Book Description

This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a historical context.Chapter topics include axiomatic systems, axiom sets for geometry, neutral geometry, Euclidean geometry of the plane, analytic and transformational geometry, non-Euclidean geometries, and projective geometry.For anyone in need of a refresher course in geometry. ... Read more

Book Description

Reviews (1)

math fun
This is a picture book about the Zills family.The family is off on an adventure to hiddenburial site of an ancient pharaoh.The twin brothers in the family get stuck inside a pyramid with their dog.They must use math to figure out a way to escape the pyramid. They must use skills to figure out the riddles written on the wall and locate the hidden burial chamber. Will they ever figure it out?Read Mummy Math to find out!

It's one of those special books which children will read without realizing they are learning a mathematical concept.

This is a recommended book for those teacher or parents that want to make math a little more exciting for children. ... Read more

Reviews (1)

Too expensive, and depends upon the teacher.
Although I applaud Kay's intentions in presenting geometry inthis fashion, I think that this book would require an excellentteacher to accompany it. In some ways, I might have predicted this, because to preserve the "discovery," you have to be a little coy about what you are trying to teach...you have to hide the point. The book would be an excellent reference text, as Kay provides the historical context of most of the theorems, and the material is presented in a rather dense format ... ... Read more

Book Description

The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geometrical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from various viewpoints and aims towards computation and visualization. Besides applications, it contains a tutorial on projective geometry and an introduction into the theory of smooth and algebraic manifolds of lines. It will be useful to researchers, graduate students, and anyone interested either in the theory or in computational aspects in general, or in applications in particular. ... Read more

Amazon.com

Reinventing the wheel is a terrible waste of time, yet legions of computer programmers do exactly that every day. Geometric Tools for Computer Graphics gives the working graphics programmer a vast collection of programming examples, complex code snippets explained and ready to use. Each chapter is filled with more than just code examples--the explanations needed to understand why these examples work the way they do are given by authors with experience both in writing and in the field.

There is nothing here for the casual graphics programmer and everything for the serious 2-D and 3-D programmer. Thirteen chapters, three appendices, and a three-column index that spans over 30 pages cover everything about computer-graphic geometry, from the basics of using matrices and linear systems to intersecting 3-D objects.

The appendices alone are worth the price: "Numerical Methods," "Trigonometry," and "Basic Formulas for Geometric Primitives" are treasures filled with hard-core examples of the kind that can be put to use right out of the box. Less experienced programmers will find these to be invaluable references, but then there's the rest of the book--nearly 1,000 pages loaded with examples and theory, page after page of information written in a clear, concise voice.

Any hard-core graphics programmer will appreciate the value of the examples presented here, as well as the discussion of theory. After all, there's no need to waste time experimenting with code once the theory is known. Geometric Tools represents the best of both worlds: discussion of theory and code examples built on and culled from years of experience. --Mike Caputo ... Read more

Reviews (4)

Way over my head
I almost gave this book 2 stars but decided that punishing the authors for my stupidity wasn't fair. This book is obviously chucked full of just about every geometric formula you will ever need in computer graphics. But you had better be a darn serious mathematician! I could simply never grasp mathematics at this level. I could never look at those formulas, written in some alien heiroglyphs, and understand them enough to translate them into code. This book is one of those "Written by Professors for Professors." I bought the book because of the reviews that wrote about the code samples. Well, they are there (pseudo-code, but that is better than nothing) but nowhere near what I was expecting. My mistake was thinking it was a programming book. It's not! Bottom line, if you are looking for computer graphics formulas and understand mathematics, this book is for you. If you are a programmer and are expecting a computer graphics library of functions, look somewhere else.

warning: first edition
First of all, I commend the authors on a timely and valuable book. However, a word of caution: this book is full of errors. Every couple of pages I am noting in the margin: did they mean A instead of B? Having encountered so many errors, I am reading every formula with scepticism. The errors are serious enough that I have trouble recommending the book without reservations, but I know of no suitable alternative. I can only hope that the errors will be weeded out of future editions.

A real Treasure,
I just got this book about a week ago and I haven't been able to put it down since. A great resource, a real treasure full of well presented gems. A large number of topics are well presented with mathematical depth that enables you to understand the code. The code is very well written and concise. Truly a great book and a pleasure to read. I hope to see more books like this in the future. I am interested in medical imaging applications and I know I will be using this book for a long time to come. In addition, the authors have a site ... that presents the code and additional very valuable materials.

