Product Description

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert?s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study (the ?axiomatic method?), which concentrates on assessing the logical weight of central propositions by exploiting to the full the method of independence proofs by modelling. This culminates in the lectures of 1898/1899 (the immediate precursor of the 1899 monograph) and 1902. The lectures contain many reflections and investigations which never found their way into print.

Customer Reviews (1)

Delightful
This book is of course invaluable for studying the development of Hilbert's Grundlagen. It also contains lectures that are not directly related to foundations, such as excerpts from a more conventional projective geometry course of 1891 (apparently taught to two students and "ein für Geometrie interessierter Mahler") and a few delightful Ferienkurs lectures (including for example three reasons why number theory is the queen of mathematics, pp. 154-156).

The foundations lectures naturally differ from the published Grundlagen in that they contain things that were already well known, such as discussions of non-Euclidean geometry. The first set of lecture notes on the foundations of geometry is from 1893/94. Most aspects of Hilbert's Grundlagen are here already. The story is still thoroughly enjoyable, however, and greatly enhanced by the editors meticulous attention to pointless details (including things like the colour of the ink Hilbert used).

Consider for example the case of the amphibiousness of Desargues's theorem. 3D Desargues is obvious, so Desargues must hold in any sensible 3D geometry. Could it be that Desargues is not only necessary but also sufficient to create a sensible 3D space, i.e., is it true that "if the Planar Desargues Theorem is added as a new postulate to the planar order and incidence axioms, then this will yield spatial consequences, so that, in particular, the full set of spatial incidence and order axioms will hold"? In his 1898/99 lectures Hilbert thinks the answer is probably yes: "Diese Frage ist wahrscheinlich zu bejahen". Apparently he did not have a proof at this stage but he soon found one; in fact, so soon that the proof appears later in the same course, prompting someone to go back to the Lesezimmer notes and cross out "wahrscheinlich" and underline "zu bejahen", "in rough hand, unlike the usual underlining of the Ausarbeitung, which is done carefully with a straightedge."

The fact that we used spatial methods to prove Desargues raises the question of the purity of method ("Reinheit der Methode"): Could Desargues be proved from plane axioms alone? We prove that the answer is no, using a contrived model later replaced by the Moulton plane. In this connection Hilbert's notes read: "It is fashionable to always guarantee the purity of method. In fact, this is appropriate: we are often not satisfied when a proof in number theory uses geometry or geometrical truths of function theory ... [But a detailed study may reveal] a deeper, legitimate basis and beautiful and fruitful connections, e.g. primes and the zeta function, potential theory and analytic functions, etc."

An appendix lists all Hilbert's lecture courses throughout his career. Hilbert was a real, classical professor. Unlike the disgraceful "professors" of today who whine about their teaching "load", he did not disrespect teaching and learning. He taught widely not only in every area of mathematics (including basic calculus courses several times as a full professor) but also in physics (mechanics, hydrodynamics, potential theory, elementary particles, electromagnetism, special and general relativity, quantum mechanics) and the philosophy of mathematics and science. ... Read more

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Provides a thorough account of many topics of geometry of numbers including lattices, reduction, Minkowski's Theorem, distance functions, packings, and automorphs. Includes excellent bibliographical references. Paper. ... Read more

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Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity.

Aimed at a general readership, the text makes accessible complex subjects such as Chaos and Fractals. It includes a wealth of the author's own illustrations and features appendices on related topics.

Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment.

Customer Reviews (1)

Gems is right word for this book
Gems of Geometry, eh?I tried the Search Inside feature here, and everything seemed pretty good, so I finally went and purchased a copy.

There is an astounding amount of great material in this book, all visually enticing, and mathematically deep.Well written explanations, and lots of good facts.

Looking through this, I get the idea that a much longer book was outlined first, and then the duller sections were pared away again and again, until a cohesive, exciting mathematical narrative remained, featuring all the best material of modern mathematics.

