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

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

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

Mission Geometry; Orbit and Constellation Design and Management (OCDM) provides greatly expanded detail on many topics first introduced in the 2 of the earlier Wertz works - Spacecraft Attitude Determination and Control (SADC) and Space Mission Analysis and Design (SMAD).

If these two books got you started in mission engineering and you need more detail on the key area of Spacecraft Orbit and Attitude Systems (SOAS), then this book provides more detail in SOAS requirements definition, mission geometry, orbit and constellation design, relative motion of satellites, observation and measurement systems engineering, orbit control and management, and similar topics. ... Read more

Amazon.com

Bernhard Riemann was an underdog of sorts, a malnourished son of aparson who grew up to be the author of one of mathematics' greatestproblems. In Prime Obsession, John Derbyshire deals brilliantlywith both Riemann's life and that problem:proof of the conjecture,"All non-trivial zeros of the zeta function have real part one-half."Though the statement itself passes as nonsense to anyone but amathematician, Derbyshire walks readers through the decades of reasoningthat led to the Riemann Hypothesis in such a way as to clear it upperfectly. Riemann himself never proved the statement, and it remainsunsolved to this day. Prime Obsession offers alternating chaptersof step-by-step math and a history of 19th-century European intellectuallife, letting readers take a breather between chunks of well-writteninformation. Derbyshire's style is accessible but not dumbed-down,thorough but not heavy-handed. This is among the best popular treatmentsof an obscure mathematical idea, inviting readers to explore the theorywithout insisting on page after page of formulae.

Reviews (38)

An Excellent Read, Highly Recommended
Prime Obsession is an excellent popularization of the Riemann Hypothesis. I found John Derbyshire's presentation of the math to be very approachable by non-mathematicians like myself. It's taken slow, one basic step at a time, and spread across a well written and fascinating history of Bernhard Riemann and other key players. Simply put, you do not need an advance degree in mathematics to enjoy this book.

My math bakground is limited to 2 semesters of calculus 20 years ago and I haven't used it since. For me, John Derbyshire's approach was both refreshing and entertaining. If you've got even the faintest interest in math, you will find this book rewarding.

Read this one for the pure entertainment value of it all.
I found this to be a rather delightful book with its arrangement of chapters alternating between historical point of view back to mathematical progress and then back to historical.

I found it very entertaining to read about the lives of the great mathematicians involved in developing the prime number theory and furthering the study of the Riemann Hypothesis. Mathematics is littered with such interesting characters that even a liberal arts major can enjoy these expository stories of their lives.

The only downside to this whole book is that he takes too much time for the non-math inclined readers to get 'caught up' with their basic skills before he jumps to anything interesting. If you have a background that is strong through calculus, then you could probably avoid reading all the math-based chapters up through the end of the prime number theory section of the book, and you most likely woud not have missed a thing.

Complex Math Made Very Understandable and Interesting
Although this book deals with a subject that no-one would sensibly place in a category below "Very Advanced," John Derbyshire treats his subject as well as any math author I've ever read, and I've read a lot of math books over the past 40-some years.

My formal math education ended after a standard introductory calculus course as an undergrad. However, I have always been, and remain, extremely interested in math -- a math aficianado if you will. As such, I've self-taught myself a lot of math -- including a lot of very advanced math -- over the past 40 years; ergo, my reading of a great many math books. And without doubt, Derbyshire's book is the finest math book I've yet to read.

I suspect Derbyshire started with the hypothesis that his readers are not familiar (or only familiar in a passing sense) with high-level, advanced math, and perhaps might even suffer from math anxiety. Any such readers, however, should have absolutely no fears. Derbyshire's exposition is superb. He clearly defines everything the reader needs to know to grasp AND understand fully the more advanced parts of the book. The book is clearly well designed to convey the information he wants or needs of convey and masterfully explains what would otherwise be quite difficult to understand.

Without any doubt this is by far the best book on any advanced and complicated subject -- the best book on ANY math subject (including a book on something as simple as how to add one and one) -- I have ever read.

Without sacrificing the complexity of the subject, Derbyshire has written his book in a very readable and interesting manner. And he does all this while making the subject so interesting you can hardly wait for someone to finally prove Riemann's Hypothesis and Riemann's zeta function so we can read Derbyshire's account of that landmark event in the history of mathematics.

splendid (though heavy math)
This book should be the first one to appear in Amazon's listings for the Riemann Hypothesis, yet doesn't even appear in the top ten. It gives fascinating historical background to a very real Riemann and his friends, traces developments to the present day in a conversational tone, and somehow manages to take the reader through the details of what the RH says so that you actually understand it. Recommended with one reservation; to understand the chapters (every other one) which bring one to understand the RH, you will need to make a considerable investment in reading and rereading to make it. That is not for the faint of heart. However, the other half of the book can be enjoyed by anyone who likes general science history books.