An incredible amount of material in a single book
This book provides a solid grounding in vectors and matrices, then covers a wide range of 2D and 3D geometric algorithms, such as object/object distance and intersection, boolean operations, BSP trees, convex hulls, and more. It is a comprehensive guide, giving relevant theory, methods, and working code fragments. It's an incredible value for the amount of material it covers. I think it is a must-have for computer graphics professionals (and others in related fields). In the interest of full disclosure, I wrote the Foreword to this book, which I did because I was pleased with how good it is.

Visit Dave Eberly's "Magic Software" site for more about the book's contents. ... Read more

Book Description

Practical exercises with step-by-step solutions are designed to make geometric concepts easy to understand and remember.This book may be used as a brush-up for test preparation, as a classroom supplement, or as a self-teaching guide for workers in technical fields. Review high school geometry without intimidation, and practice with examples from the world of work and everyday life. ... Read more

Reviews (1)

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

Book Description

Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy.

Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology.

This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject. ... Read more

Book Description

Stimulating collection of unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and many other topics. Arranged in order of difficulty. Detailed solutions.
... Read more

Reviews (2)

Great book on geometry.
Geometry problems are my favorite sort of math problems to do, because many geometry problems require, literally looking at the problem in a different way; a slight twist on the facts that you are using and the problem becomes much easier. It's usually a simple, yet ingenious insight that often solves the problem.

To that end, this book does not disappoint. I highly recommend this book, for it contains such problems, and at the end of the first section of problems, I had developed a sort of intuition for Euclidean 'way' of thinking. I am far from finishing this book, but I think it would take me a few years to do so.

The book is broken down into several chapters. The first chapter contains the problems, the next are the solutions, the next are hints to the problem, and finally an appendix of useful theorems and formulas. The useful theorems are mostly the results of Euclid's Book 1 and 3, and the immediate consequences of those theorems, e.g., the sum of the angles of a convex quadrilateral is 360.

The hint chapter may be too helpful for it usually outlines the steps you need. I would have preferred several hint chapters that are progressively more helpful. The solution section may show more than one solution to a problem. There were a few times my solution was not found in the back of the book, but that's not a fault of the book, but a delight if you can come up with an original solution!

The problem chapter is broken down into what I would call fundamentals and advanced sections. There are over 200 problems.

The fundamental section is further broken down into parts, either by method, e.g., similar triangles/pythagorean's theorem, or theme, e.g., problems concerning 'circles' and problems concerning 'areas'. Many the problems can be solved in different ways. The first section of problems can be done with a purely Euclidean style approach. But lots of problems require a *little* algebra, mainly to economize on thought, e.g., a variable place holder for proportions, and a simple formula or two, and of course Euclid's theorems. Each section is not isolated, they sort of build on the first part of this section.

The advanced section has a part containing a 'mixture' of techniques to use, and again themes which may not be familiar to the beginner, e.g., Simson lines, and Ceva's theorem.

The problems are of proof, or finding the measure of a line, angle, area, or finding the algebraic formula for a collection of objects. So far, I have not encountered a single construction problem. Some of these problems may be quite easy to solve, and some can be quite hard! For instance, one of the problems asks you to prove Heron's formula. The Euclidean proof takes several pages, and I would say is beyond that for a math olympiad. Most problems, are of course, not this hard.

You may have a tendency to want to 'angle-chase' or plug and play a formula. Such thinking will cause you to go mad! You'll endlessly try to some up combinations of angles, and construct new ones. Luckily, I broke that habit, and there are enough of these problems for you to break the habit in order to keep your sanity. Find the elegant solution, if you can, and most of these problems have them. And when you do -as George Polya said in "How to Solve It"- you'll see the solution 'at a glance'. (It is more rewarding and more difficult, to do away with algebra, and think 'purely' geometrically. It's an intuitive appreciation for the problem, and you can hold a longer argument chain in your head. Then, You'll begin to appreciate the qualitative style of thinking that is Euclidean. It's impossible, however, for many cases.)