Try out the "Surprise Me" option in Search Inside.If you like those random pages, you'll like the whole book. ... Read more

Product Description
The great work that founded analytical geometry. Included here is the original French text, Descartes’ own diagrams, together with the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences."— John Stuart Mill.
... Read more

Customer Reviews (5)

Enormously important in the history of mathematics
Descartes' Geometrie, published in 1637, is possibly the second most influential book in the history of mathematics, after Euclid's Elements.In it, Descartes introduces analytic geometry, that is, the connection between geometry and algebra, in order to use algebra to solve geometric locus problems.The book's influence is reflected in the fact that Descartes' notation is far closer to the notation used today than anyone else's from that period (for example, Fermat or Viete).But it is not a book for someone who is not already knowledgeable.As Descartes himself wrote, (as translated and quoted in a footnote on page 10), "In my previous writings I have tried to make my meaning clear to everybody; but I doubt if this treatise will be read by anyone not familiar with the books on geometry, so I have thought it superfluous to repeat demonstrations contained in them."The 17th century mathematicians who read La Geometrie found it difficult, both because it was in French and because of its uncompromising exposition.Thus the book only became understood after the publication in 1649 of a Latin translation with commentaries by Frans van Schooten.

For the modern reader the book is a fascinating record of the state of mathematics in the early 17th century, and the format, with Descartes' 17th century French (readily readable to someone with some knowledge of modern French) opposite the reliable English translation, is very helpful for understanding what Descartes does in the book. How can it not have five stars?

Fabulous
This is a cheaply printed book with unquestionable value for any mathematician or liberal arts major.It has facing-page French with an English translation (which is fairly strict and literal), with great diagrams.It's difficult to read, and that's okay, because when other mathematicians at the time read it they thought it was impossible and that Descartes was insane.

Descartes, apart from this edition, is brilliant and worth the time to study.

This book is a bad choice for anyone not familiar with Euclidian and Apollonian geometry.Period.If you're not, you should find some commentary on Cartesian geometry instead of tackling this monster head-on.

has only limited historical value
The problems discussed in this book are very remote from our
present day geometry. The English translation uses a smaller font
than the French original, which makes the book even harder to read.

Great book to work through
This book contains a facsimile of the original version which runs nearly page for page with the English version.This is a true mathematical masterpiece.This was the supposed beginning of analytical Geometry(although it is now known that this was not true).It's a great book to work through that should be accessable to a high school student with some Geometry background. A Fantastic Book!

Enter Modern Mathematics
Using the locii problems investigated by Apollonius, Descartes employs the rules of his "method" in this treatise on geometry. By approaching geometrical problems with algebraic processes and vice versa, he manages to create point coordinate geometry. This work drastically changed the way in which we view conic sections as well as the very process of analytic inquiry. The math is mostly straightforward and more familiar to the reader than the works of the ancient mathematicians. It is not neccesary to have studied much previous mathematical works to gain a basic comprehension of Descartes' solutions. Attempting at most times to maintain the simple and straighforward presentation advocated by his method, Descartes will give you most of the basics that you need to understand the rest of the work. However, close concentration must be paid for the math to mean anything. It is easy to skip a step in a proof and find yourself completely lost. Given the proper patience, this work is invaluable for anyone who wants to see the origins of our method of thought today. Fascinating both as a mathematical treatise and as a perfect trial run for anyone wanting to follow the cartesian method of learning. ... Read more

Product Description
...will spark new excitement in your geometry classroom, involving your students and making them active participants in their own learning ... Read more

Customer Reviews (29)

Best Geometry Book Ever
This geometry book is clearly written, has interesting visuals, usea excellent teaching strategies, and is simply the best book available.High school students at various levels seem to respond well to the textbook.I know math teachers who think this book is far superior to any other.

I wish they'd had geometry books like this one when I was in school!

AWFUL
I am an eighth grader taking Geometry, so it is obviously advanced.However, this book is not helpful AT ALL in learning.It is so frustrating to not even have a glossary in the back to find definitions, and the book does a very bad job of explaining tough concepts.If you are a teacher, please try a different book.

Worst text book ever made
This is by far the worst text book i have ever seen or had to use. Unless you are an expert at geometry or have a great teacher this book will be useless to you. It gives no anwsers to the odd problems and there is no glossary. Because of this i dont know if my answers are right or wrong. I usually try to find the way to solve problems myself but since this book gives no examples on how to do anything i cant. I feel sorry for any other person who is like myself, and is forced to use this sorry exuse for a text book.