What a piece of work a man is!
"Prime Obsession" is a fascinating book for several reasons: the author explains a difficult topic with such clarity that it's simply amazing. For those who are more skilled in math, this book would also be very enjoyable to read, except that they might find some of his explanations redundant because he really assumes that the we don't know anything (and I mean anything!).
Mr. Derbyshire obviously understands the topic quite well himself. He has written an amazing book for everyone to enjoy.
200 years since Riemann first presented the problem, we are still desperately trying to solve it, and one day, you never know... what a piece of work a man is! ... Read more

Reviews (2)

The man was a complete loon, but in a good way.
The previous review is amazingly perceptive into Bill Burke's personality and thinking. He was not the most discplined writer or lecturer, (I had no less than 4 courses from him) but his insight and intuition could be amazing. I would recommend this book as a companion to something more traditional. If you are interested in General Relativity, which is what the book was suppose to be a precursor for, get Schutz or Misner, Thorne and Wheeler, or Wald.

Also, if you do want this book, get the errata from Burke's webpage,...is quite helpful.

I would also hearitly recommend Burke's best book: Geometry, Spacetime and Cosmology which is out of print. It is much physical and the examples are clearer. He taught english majors and theater students general relativity with that book.

It's a lot of work but I like it.
I'm not a physicist or mathematician but I play one on TV. So I am more qualified to review a book on differntial geometry than either of the above professionals. This book is a very good introduction to all the hairy squibbles that theoretical physicists are writing down these days. In particular if you are perplexed by the grand unification gang then this book will help you understand the jargon. However, having only had physics when advanced vector calculus was enough to get by, it is a bit hard going due to the frequent errors and glosses the author makes. Burke gives a very hip and entertaining introduction to some of the most beautiful ideas in physics. It is enjoyable to read if you like sinking your teeth into something more rewarding than Ann Rice. I gave it a six rating because the errors and glosses are so annoying. I suspect Burke's puckishness is responsible; the book has no actual problem sets but he does work out problems that don't always work out. So the reader really has to work at understanding by correcting the possibly(?) intentional errors. Very sly of him. I am on my second reading and suspect that several readings down the line I will probably get the message. The book deserves loving attention. ... Read more

Book Description

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris.After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years.In 1972 he moved to California where he is now Professor at the University of California at Berkeley.He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles.His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively.Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons.He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi. ... Read more

Reviews (5)

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.

Experiences of a rather below-average graduate student
(that's me.)

I agree with the other reviewers' comments concerning the phenomenal depth and breadth of the topics covered in this book. Hartshorne builds the soaring edifice of modern algebraic geometry from the ground up. All the way through, the exposition is concise and absolutely clear. The proofs strike an excellent balance between meticulousness and readability.

The approach he takes seems to be to try to acquaint the reader with as much formalism as possible as quickly as possible, and he seems reluctant to offer any sneak previews of vital concepts such as divisors, differentials, and flatness until the reader's brain is "ripe". As a result, Hartshorne is able to state and prove results under extremely general hypotheses. This approach also benefits the kind of reader who wishes to use this as a reference book.

It's important also to note the disadvantages of Hartshorne's approach: Time and again, I found myself utterly baffled by the definitions, because the motivations for them are lacking.

To give a minor example, take the definition (in chapter 1, part 3) of a morphism between two varietes. First, regular functions from a variety over k to k are defined as those that are locally representable as quotients of polynomials (without bothering to give an example of a case of a regular function for which more than one such representation is needed). Then a morphism f: X -> Y is defined as a Zariski-continuous function with the property that whenever you have an open subset V of Y, and a regular function V -> k, then f^-1(V) -> V -> k is regular. There's nothing wrong with this definition, of course, but I found it very difficult to make sense of, initially. A morphism, after all, is supposed to be something that preserves structure, but it's not immediately obvious what "structure" is being preserved in this case (and the full details of this aren't spelt out until much later, after sheaves have been defined). A better didactic approach, I think, would be either (1) to define morphisms of affine varieties simply as functions given by polynomials, and then show that the above definition is the only natural way of generalising this, or (2) to briefly introduce sheaves at the outset, making it clear that the "structure" we wish to define on a variety consists precisely of the sheaf of regular functions.

Another negative effect of Hartshorne's approach is that, if you have to traverse a mire of formalism before meeting an idea, it makes the idea seem more complicated than it actually is.

Certainly there's nothing to stop a dedicated reader just ignoring any temporary befuddlements, secure in the knowledge that eventually everything will make sense, but not all of us have the patience. This book contains an almost ridiculous number of exercises - most of which are supposed to be "formalities", there to flesh out the definitions, but many contain absolutely crucial definitions and lemmas. Attempting to do all the exercises as you go along is very taxing work indeed, and becomes demoralising whenever you get stuck. Perhaps the best strategy is to do only those exercises that are interesting or important for later work.
Also, as others have noted, this book is very tough going on those who don't already have some familiarity with commutative algebra and (later on) homological algebra.