Also, you will need to have another geometry book handy. There were one or two definitions that were unfamiliary to me, and I could not find them anywhere defined in the book. It would be nice on the next edition if they gave definitions of some of the terms. Dont' be alarmed, they were not technical terms, and more along the lines of 'what is a median?'

Finally, these problems are a good starting point for your own investigations into geometry. By varying a problem found in the 'Geometric Potpourri', I was able to finally figure out how to construct a pentagon, which has been stumping me for many years.

To round out your geometry skills, you will also want to do construction problems. I recommend the book 'Geometric Constructions' by George E. Martin, it is text book; so it contains more than just problems, but the problems also require ingenious solutions. (I hope to review this book.)

Mr. Posamantier, please print the next volume!! And for those who obtain this book, happy solving!

Superb book
This book is a great one. Invaluable as a supplement to a basic geometry textbook. It includes approximately 200 problems dealing with congruence and parallelism, circles, area relationships, collinearity and concurrency and many other subjects. Detailed solutions and hints are provided for all problems, and specific answers for most. I highly recommend this book to anyone looking for a great book at an affordable price. Buy it. You won't regret it. ... Read more

Book Description

For all math teachers in grades 6-12, this practical resource provides 130 detailed lessons with reproducible worksheets to help students understand geometry concepts and recognize and interpret geometry's relationship to the real world. The lessons and worksheets are organized into seven sections, each covering one major area of geometry and presented in an easy-to-follow format including title focusing on a specific topic/skill, learning objective, special materials (if any), teaching notes with step-by-step directions, answer key, and reproducible student activity sheets. Activities in sections 1-6 are presented in order of difficulty within each section while those in Part 7, "A Potpourri of Geometry," are open-ended and may be used with most middle and high school classes. Many activities throughout the book may be used with calculators and computers in line with the NCTM's recommendations. ... Read more

Reviews (2)

Most material in this book is available elsewhere
My school uses the University of Chicago School Mathmatics books, and most of the material in this "Activities Kit" is just a duplication of what I already have. I'm also not sure why it is called an "Activities Kit" since 95% of it is just worksheets. My students are tired of worksheets!

Really Usable Activities!
I've been teaching geometry for several years and this is the first book that I have found that has almost everything in it that I need. The teacher pages are well-written and the student pages are very well done. This book works well for both high school students who are studying formal geometry and for younger students who may not be as advanced. Thanks! ... Read more

Book Description

Reviews (14)

one of the best scientific works
Heath does a better job than most in his notes-almost all commentary written in modern editions of great scientific works is hilarious-usually some half brite clown trys to find a million faults in the writing of someone who is obviously one hell of a lot more intelligent. Heath just gives the likely facts surrounding Euclid's life, works, and the evolution of the math contained in The Elements.
This is math that is accesible if you're willing to put in the time, because it starts with principles we're all familiar with and can agree on (such as the whole being greater than the part), and slowly and methodically works it's way to comparisons of the 5 Platonic solids. Along the way he covers number theory, plane and solid geometry, and provides an early basis for calculus and even certain branches of physics, although the terminology is obscure if you're familiar with more modern methods. Approach this work as a puzzle book, and try to solve the proofs yourself, or even try to disprove them; proceed slowly, it will take more than a year to work through all 13 books, but you will understand these things much better than the average math teacher when you're done. It's also more fun to try to understand the work of one of the greats than it is to study from one of those overpriced college calculus books-don't worry. The principles of Math and Physics don't change, this book is as valid now as ever!

Order Your Thinking
Euclid teaches us step-by-step how to prove the most fundamental and complex concepts of geometry in such a systematic and understandable way. By learning Euclid's propositions, we also find ourselves thinking and speaking in a more ordered fashion. I recommend these books to anyone interested in math as well as those who want to improve their debating and reasoning skills.

There's a Better Way
If you like long, tedious introductions and the need to sort through endless words to find what you're looking for, then you might want this version of Euclid's work. On the other hand, if you want to get to the point and prefer a clear resource for study, the version published by Green Lion is FAR superior to this one.

I think we're missing something here.
I read most of the twelve reviews. I gleaned from them several quotes which demonstrate my point. First, the quotes:

"The principles of Math and Physics don't change, this book is as valid now as ever!" from the review by Carl Slim

[I disagree. Neither math, nor physics are unchangable. They evolve, expand, modify, and make new discoveries regularly.]