Stupid, Childish Book
This book was the bane of my existence throughout 9th Grade Geometry. Having had a year of arealmath book this year I am finally able to realize just how stupid the book was. It treats the student like he or she is about two years old, does not provide the information necessary for exam review, and is far too colloquial in general. In addition, it has no answers in the back, just "Hints" in the back of the book that either do nothing at all to help or solve the problem completely without explanation. It also says "SHAME ON YOU" if one looks at the hints without first trying the problem. Personally, I don't enjoy being chastized by a math book, especially one with such a bad approach to Geometry,

I HATE THIS BOOK!!!!
OMG! This book was so complicated to understand. They expect you to know everything. Because of this mindless crap, I failed Geometry and had to take the regular one. And the worst part is that they don't include enough examples to explain how to work the problem. I wouldn't recommend this God forsaken piece of crap to anyone who wants to do good in Geometry. ... Read more

Product Description
Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry. ... Read more

Customer Reviews (2)

Unreadable
This is a very poorly written and highly opaque book. For example, chapter 2.7 (sic) is called "Classification of Conic Sections", but conic sections are not even mentioned until five pages into this 12-page chapter. Apparently, Banchoff and Wermer finds it appropriate that a reader who wants to learn about the classification of conic sections should be forced to wade through five pages of technicalities, including things like six exercises on computing powers of various matrices, without the slightest indication of what this has to do with the classification of conic sections. Another instance, one among many, where Banchoff and Wermer demonstrate their commitment to technical nonsense and aversion to broad understanding is chapter 2.5 on determinants. "The quantity ad-bc is called the determinant", etc., and then the opening paragraph ends "We shall see that the determinant gives us further information about the behaviour of A" (p. 61), and there follows a devastatingly boring and longwinded five-page discussion on the orientation of an ordered pair of vectors, which is a technicality that could and should be dismissed in one paragraph. Only after this do we see that determinants have to do with area, which is the defining geometric property of the determinant, and of enormous importance. Why not do it the other way around? Why not say straight away that determinants are areas and then deal with the technical matter of orientation and signed areas at the end of the section, instead of keeping the reader in the dark with the secretive and mysterious proclamation that the determinant "gives us further information about the behaviour of A"? Banchoff and Wermer also adhere to a most unfortunate dichotomy between two, three, and n dimensions, which makes the book clumsily structured and repetitive. So, for example, there are three sections called "Linear transformations and matrices" (2.2, 3.2, 4.2), which all do basically the same thing, but our authors still pretend in 4.2 that we know nothing about linear transformations and matrices: "The symbol [(a_ij)] is called the matrix of the transformation ... Any transformation which can be written in this form is called a linear transformation", etc. (p. 213).

A wonderful introduction
A crystal clear book.It shows the geometrical significance of topics like eigenvalues/eigenvectors without losing the intuition in the formalism, like so many other books on Linear Algebra.The book would be particularly suitable for scientists, though prospective mathematicians would appreciate the "whys" too.

I only wish there were follow-on, more advanced, volumes! ... Read more

Product Description
Anticipating the New York State Board of RegentsÂ' new examination in geometry, this brand-new classroom text presents a detailed review of all topics prescribed as part of the high school curriculum. Separate chapters analyze and explain: the language of geometry; parallel lines and polygons; congruent triangles and inequalities; special quadrilaterals and coordinates; similarity (including ratio and proportion, and proving products equal); right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and working in space (an introduction to solid geometry). Each chapter includes practice exercises with answers provided at the back of the book. ... Read more

Customer Reviews (3)

Used it last year, scored well above 90 on the Regents
This review book might be a little too comprehensive for last minute review, but it works well as a supplement to the class. Some students find certain concepts to be difficult to grasp at first take, so this book provides good all around exposure through examples and Regents-level practice questions. I used this book to prepare for the June '09 Geometry Regents (the first administration of the exam after the transition from Math A/B) and scored well above 90 on the exam. Would not recommend it for last month review, but would rather purchase it some time early in the year to help thoroughly review topics one by one, taking a more systematic approach as the exam gets closer and closer.

a teacher but whole years material
this is a great book but suggest to buy long time before regents because its practically everything the teacher taugt in class

Well Written Complete and Way Way Too Long for My Students
This is a well presented review of geometry and for students preparing for a comprehensive final or the New York State Regent's Exam, it is good to see the practice exam in the back. But this book is too long. If I could get a student to read this book, I could get them to read our text the way it should be read.