All in all, I think this book will be most useful for people who already know quite a lot of algebraic geometry, commutative/homological algebra etc., and are wishing to consolidate and "modernise" their understanding. For beginners, it's a struggle, but not an unproductive one, especially if assisted by other, less demanding books.

Be prepared...
This book is one of the most used in graduate courses in algebraic geometry and one that causes most beginning students the most trouble. But it is a subject that is now a "must-learn" for those interested in its many applications, such as cryptography, coding theory, physics, computer graphics, and engineering. That algebraic geometry has so many applications is quite amazing, since it was not too long ago that it was thought of as a highly abstract, esoteric topic. That being said, most of the books on the subject, including this one, are written from a very formal point of view. Those interested in applications will have to face up to this when attempting to learn the subject. To read this book productively one should gain a thorough knowledge of commutative algebra, a good start being Eisenbud's book on this subject. Also, it is important to dig into the original literature on algebraic geometry, with the goal of gaining insight into the constructions and problems involved. The author of this book does not make an attempt to motivate the subject with historical examples, and so such a perusal of the literature is mandatory for a deeper appreciation of algebraic geometry. The study of algebraic geometry is well worth the time however, since it is one that is marked by brilliant developments, and one that will no doubt find even more applications in this century.

Varieties, both affine and projective, are introduced in chapter 1. The discussion is purely formal, with the examples given unfortunately in the exercises. The Zariski topology is introduced by first defining algebraic sets, which are zero sets of collections of polynomials. The algebraic sets are closed under intersection and under finite unions. Therefore their complements form a topology which is the Zariski topology. The properties of varieties are discussed, along with morphisms between them. "Functionals" on varieties, called regular functions in algebraic geometry, are introduced to define these morphisms. Rational and birational maps, so important in "classical" algebraic geometry are introduced here also. Blowing up is discussed as an example of a birational map. A very interesting way, due to Zariski, of defining a nonsingular variety intrinsically in terms of local rings is given. The more specialized case of nonsingular curves is treated, and the reader gets a small taste of elliptic curves in the exercises. A very condensed treatment of intersection theory in projective space is given. The discussion is primarily from an algebraic point of view. It would have been nice if the author would have given more motivation of why graded modules are necessary in the definition of intersection multiplicity.

The theory of schemes follows in chapter 2, and to that end sheaf theory is developed very quickly and with no motivation (such as could be obtained from a discussion of analytic continuation in complex analysis). Needless to say scheme theory is very abstract and requires much dedication on the reader's part to gain an in-depth understanding. I have found the best way to learn this material is via many examples: try to experiment and invent some of your own. The author's discussion on divisors in this chapter is fairly concrete however.

The reader is introduced to the cohomology of sheaves in chapter 3, and the reader should review a book on homological algebra before taking on this chapter. Derived functors are used to construct sheaf cohomology which is then applied to a Noetherian affine scheme, and shown to be the same as the Cech cohomology for Noetherian separated schemes. A very detailed discussion is given of the Serre duality theorem.

Things get much more concrete in the next chapter on curves. After a short proof o the Riemann-Roch theorem, the author studies morphisms of curves via Hurwitz's theorem. The author then treats embeddings in projective space, and shows that any curve can be embedded in P(3), and that any curve can be mapped birationally into P(2) if one allows nodes as singularities in the image. And then the author treats the most fascinating objects in all of mathematics: elliptic curves. Although short, the author does a fine job of introducing most important results.

This is followed in the next chapter by a discussion of algebraic surfaces in the last chapter of the book. The treatment is again much more concrete than the earlier chapters of the book, and the author details modern formulations of classical constructions in algebraic geometry. Ruled surfaces, and nonsingular cubic surfaces in P(3) are discussed, as well as intersection theory. A short overview of the classification of surfaces is given. The reader interested in more of the details of algebraic surfaces should consult some of the early works on the subject, particularly ones dealing with Riemann surfaces. It was the study of algebraic functions of one variable that led to the introduction of Riemann surfaces, and the later to a consideration of algebraic functions of two variables. A perusal of the works of some of the Italian geometers could also be of benefit as it will give a greater appreciation of the methods of modern algebraic geometry to put their results on a rigorous foundation.

Terrific, if you want it.
This book hardly needs a review on Amazon, because if you have as much math background as it needs, then you must already know it is indispensible for learning about schemes in algebraic geometry. The book is clear, concise, very well organized, and very long. If you do not already know the Noether normalization theorem, and the Hilbert Nullstellensatz, then you do not want this book yet--you want an introduction to commutative algebra.