"I can understand high level math books in Algebra and Analysis, but this book confused me with words. Frankly, I do not see why a math book is supposed to explained in words after all this development of mathematics.These notes are not all that easy and at a higher level than the postulates of Euclid, and I found them irrelevant....It even, proves the Pythagorean theorem. This proof was a bit difficult, a simpler proof can be found elsewhere, but, after all, it is amazing how mathematicians could have solved such a problem thousands of years ago."
according to the reviewer from Qatar

[This is a lengthy quote, however, it points out the misunderstanding regarding Euclid's treatment of the Pythagorean Theorem. Euclid's Prop. 47 gives a visual representation and proof, whereas the equation used in algebra is abstract (this is why many struggle with algebra--it is highly abstract where geometry would treat the same problem concretely).

"Euclid teaches us step-by-step how to prove the most fundamental and complex concepts of geometry in such a systematic and understandable way. By learning Euclid's propositions, we also find ourselves thinking and speaking in a more ordered fashion. I recommend these books to anyone interested in math as well as those who want to improve their debating and reasoning skills."
according to a reader/reviewer in Eastern Pennsylvania (bless you)

What's missing from the first two altogether, but pointed to in the third, is this: Euclid,his contemporaries, and many who followed in his footsteps were philosophers as well as mathematicians. Both math and philosophy try to produce certainty through systematic methodology. Euclid's Elements therefore, are not only profitable for developing an understanding of geometry, it can also aid in the development of disciplined and logical thought. Just listen to philosophy students; they use terminology similar to that of mathematicians. In fact, this is one reason classical home schoolers are sometimes taught Euclid; it compliments the study of the Great Books, logic, philiosophy, and forensics.
I actually heard recently that a new translation is coming out real soon, if it's not out already.
I hope I don't come off as a smartypants, writing essentially a review of the reviewers. I don't have advanced degrees in math, physics, or philosophy, but I believe the reviews are incomplete without this understanding of the historical relationship between math and philosophy and the use of Euclid. Blessings.

Classic = Elegant, if not for the notation!
We, the children of this new age, are deprived of major classics and beautiful mathematics because of the tediousness of the notation. Oh, do not be optimistic, this is not the only book with forbidding notation, see Artin's Galois theory, which is an excellent book if someone just tries to update its notation.

Aside from that the book was a merry one. It contains more books than the first one. It contains the books 3 up to 9 of Euclid's 13 books of the elements.

Book 3 is a delightful one. Its sole purpose is to characterize circles. It goes with the same style of the first two books given the first volume. Books 4 continues in the same fashion and studies circumscribing and inscribing figures by others.

Book 5 is the first attempt to bring geometry near to algebra. It deals with proportions. The notation started getting more and more cumbersome. He continues giving us things that we know already. And all through the volume until book 9 we see results commonly given in simple college algebra in the most tedious fashion.

I praise this volume only for the material on circles and I see that it is worth reading if you have a strong constitution. As for me I am not going to read the third one about the out of date commensurable numbers. ... Read more

Book Description

Geometry is one of a group of special sciences - Number, Music and Cosmology are the others - found identically in nearly every culture on earth. In this small volume, Miranda Lundy presents a unique introduction to this most ancient and timeless of universal sciences.Sacred Geometry demonstrates what happens to space in two dimensions - a subject last flowering in the art, science and architecture of the Renaissance and seen in the designs of Stonehenge, mosque decorations and church windows. With exquisite hand-drawn images throughout showing the relationship between shapes, the patterns of coin circles, and the definition of the golden section, it will forever alter the way in which you look at a triangle, hexagon, arch, or spiral.

Small Books, Big Ideas Historically, in all known cultures on Earth, wise men and women studied the four great unchanging liberal arts -numbers, music, geometry and cosmology-and used them to inform the practical and decorative arts like medicine, pottery, agriculture and building. At one time, the metaphysical fields of the liberal arts were considered utterly universal, even placed above physics and religion. Today no one knows them.

Walker & Company is proud to launch Wooden Books, a collectable series of concise books offering simple introductions to timeless sciences and vanishing arts.

