed as used-very good with cover edges worn. The actual condtion was the binding was tape repaired and seperated from the cover. Very used poor conditon.

It makes words fun to be memorized
My daughter in her middle school found it an excellent book. She now can learn 20 a day in about one hour.

School Book
I use this book in school and it makes math really easy to learn!If you are looking for a book with algebra and geometey questions, this is the book for you.With thousands of questions, their answers, and explanations, this book will help you learn good math skills. ... Read more

Product Description
This classic study probes the geometric interrelationships between art and life in discussions that range from Plato, Pythagoras and Archimedes to modern architecture and art, flowers, shells and marine life, the human face and much, much more. Also explored: the Golden Section, geometrical shapes on the plane, geometrical shapes in space, crystal lattices and many other fascinating topics.
... Read more

Customer Reviews (8)

Golden.
I read this book 36 years ago , when finishinginternship in an architectural firm. While I did not pursue Architecture , I discovered this gem of a book , which explains to you in simple terms what the Golden Number is , and how theGolden section is used in Art. A must for those who believe in aesthetics rules for just about everything created by an artist, or by nature.

Managing Geometry In Time and Space
The Geometry Of Art And Life by Matila Ghyka is an interesting book that pertains primarily to ancient information regarding the fiine arts. Geometry unites all aspects of this book. All aspects of geometry are utilized to manage the organic and inorganic in time and space.

Excellent and Insightful
This short paperback is a hidden gem.It contains so many insightful pithy clues about life, along with easy to understand mathematical paradigms.Every item will have you saying is this math, is it philosophy, is it religion, or is just true in many, many ways.

Shows how mathematics intertwines with the arts and biology
This book is a unique one that combines mathematics with art and somewhat quantifies that which we call beauty. The mathematical concepts presented are not difficult. If you've been exposed to algebra and geometry you should have no trouble. What will definitely help is having studied art, and in particular, art appreciation. With no real feeling for symmetry or form you might not appreciate this book as much as you could.

The book's central focus is to show that patterns, themes of symmetry, and spirals discovered in living forms and living growth are the same themes of proportion that were used by Greek and Gothic architects. It also shows that the proportion known as "The Golden Section" appears to be the principle invariant. The Golden Section's algebraic and geometric properties are discussed, as are its role in biology and in aesthetics.

This book is very accessible, but it is not something you will want to read quickly cover to cover. Instead, the best way to read this book is to read a short section, make sure you understand the underlying mathematics, and then think about what that particular section of thebook says about the application of that mathematics to the arts or biology before returning to the book for further reading.

Lacking depth in analysis
Ghyka attempts to show the objects in nature are not randomly formed; he begins the with the concept of ratio and proportion in the plane; the golden section; and then to the regular polygons and geometric shapes in 3 dimensions.Then he rambles onto hypothesizing why an architecture design may seem striking. In doing so he makes gross assumptions which are to the point of being forced to fit his theories.The basic concepts that he delves; one can familiarize oneself with by a quick reference on the internet. Hence I do not recommend spending the time and money to read this book.

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Teacher's Edition ... Read more

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This text has been adopted at:

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

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

- Revue Romaine de Mathematiques Pures et Appliquees

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

- Monatshefte F. Mathematik

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

- Publicationes Mathematicae

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

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

Customer Reviews (8)

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

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

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

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

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

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

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

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

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

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

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Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity and shape of space-time. Accessible to layman but also of interest to specialist. 141 illustrations.
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Customer Reviews (22)

geometry, relativity and the fourth dimemsion
too abstract. Didn't touch on relativity until the 4th chapter and had trouble following the book til then.

Well Written Introduction to the Fourth Dimension
A great mathematical read! Fascinating diagrams. Begins with accessible concepts for all who love geometry. Gets into spacetime later in the book. Considers some philosophical/spiritual elements too, but mostly geared toward math and physics. A classic read. Highly recommend!

Good intro to related topics to Special Relativity
I found this work to be quite readable and something I can introduce to people with less math background.However, reading the book raises more questions than answers in my mind regarding the history of mathematics.For example, non-Euclidean geometry has been around for a long time and is the basis for ancient systems of navigation.

Similarly, for those who have studied the history of astrology (and its initimate relationship in the ancient world to navigation and agriculture), a great number of things (for example, the divisions of the houses) are all based on spherical geometry and many go back nearly two thousand years.For anyone who has ever known that the earth was a sphere, many of these problems were largely taken for granted.The only real problem with disproving Euclid's 5th postulate has been defining parallel lines on a sphere.I am not entirely sure that Rucker answers this in looking at the flattened sphere because the sphere could be rotated to make any two lines parallel.

Otherwise, I think this is a decent beginner book relating to the subjects in question.It is a useful work and I would generally highly recommend it as an introduction.

Instructive, and interesting
I found the book to be both educational, in that I learned great deal about geomtery and the history of diemsions from this book, as well as being fun to read. Both interesting and intellectually stimulating--I find this combination rare. I recommend ths book to anyone interested in the field.

With few exceptions, it is a readable, stepwise explanation of how the universe is structured
To understand relativity, it is necessary to understand geometry, specifically how a straight line can be curved. For nearly everyone, any attempt to understand four-dimensional space begins with understanding how a three-dimensional creature would appear to a two-dimensional one. One of the earliest and still the greatest of all introductions to going up a dimension is "Flatland" by Edwin A. Abbott. Quite naturally and sensibly, Rucker starts with Abbott's rendition of the properties of Flatland.
Rucker then moves on to the idea of curved space, where the shortest distance between two points is a "straight line", which is curved by the properties of the space. The space that we occupy is curved by the presence of matter, as Einstein claimed in his relativity theories. Furthermore, movement causes shrinkage in the direction of the movement and the slowing of time, which causes time to become just another dimension of space. As counterintuitive as this may appear, Einstein's relativity theory has been verified over and over again to a large number of significant figures.
One of the best things about this book is that Rucker has included problems at the end of each chapter. These problems reinforce the concepts of the chapter; it is unfortunate that no solutions were included.
In this book, Rucker steps the reader through all of the background material necessary to understand relativity and four-dimensional space. With few exceptions, the accounts are understandable to anyone with an understanding of college algebra.
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Don’t Just Learn Geometry...Master It!

Brimming with fun and educational games and activities, the Magical Math series provides everything you need to know to become a master of mathematics! In each of these books, Lynette Long uses her unique style to help you truly understand mathematical concepts as you use common objects such as playing cards, dice, coins, and every mathematician’s basic tools: paper and pencil.

Inside Groovy Geometry, you’ll find all the geometry basics, plus information on how to figure out the height of any object from its shadow, find distances "as the crow flies," estimate the area of any space, and much more. While you play the Name Game and Rectangle Race, you’ll learn how to draw, measure, and identify different kinds of angles, triangles, and quadrilaterals. And with fun activities like Bull’s Eye and Pizza Party, you’ll practice plotting coordinate points on a graph and measuring the area and diameter of a circle. Most important, you’ll have a great time doing it!

So why wait? Jump right in and find out how easy it is to become a mathematics master! ... Read more