Indispensable!
Excelent and useful text, indispensable for graduate students and research ,athematicians working on algebraic geometry. Hartshorne walks the fine line between commutative algebra and their geometrical counterparts with elegance. The book is also rich in references, providing many directions for further study. ... 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

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

The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material.

Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbf{C}$ and Cartan's classification of simple Lie algebras over $\mathbf{R}$.

The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book.

For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume 39.

Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis. ... Read more

Book Description

In the past decade the systematic study of geometric algorithms has evolved to form the very active field of research known as computational geometry. Computational Geometry: An Introduction presents a comprehensive, systematic, and coherent treatment of its subject.

A fundamental task of computational geometry is identifying condepts, properties, and techniques which aid efficient algorithmic implementations from geometric problems. The approach taken here is the presentation of algorithms and the evaluation of their worst-case complexity. The particular classes of problems addressed include geometric searching and retrieval, convex hull construction and related problems, proximity, intersection, and the geometry of rectangles.

Computational Geometry: An Introduction presents its methodology through detailed case studies. The book, primarily conceived as an early graduate text, should also be essential to researchers and professionals in the fields of computer-aided design, computer graphics and robotics. ... Read more

Reviews (5)

This book is history
This book is a classic, in fact the author's PhD thesis created this field, but this book is too old for any meaningful graduate work. There are new bounds and algorithms on almost all topics, which makes this a somewhat undesirable book. Also, this book has failed to keep me interested in it, while I am reading it...

Very useful for code development. Very clear and readable.
The ideas and algorithms presented in this book are clear enough for straight implementation in code. I have long experience in developing comercial and production software for VLSI layout applications, which made extensive use of the algorithms presented in this book.
I also use some chapters of this book as a part of a graduate course in VLSI layout algorithms being tought at the Technion, Israel. The contents of this book is well understood by EE and CS students.
I personally love this book, which introduced me into the area of computational geometry and its applications.

Useful but thick
Most of the papers that I've read on computational geometry refer to this text -- and for good reason. There's many good algorithms to be found here.

The book only gets 4 stars because it's hard to read. It took me several tries to pick up the ideas in this text. I think the De Berg text is MUCH easier to read.

The book is also getting a little dated. Some of the topics have come a long way since the 80's.

This book seems to be in most University libraries if you have that option.

Still interesting after so many years ...
I have just happened to exhume this book from my library, after it spent some years gathering dust above the shelf. In spite of the long time I have not being reading it, it still retains the full meaning it showed me when I was using in calculations relating radar domain definition. May be the textbook wins by far the comparison to the current vague and inflated computer publications, may be it is not a manager-oriented issue but it is for nearly specialistic use, you find in it clearly stated, and straight, answers to the questions you meet, or at least a definite reference where a more detailed explanation can be find. It presents interesting problems, and explains you how to solve them. I think it is the best you can say about a computer science book.

A very good book, but difficult to understand !
The book is comprehensive in computational geometry, and is suitable for research. But really difficult to understand. A student is difficult to read it without teacher's teaching. But people who research in computational geometry need the book. ... 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

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

The topology optimization method solves the basic engineering problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design, which is concerned with the optimization of structural topology, shape and material. This edition has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state of the art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also MEMS and materials. ... Read more

Book Description

Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study.

Reviews (1)

Differential Geometry - A Schaum's Outline Series
As with all of the Schaum's Outline Series, this book is particularly useful if the readers intent is to gain a working knowledge of the subject. The subject of Differential Geometry is no exception. Dr. Lipschultz has done an excellent job of communicating the essential aspects of differential geometry to the reader. The book assumes a fairly low level of mathematical ability having calculus as the primary prerequisite. From this humble beginning, Dr. Lipschultz takes the reader through the necessary discussions of vector functions, curvature, fundamental forms, and tensor analysis. Given the theoretical nature of the subject, Dr. Lipschultz has included most of the theorems and associated proofs necessary for a general understanding of the subject. However, this book is not a substitute for a serious study of differential geometry. In addition most of the problems are limited to two dimensional surfaces and this reader would have enjoyed a more adventurous investigation of higher dimensional spaces. Like all Schaum's series, the text is chock full of problems and their solution. I recommend this book for anyone interested in quickly gaining a working knowledge of the subject. ... 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

This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds can carry, such as Riemannian metrics, symplectic structures, and foliations. The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of two previous Springer books, Introduction to Topological Manifolds (2000) and Riemannian Manifolds: An Introduction to Curvature (1997). ... Read more

Reviews (2)

Excellent, lucid book on manifolds
Topics are explained with exceptional clarity; portions of the book are well tied together; and the order of exposition flows very well. Lie groups are introduced quite early on, but their full power is not revealed until later in the book. I can't laud this book enough. I had a firm, well-developed basis of differential geometry after reading through this book for a course. The excersises are illuminating, a