Attractively simple in their appearance yet extremely informative in content, these unusual books are the perfect gift solution for all ages and occasions. The expanding title range is highly collectable and ensures continuing interest. In addition, the books are non-gloss and non-color, appealing to a greener book-buying public. Wooden Books are ideally suited to non-book outlets.

Wooden Books are designed as timeless. Much of the information contained in them will be as true in five hundred years time as it was five hundred years ago. These books are designed as gifts, lovely to own. They are beautifully made, case-bound, printed using ultra-fine plates on the highest quality recycled laid paper, finished with thick recycled endpapers and sewn in sections. There are fine, hand drawn illustrations on every page.

The fast-moving world of Wooden Books brings you a selection of fascinating titles. All hardcover, 64 pages, 100% recycled paper at $10.00 each. ... Read more

Reviews (7)

Fascinating Mathematics....
This is a delightful little book.If you have any interest in Geometry,Math,Design,Shapes,Tile patterns,Puzzles,etc.you'll really enjoy this book.Surprisingly ,you can grasp most of this book knowing high school math,;while at the same time those with more math knowledge will also enjoy it as well.I guess it falls right in the realm of Mathematical Recreations.I am amazed that the author has put together a beautifully writen book,including 168 drawings,figures,diagrams and on top of that shows how most are constructed.All this has been accomplished in 64 pages ,including an introduction.

I just loved this book
This book is a treasure. I was given it as a present and I find myself turning to it for all sorts of ideas and also give it as a present quite regularly. She has managed to pull together a huge amount of wonderful information into a relatively small space. This is an inspiring, beautiful, thought provoking and even useful book. I am a graphic and fabrics designer and I had not come across some of these things before so I am very grateful for them.

I also really like the way the book is put together, lush textured paper (recycled I note) and quality illustrations. The way the subject is built up stage by stage until we reach the more complex set pieces at the back is very good. It helps you understand the basics of good design, and the use of geometry in this process.

I think the new-age overtones work very well too. She manages to convey some of the real mystery and magic of the field while never losing sight of the practical purpose of it all.

Highly recommended.

Looks nice, but the content is weak
This is a very attractive-looking book, and I am very happy if it can make some people more appreciative about mathematicas. But if you are looking for correct info about mathematics or its role in art and culture, then this is not the place to look.

Most of the claims you read about the golden ratio in art and architecture are not valid. The best source of info is the paper "Misconceptions about the golden ratio" by George Markowsky from the College Mathematics Journal v. 23 (1992), 2-19.

If you are interested in the pyramids, please read "The shape of the great pyramid" by Roger Herz-Fischler. Just do it! You will thank me for it!

She claims that there are 14 "demi-regular tilings" of the plane. She defines demiregular to be a tiling (edge-to-edge of regular polygons) with two or three different types of vertices. According to "Tilingss and Patterns" by Grunbaum and Shephard, there are 20 2-uniform tilings and 61 3-uniform tilings.

If you are bothered by statements like "It is nearly impossible to draw a precise heptagon using ruler and compasses alone", then this book is not for you.

Her pictures of the 17 wallpaper groups is wrong. She gives two examples of p1, but misses out on p4g.

Having said this, I must say again that she has a lot of beautiful material in the book. I just think that it is important to be mathematically and historically correct.

A really useful little book
This is a great book - I wish I'd had a copy when I was 18! Really useful for design, architecture and other visual arts. Lundy keeps it deep and yet simple while managing to pack in a huge amount of information and detail. The larger format Robert Lawlor book is also well worth reading, as are Keith Critchlow's 'Order in Space' and John Michell's writings. Daud Sutton's little book on Platonic and Archimedian Solids is also excellent.

Accessing Sacred Geometry
This splendid little book is suitable for all ages to introduce them to the wonder of high architecture and interior design. Very simple explanations and illustrations show how the basic patterns of nature echo in human consciousness in what has been conceived in the mind and wrought by the hands over the centuries. Highly recommend for artists and draftsmen as well who wish to research or emulate classical ideas for themselves. ... Read more

Book Description

Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition.
* Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.
* Each topic is carefully explained and illustrated by examples and figures.
* Includes all necessary mathematical background material.
* Includes notes and references to enable the reader to pursue individual topics.
* Features a wide selection of exercises, enabling the reader to develop their understanding of the theory.
* Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers.
Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences.
Also by Kenneth Falconer and available from Wiley:
Techniques in Fractal Geometry
ISBN 0-471-95724-0

Please click here to download solutions to exercises found within this title:

http://www.wileyeurope.com/fractal ... Read more

Reviews (4)

What every student should know about fractals.
Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

Theoretical as well as practical insight
The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).