Here's the problem. Kids flunk geometry because they won't take the time to learn, much less understand, the language of geometry (definitions, theorems, postulates). For help in learning and understanding what high school (and junior college) students need to learn to be successful, I recommend Tutor in a Book's Geometry. (And for Algebra 1, Garlic Press' Books 1 and 2).

For the SAT's there are only 14 geometry problems so the Barron's geometry section in its SAT Review book is best.

It just seems to me, that as good a job as Leff does with his Geometry review, no student that I have had who had the discipline to read through all this material, would need to read it to begin with. I do think Leff did a fine job in presenting a comprehensive review for test preparation, especially for a student who as we say in education, "didn't hear the music the first time". But either a dedicated parent or a tutor would have to continuously monitor the student's progress or I doubt very much that the average student will even bother to read it. Unmotivated students need more visuals and encouragement and graphic organizers (TIB's Geometry has all of that). ... Read more

Product Description
Demonstrates in a clear and lucid manner the relationships between several types of geometry. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts. Preface. Index. Bibliography. Exercises (no solutions). 98 illustrations.
... Read more

Product Description
Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen.

The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. ... Read more

Customer Reviews (5)

Amazing book
Just an all around great book; interesting way to explore geometry, in a format that's easily understandable for both beginning & advanced students.

Good enough
Not as new as I expected. Doesn't have original cover, though I can settle with the enforced hard cover.

forward thinking book about using the computer for mathematics education
Turtle Geometry teaches mathematics and physics via the computer and the Logo programming language. The mathematics covered is pretty advanced, including topology, and general relativity. Yet, through the use of turtle geometry this advanced math and physics becomes accessible to the layperson. Although all of the examples are in the Logo programming language there are listings of Basic routines in the back of the book. With the help of the Basic routines I was able to easily translate the Logo/Basic code to the Python programming language which I choose to use for reading this book. The reviewers of this book mention it as the beginnning of a revolution in mathematics education. It seems though, that this revolution did not come about as computers are still not used very effectively in the classroom. I think this is very sad as the teaching approach used in Turtle Geometry could be very successful in the classroom.

My favorite geometry textbook
I discovered this little gem of a book while exploring the stacks in the library when I was attending a local junior college back in the 80's.The author uses Logo's turtle graphics as a way of exploring the properties ofgeometric space.From very simple beginnings drawing regular polygons andother simple shapes, the book gradually works its way to more and morecomplicated scenarios.After exploring the properties of ordinary turtlegraphics, turtle graphics are tried on the surfaces of spheres and cubes,then on more complicated surfaces.Little by little, concepts ofnon-Euclidean geometry are introduced, until the final chapters in whichthe turtle is used to demonstrate the geometric nature of gravity inEinstein's general theory of relativity.

I strongly recommend this bookto anyone with interests in computer programming, geometry and physics. The unusual approach this book takes to the understanding of curved spaceis deceptively simple and surprisingly powerful.

Very good book to show how to use logo as a tool for math
Anyone interested in logo from beginners to advanced users will benefit from reading this book.It has very easy and simple to understand examples, along with a review, and questions at the end of every chapter.Some solutions are provided at the end of the book, (and their even correct, as opposed to many other text books I've read).The pace of the book gets gradually more difficulst, yet more interesting as you reach the climax at the end.A must read for anyone interested in Mathematics. ... Read more

Product Description
Unit 1: Geometric Structure.Unit 2: Congruence.Unit 3: Similarity.Unit 4: Two-and Three-Eimensional Measurement.Standards Review.846 pages. ... Read more

Customer Reviews (2)

class required textbook
This is a required textbook for my kids and they have not trouble to understand.Good organization and covered most of the concepts in Geometry for high school student.

Textbook
The book arrived on time. It was a great help to find this book used and at a very reasonable price. Thank you. ... Read more

Product Description
Written for students who need a refresher on Plane Euclidean Geometry, Essentials of Geometry for College Students, Second Edition, incorporates the American Mathematical Association of Two-Year Colleges (AMATYC) and National Council of Teachers of Mathematics (NCTM) Standards on geometry, modeling, reasoning, communication, technology, and deductive proof. To make learning interactive and enjoyable, this new edition includes exciting new features such as Technology Connections and Hands-on Activities. Knowledge of beginning algebra and a scientific calculator are required for this text. ... Read more

Customer Reviews (2)

Essentials of Geometry for College Students
I'm very pleased with this purchase. The book came promptly and was in good condition. I would definitely order from this seller again

Not for serious geometry students
I only own a copy of the first edition (1990), but unless adding a new author (Brown) or drastically changing the text has greatly improved anything, the book doesn't try for much more than its title indicates.Like many other college introductory geometry texts, this isn't much more than high-school-level geometry without all the colorful pictures and stories that are supposed to make the topic fun and show the application of geometry to our lives (making this book about a third the size of most high school texts).
This book is not bad, and is probably fine for the student whojust needs a basic understanding of Euclidean plane geometry (with chapters on solid and analytical geometry, and trig).Many of the theorems are proved (two-column proofs).The exercises are more into reinforcing the chapter contents (solving numerical problems and showing concept understanding) than in exploring new material and applications.
For authors that introduce a more rigorous approach, and show how beautiful geometry can be; try Coxeter and Posamentier. ... Read more

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

Customer Reviews (9)

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

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

Thank you
Sharon D

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

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

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

Product Description

This book offers an introduction into projective geometry. The first part presents n-dimensional projective geometry over an arbitrary skew field; the real, the complex, and the quaternionic geometries are the central topics, finite geometries playing only a minor part. The second deals with classical linear and projective groups and the associated geometries. The final section summarizes selected results and problems from the geometry of transformation groups.

Product Description

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants

Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic

Abundantly supplemented with figures and exercises

Customer Reviews (4)

Many Mistakes
While this book is a cheaper alternative to the hardcover, there are many mistakes in the printing.There are little dots where there should be parentheses, brackets and square root signs in the problem section.It makes the problems hard to understand if you do not know what symbols are supposed to be there.If you are using this for a class, make sure have someone else's book to compare it to.I know it is not just my book because everyone with the soft cover in my class has the same problem.

Fine for School
This is a fine book for learning Euclidean and non-Euclidean geometry. Fairly clear. I wish it had more examples.

Makes the connections, simply, readably
This text makes the connections simply, readably among various interrelated branches of mathematics including geometry (four of them), trig, group theory, complex variables, and linear algebra.Recommended for every high school mathematics instructor.

A textbook for that geometry course you wish existed
This nice book contains many things that every mathematics student should know (but don't). Chapters 1-2 are on Euclid. The main ideas are picked out very nicely, in welcome contrast to the usual "let ABCD..."-style books. Chapters 3-4 on linear algebra in geometry will probably be skimmed by most readers. This is perhaps just as well, since it consists of little more than the pearls from the usual linear algebra course and since the presentation feels somewhat forced (e.g., things like the inner product are cheerfully defined out of thin air) compared to how naturally the rest of the book flows. Chapters 5-6 on projective geometry are more interesting. Perspective in art sets the stage, but we quickly move to purer things. Stillwell is very fond of the mysterious and fascinating connection with hypercomplex number systems one obtains by building up an arithmetic from within a projective plane. Then in chapter 7 we learn that transformation groups are a clarifying and unifying idea, and we play around with them a bit, somewhat aimlessly it seems, until we finally get to hyperbolic geometry in chapter 8. This chapter crowns the whole book beautifully, showing how projective geometry explodes into hyperbolic geometry through transformation-group thinking. It ends with an excellent short survey of the history of non-Euclidean geometry. ... Read more

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About the Art & Imagination Series: Explore a range of interests, philosophies, religions, and cultures—from Kabbalah to Freemasonry, Buddhism to Hinduism, myth to magic. The distinguished authors bring a wealth of knowledge, visionary thinking, and accessible writing to each intriguing subject in these lavishly illustrated, large-format paperback books. ... Read more

Customer Reviews (14)

well written - good examples.
this book has a good balance of the practical and the metaphysical for someone looking to understand the inner workings of geometries in more detail.it is the most comprehensive of the books i have found on the subject.

A Text Book of Secret Geometry Proofs ("One" not used in schools)
This is an amazing book.This book may appear to be a small book but it is not.Yes it is small physically but spiritually, it is a very condensed text book.The author takes you on a journey of sacred geometry.Reading thru the text is relatively easy but it is time consuming to go thru the proofs.....but well worth the time, effort and work.The author goes back in time to a state of existence when the concept of zero meant literally nothing; when the first number was "One".One meant and still means "Unity".The author provokes the thought of what would our perception of the world be today if the concept of "zero" did not exist?Does it really exist or have we blindly accepted everything that we were taught by those that were here before us?