Excellent for understanding the geometrical properties of fractals.

Exposes fractal geometry as a real mathematical discipline.
I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.

It begins introducing basictopological concepts and then proceeds to develop the theory for severalpossible definitions of fractal dimension, showing the relations betweenthem. Then it explores deeply the local geometry of different kinds offractal objects, and studies some other geometrical situations, like thepojection of fractals (ever thought of a DIGITAL sundial? Here it isdescribed!).

The book also includes a lot of applications to other areasof mathematics and physics, a great amount of graphics, and muchmore.

The text is suitable from third year undergraduate school and on.It is a larger but lighter version of "The Geometry of FractalSets".

One of the best books on fractals to be found anywhere!
The book opens the doors of mathematics: it isn't an easy door, but well worth the effort. It bridges the gap between beginner texts and advanced study and covers the basic material in a hard hitting manner. Those looking for "giltz" should look elsewhere. It is a book of great understanding and depth. Your unique Associates ID is:thefractaltransl. ... Read more

Book Description

This text is suitable for introductory students, perhaps in programs such as education, art and architecture. The text contains some traditional material from geometry as well as more innovative topics. Throughout the text, the authors place strong emphasis on pedagogy, hands-on model building, a guided discovery method of learning, etc. Much of the material is written in such a way that it can be used in the classroom for enrichment projects, by prospective mathematics teachers. ... Read more

Book Description

This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics.They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis. ... Read more

Reviews (2)

A very nice little book
This is a very nice, short introduction to the subject -- This series of blue paperbacks by CUP is excellent. Typically, all books in the series are readable introductions. Somewhat higher level than the corresponding series from Springer (the one where all exercises have full solutions).

Incidentally, the author is a very attractive woman.

Well suited as an introduction to algebraic curves
The book gives a good general overview of algebraic curves using only elementary algebra, topology, and complex analysis. There are lots of diagrams of elliptic curves in the historical introduction in the first chapter and the subject is well motivated. Hilbert's Nullstellensatz is introduced in the context of real algebraic curves as an answer to the question of when the polynomials definte the same curve. The visualization approach taken by the author in the first chapter has taken on dramatic proportions do to the computer graphics packages currently available. The author introduces complex algebraic curves in complex 2-dimensional space in the next chapter. Recognizing that such curves are not compact, he compactifies them by adding suitable points at infinity, giving complex projective curves. The algebraic properties of these curves are studied in the next chapter. He does a good job of motivating the group law on elliptic curves on the last theorem of the chapter, leaving the proof of associativity to the reader in the exercises. The topology of complex projective curves is taken up in Chapter 4. The author gives two proofs of the degree-genus formula, one geometric and the other from a holomorphic point of view. This leads to a consideration of branch points and ramified covers. The author's outline of the proofs is very detailed and therefore very helpful to one encountering the proof for the first time. The statement of the formula via the Riemann-Roch theorem in more formal treatments (and later in the book) can then be appreciated more. The subject of non-singular complex projective curves, namely Riemann surfaces, is effectively discussed in Chapter 5, with holomorphic differentials outlined in Chapter 6. The Riemann-Roch theorem makes its appearance here, and the author is careful to point out its use as an alternative characterization of the genus given earlier by topological arguments. Divisors are introduced as formal sums, but their understanding is straightforward here because the author has motivated them with a discussion of the properties of holomorphic and meromorphic functions earlier in the chapter. The proof of the Riemann-Roch theorem is very detailed and understandable. The book ends with a discussion of singular curves via resolution of singularities. Newton polygons and Puiseux expansions are used to investigate the behavior of degree d projective curves near a singular point. The geometrical constructions used here by the author are of great help in understanding the behavior of these curves. A very well-written book for students and new-comers to the area of algebraic curves. It will pave the way for more advanced reading on the subject. ... Read more

Book Description

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. This book lays the foundation for a topic with wide appeal and a bright future. ... Read more

Book Description

Hardbound. This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include:

Historical outline

Curve and surface methods

Scientific Visualization

Implicit methods

Reverse engineering.