"The notion of zero also had its effect on our psychological conceptualizations.Ideas such as the finality of death and the fear of it, the separation of heaven and earth, the whole range of existential philosophies based on the despair and absurdity of a world followed by non-being, all owe much to the notion of zero."

The author recommends that you recreate the proofs thru his process of instruction of actually drawing the sacred geometric configurations.The author goes thru many geometric exercises described as workbooks of geometric configurations to prove secrets of creation or of God; following these workbooks results in experiencing creation itself.

"The primary geometric forms are considered to be the crystallizations of the creative thoughts of God, and the human hand, manipulation and constructing these forms, will learn to position itself in the essential poses of gesture-language."

"Why, it may be asked, cannot Unity simply divide into two equal parts?Why not have a proportion of one term, a:a?The answer is simply that with equality there is no difference, and without difference there is no perceptual universe..............An asymmetrical division is needed in order to create the dynamics necessary for progression and extension from the Unity."

Sacred geometry is the crystallization of music frozen in time where music represents time and sacred geometry represents space.

A Book of Wisdom to Be Read Slowly
Very, very insightful intro to sacred geometry. If not familiar with this topic, I would suggest one first read the book to get your feet wet in a new way of perceiving what's around you. Then go back, re-read it slowly, and carefully do the math (which isn't difficult, really) and make the geometric constructs on graph paper like the author suggests.You have to do the exercises for it all to fully sink in, and achieve greater comprehension.This book is quietly profound. I only wish it was longer and for this talented author to get into the deeper end of the pool.Lawlor's commentary is often provocative and compelling.

A Rare Resource
If you have been looking for the secrets of the Pythagorian Brotherhood, then look no futher - this is the book.Robert Lawlor takes you step by step into the realm of Hermetic Knowledge and connects it all together.

Not for the meek.
Great source for a workbook; not an elementary book for the true beginner. ... Read more

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Customer Reviews (14)

An added layer to the Geometry you learned in school
Tight, neat and succinct chapters throughout this book show that the ancients assumed the world was a Cosmos in the sense it was ordered and could be understood.Skinner begins with arithmetic, and Pythagorean number theory, highlighting the Lambda and it's relationship between the order of the planets and the notes on a stringed instrument. Skinner continues on through Geometry as it applies to the Universe, the World, the Landscape, and Man himself.Interestingly, for example, the Yard is a function of Time as well as Length, for example.Early Temples and other constructions are shown to have a relationship to either the Zodiac, the Earth, or Man, sometimes all three simultaneously!Sadly to my knowledge, we have lost the Art of Sacred Geometry for use in our Temples, but the Work has continued on in our mundane architecture, where Skinner presents modern day examples of these principles being applied by modern architects.

Don't let this one slip by if you've developed an interest in the subject!

Not useful for education
I bought this book hoping that I could use some of the connections with art in a mathematics course on Geometry.After a more careful reading, I must agree with the previous reviewer who notes the weakness of the mathematics in the book.In addition to the errors regarding irrational numbers, the author misunderstands the concept of fractal geometry and how it truly does relate to chaos theory.On page 59 the author makes the case that the two are unrelated.In fact, the Mandelbrot set, for example, is defined by the boundary between chaotic and ordered recursive behavior.It is all too clear that the author is no mathematician.I appreciate his efforts to connect Geometry to mystical human endeavors, but I wish he had co-authored with a mathematician.I cannot recommend this book for use in mathematics education.

Sacred Geometry: Deciphering the Code
Skinner's foray into the fundamentals of sacred geometry lays a sound historical foundation for the mysteries yet to be discovered in other works.Skinner provides the bread crumbs that can lead the serious student down the rabbit hole of Euclid, Plato and the rest of my fellow ancient Greeks as well as the non-Greeks like Kepler, et al. For a modern take on the subject,see Bucky Fuller's friend, Keith Critchlow, and his Order in Space, as well as Robert Lawlor's take on the subject.If your interested in the actual implementation of such designs with your own square and compass (which is the real way to discover the deepest mysteries), check out the Wooden Books series (with an emphasis on the texts: Sacred Geometry, Platonic and Archimedean Solids, A Little Book of Coincidence) or just buy them all like I did.If you are feeling really adventurous and are willing to suspend your disbelief at concepts and experiences that may seem... strange to today's average human, then check out Drunvalo Melchizedek's Flower of Life (Volumes 1&2). Dru dropped some geometry gems in there, no doubt.