This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposure to this subject. ... Read more

Book Description

Benoit Mandelbrot discovered what is now called the M-Set in the early seventies and coined the term ‘fractal’ to describe the geometry behind it. The power and the beauty of fractals were only capable of being seen with the advent of computers, which become psychedelic windows on the infinite when using simple fractal equations.

In 1992 Nigel Lesmoir-Gordon made the TV documentary, The Colors of Infinity about the Mandelbrot Set and fractals, which has since been seen right round the world. Nigel’s enthusiasm brought together a dream team of contributors for the film who all now contribute to the book tracking how fractals have developed since the film was made. Sir Arthur C Clarke presented the film and in the book gives a lucidly simple account of the mathematics of the M-Set. Benoit Mandelbrot, the Belgian mathematician explains how it began. Professor Michael Barnsley, the computer graphics researcher who developed fractal image compression technology, explains the applications of the breakthroughs. Professor Ian Stewart, author of Does God Play Dice? adds his insights into the beautifully simple equation that gives birth to fractals.

Two of the most interesting applications of fractal geometry, reflected by the two new contributors to the book, are to the Internet and to the Stock Market. Dr Gary Flake, Chief Technology Officer at Overture, the leading provider of commercial search on the Internet and just taken over by Yahoo for 1.6 billion dollars, discusses the profoundly fractal nature of the Web in his article: The Self-ish Web. Robert Prechter Jr is President of Elliott Wave International, Inc. and founder of the Socionomics Institute. His latest title is Socionomics: The Science of History and Social Prediction (2003). He writes about how fractals can help us understand the oscillations of stock markets.

In the back of the book is a DVD of the original documentary with soundtrack by David Gilmour of Pink Floyd PLUS a 30-minute fractal animation to the music of members of Quintessence. ... Read more

Amazon.com

Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.

The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds. ... Read more

Reviews (9)

A dated but still fascinating book
This was the book that first caught my attention. It was the cover diagram: a figure the like of which I had never seen. One thing led to another until I finally wrote my own application of fractals, Fractals in Music.

Mandelbrot is an odd character, but a superb thinker. His book does not offer a lot of science, but rather a compelling view of how this fascinating and growing topic developed. I recommend it highly.

A review on the book -- not on Mandelbrot
Mandelbrot is the person who introduced the fractal theory to the world in its present form. Many fields of science including geophysics have gained from fractals. However, this is not the book one should read to gain knowledge on the subject.

It is not an easily readable book. 1. It is not well-organized 2. It does not cover necessary things in detail 3. Frustratingly long in some parts. Instead the books: Feder, Fractals; Turcotte, Fractals and Chaos in Geology and Geophysics can be recommended.

Fractal geometry may be interesting as a historical book, after one gains a sufficient knowledge on fractals.

a unique personal account of a (then) new science
highly personal, highly self-congradulatory, highly-amusing, highly interesting, a great read! More math/sci authors should tell us how they really feel like Mandelbrot!

Not as good as I expected
After having studied fractals in school and reading numerous books on chaos and fractals on my own, I figured that Mandelbrot's book would be the pinnacle, surpassing everybody else's interpretations and getting the information "straight from the horse's mouth". I was wrong. Mandelbrot, while he may be a brilliant mathematician, has not quite mastered the English language. The topics that he speaks of in this book are basic, not exactly what you would expect from the leader in his field. He doesn't even go into real specifics, or not the specifics that I wanted to see going into this book. In fact, I didn't even bother finishing it. There was nothing new, no powerful insights that other books may have missed. Mandelbrot, it seems is much better at mathematics then at writing. My suggestion is to buy a different book on the subject.

Good, one of the first, but not the best
The book is still a milestone in the history of fractals, but it gets currently lost among the many available publications. Surely a good book, but there now exist other texts that can be considered more advisable to a reader, particularly to a computer-oriented one. ... Read more

Book Description

This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms throughout.Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. ... Read more

Reviews (5)

Not for everyone, flawed in basic ways
I disagree with reviewers who found this book useful for self-study. I would not recommend it for individuals first learning this material. The book is frankly contradictory in places, and frustratingly repetitive in others. In the early chapters it assumes concepts not yet explained, and introduces terminology and symbols that are nowhere defined.