Also check out the Geometry Junkyard website for more geometry fun!I found that the hands down best way to grasp the relationships between all geometric forms including (but not limited to) the regular polyhedra is to find the free "Nets" online [...] Then, simply print 'em out and glue them together.Of course, if one can draft the nets with a compass oneself, even better.... but then one wouldn't be reading this review,would one?No book can compare to actually holding such shapes in your hand.

I enjoyed Stephen Skinner's work even though he was often frustratingly vague and lacked a significant depth to some of the more interesting math and geometry to be found all around in nature.However, its an all around good book... Its got a great beat & I can dance to it.

Perhaps I can even excuse Skinner's horrendous blunder on Page 9 that labeled a famous DaVinci rendering of a pentagonal dodecahedron as a "regular icosahedron." (Really Stephen, for shame)!

Pretty, thought provoking, but full of errors
I was attracted to the high quality of this book and many illustrations and diagrams which aid in understanding.The book is arranged in short, readable, 2-3 page chapters per topic which can mostly be read separately as you have time.

Unfortunately, a number of errors in the text and poorly written descriptions of the diagrams actually detract from understanding the subject.This is especially true if you want to better understand the relatively simple geometry or math behind the beautiful shapes and natural patterns.The sidebar on the quadratix and custructing root rectangles are frustratingly incomplete for no apparent reason.Other reviewers have pointed out other silly mathematical errors in the book.The author gives you plenty to think about, but you'll have to look elsewhere for accurate description of the concepts.

Perhaps the author was not able to clearly explain understand some of math he didn't understand and the publishers certainly rushed the book to market without a mathematical proofreading.Maybe a second printing will correct these flaws in a book with great potential.For now, I'm glad I picked it up off the clearance rack for under $10.

Good book
I would have given the book more stars, unfortunately the last few sections of the book are too christian for my own tastes. The book is well written and presents the information well, but it does fall apart in the end. With all the material of sacred archeological sites, I dont know why the Author chose to stay within the scope of christian churches, when most people who pick up this book are more intrested in the true sacred. ... Read more

Product Description
Over the last forty years, researchers have made great strides in elucidating the laws of image formation, processing, and understanding by animals, humans, and machines. This book describes the state of knowledge in one subarea of vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of mathematics, is the natural language for describing three-dimensional shapes and spatial relations. Projective geometry, the geometry that best models image formation, provides a unified framework for thinking about many geometric problems relevant to vision. The book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry.Images play a prominent role in computer communications. Producers and users of images, in particular three-dimensional images, require a framework for stating and solving problems. The book offers a number of conceptual tools and theoretical results useful for the design of machine vision algorithms. It also illustrates these tools and results with many examples of real applications. ... Read more

Customer Reviews (1)

Thought Provoking
My interest in this item largely stems from its use of the language of differential forms in its treatment of the mathematics of vision and the geometry of image formation. The index free tensorial background is a very natural framework for geometry albeit its heavy use has been limited to those in the theoretical physics community hitherto. In this respect this is pretty much the only treatment on the uses of those methods in vision and image construction. It is, however, a very solid text. In addition to the exterior calculus language used, it is a nice refresher of geometry in general. I figured out that my understanding of the concept of perspective was rather limited prior to reading it. Moreover, the treatment of the affine and projective geometries is very well motivated and would benefit anyone whose work partially or fully make use of those concepts. I wish visual art students could also dig into it and take out as much as they could.

In the final analysis, the nature of image formation is a very fundamental issue in vision and in this respect the rigorous use of geometric tools is instrumental and instructive. With that said, this is a rather well written account of the mathematical foundations of image formation. The price is very enticing as well. Not to be missed by anyone who is moved by the marvels of geometry. ... Read more

Product Description
The Study Guide & Intervention Workbook contains two worksheets for every lesson in the Student Edition. Helps students:

• Preview the concepts of the lesson,
• Practice the skills of the lesson, and
• catch up if they miss a class.