If you already know quite a bit, you may find this approach enlightening. But if you're just beginning to master these concepts, I suggest you look elsewhere.

I also suggest that much tighter editing would do this book a world of good. Go with Kreiszig, or Lovelock and Rund instead.

Excellent book
This is a very modern, very concise, and very efficient book. By using vector bundles the curvature forms on semi-Riemannian manifolds are introduced. Definitions are given clearly and intuitively. Without spending tons of pages on digression to minimal surfaces, Hopf-Rinow thm, Gauss-Bonnet thm, etc., the book builds enough machinery to describe the gauge field theory in the last chapter. Most other differential geometry books either throw in too many applications to waste reader's time or give vague definitions (too bluntly abstract or not self-contained) to confuse the reader.

All exercise problems are interesting and important. Hints are given to some of them.

I found Warner's "Foundations of Differentiable Manifolds and Lie Groups" is a good complement to address the algebraic and topological side of differential geometry.

The ONLY book really suited for self study
I would just like to point out that Darling's book is the only book I've encountered which is suited for self study. It resembles someone's classroom notes - i.e., nothing fancy, no glossy color 3-d graphics or such - but it is very neatly organized, with many examples and helpful problems, and it is really, really suited for someone trying to study the subject by him/herself (me ... ). It is not very physically oriented - not many physical examples are provided throughout the text, and it is mathematical in nature, but don't let that deter you! In fact, the sharp distinction between mathematics and physics is pedagogically wise.
Another good thing about this book is that it does not begin with completely abstract definitions. First of all it develops exterior calculus and diff. manifolds in ordinary Euclidian space. This is a must for anyone studying on their own, believe me! No matter how mathematically mature you are, those things just don't make sense unless you've seen how they work in familiar settings. You don't have to worry, though - Darling keeps his notation clean; Darling tries as hard as he can to keep everything in pure geometrical language, referring to a specific basis only when absolutely necessary (or when it helps one understand).
I cannot say how good a classroom text this is, but do yourself a favor and check it out if you're thinking of studying this on your own! Darling is a clear and (equally important!) responsible teacher.

A must for both the physicist and mathematician
RWR Darling should be the first and foremost book for learning about differential geometry both for physicists and mathematicians. I have learned from numerous books on this subject, and while I can't say Darling includes everything one could want (I can't say anyone ever does), his text explains some very esoteric ideas in terms of linear algebra and vector calculus.

A notable departure this book makes is dispensing with the usual coordinate basis for tangent spaces which is commonly used by physicists. To the experienced physics reader, this may seem daunting, and unnecessarily abstract at first. However, the pay-off in the ability later on to discuss gauge theories and fiber bundles is huge.

This book is also suited for mathematicians less interested in physics. Darling does not always assume that a manifold has some metric, and discusses the subtle differences between vectors and co-vectors in modern mathematical language. Secondly, he provides a lot of motivation for the mathematical constructions and takes great care to present key definitions in extremely coordinate free ways.

Gauge theories in the mathematical way
The main difficulty found by physicists in the learning of modern differential geometry is topology. The various constructions introduced by Cartan and others, differential forms, connections, even fiber bundles, on the contrary, pose no difficulties: it is only a question of developing the appropriate muscles and reflexes. R. Darling wrote the ideal book to teach connections on a G-bundle (gauge theories, in the nomenclature of physicists), by refraining, as much as possible, to use explicit topology. As physicists are not a special kind of human beings, I believe what I said above is also true of (beginning) mathematicians. Otherwise, why would Darling choose such course (in the navigational sense). The book starts with Cartan calculus in Euclidean space, continues there up to surface theory, then introduces (intrinsic) manifolds. Perhaps the key concept of the book comes next: Vector Bundles. All previous constructions are extended to bundles, and the concept of conn! ections on vector bundles deserves a special chapter. The book ends with Applications to Gauge Field Theory (mathematics-wise, but quite accessible). There are many pedagogical virtues in this much welcome book. Finally a good alternative to Bishop-Goldberg`s "Tensor Calculus on Manifolds". ... Read more