Escher, M. C.

Godel, Escher, Bach: An Eternal Golden Braid

Average customer rating:

Down the Rabbit Hole...
Come one, come all
Bound with the "braid"?
Item is in good condition and I recommend buying from this seller
"This sentence is false."

Godel, Escher, Bach: An Eternal Golden Braid
Douglas R. Hofstadter
Manufacturer: Basic Books
ProductGroup: Book
Binding: Hardcover

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ASIN: 0465026850

Amazon.com

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

<B>Topics Covered</B>: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.

Book Description

Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern mathematics to the study of the human mind and the development of artificial intelligence.

Customer Reviews:

Down the Rabbit Hole..........2007-05-18

This is a difficult book.

Difficult to read. Difficult to understand. And, I'm finding, difficult to review. What's it about? Good question. The author, himself, isn't very clear on this point, describing it as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll." I'm not sure I can do better than that. I will tell you this, however: if the book has a "point," it does seem to be that man's consciousness is ultimately mechanical and, therefore, that there is no reason that machines cannot finally be intelligent in the same sense that man is. (And, in fact, be as man in just about every internal way.)

While I take issue with this conclusion, and some of Hofstadter's reasoning along the way, I don't think that my debating his points is the basis on which a prospective reader should decide whether or not to pick up this book. Instead, the prospective reader should know: that this is a lengthy and deep work. It will take a *long* time to read properly, and most readers should not read more than a chapter a day. Many of the sections, and especially the various dialogues that preface the chapters, are quite clever. (These dialogues are usually between Achilles and the Tortoise, of Zeno's paradoxes, and their friends.) Some of the chapters grow incredibly technical. The subject matters vary, wildly and rapidly, and there will be points in reading where you will question your investment.

In the end, you will feel good for having pushed through the hard bits. It will coalesce, more or less, into a whole. Whether you finally agree with Hofstadter's conclusions or not, you'll have learned much and thought about important topics you might otherwise not have.

A good book, certainly not for everyone... but, if you're the "right" audience--someone deeply interested in questions of intelligence, mathematics, computer science and free will, and possessed of a bit of an ironic sense of humor--then this book cannot be recommended highly enough.

Five stars, for the work it represents, and the doors it opens to the reader.

Come one, come all.......2007-05-16

As you can see from other reviews, people tend to walk away from this book with a variety of different impressions. Math, Art, Logic, Philosophy, Human Perception and Thought, it has it all. This is second to the Bible in my collection as a book I've read multiple times and can still come back to a read again for even more insight and perspective.

Bound with the "braid"?.......2007-05-14

Can someone tell me, in plain English, what this book is about? On the little matter of determinism--is he for it or against it? He does not seem to have come to praise Godel, Escher, Bach for their strangeness but rather to bury strangeness and its resistance to materialism. He seems to be saying that strangeness is hardwired and can be programmed into a formal system by someone who sees it for what it is--in short, that computers will some day rise to the level of consiousness and self-reference. But wouldn't such a system be curved in upon itself and lack strangeness? If strangeness could be hard-wired into AI, would it still seem strange? Nothingness annihilates strangeness, but then the absense of strangeness is the actual limit of the theories of value seen in those who follow Heidegger. In order to eliminate the difference between soul and matter, they must give up the resistance of soul to the limitations of material existence; at which point "strangeness" becomes a matter of verbal virtuosity and conceptual sleight of hand. "Strangeness" becomes the same thing as cleverness. Or am I misreading this fascinating book?

Item is in good condition and I recommend buying from this seller.......2007-05-14

Item is in good condition and I recommend buying from this seller.

"This sentence is false.".......2007-03-19

A simple example of recursiveness in music is the song "row, row, row your boat." The song becomes recursive as each new line is started when the original line makes it to "gently down the stream." In this way, we have a musical example of the artistic portrayals of Maurits Cornelius Escher whose paintings invariably fosuc on recursive visual themes such as two hands in the process of drawing each other.

In each case, the depiction challenges our ability to pidgeon hole the phenomenon we are examining. Which line is the harmony, which is the melody in "row, row, row your boat"? Which hand is drawing which in the Escher print?

Liguistically, the same effect occurs when we examine the statement "This sentence is false." Logically if we accept the statement at its face value being false then it becomes an accurate representation (in that it correctly asserts its falseness). On the other hand, we are also drawn to the conclusion that the statement is true (again because it is self referentially accurate).

Ultimately, we are forced to logically conclude that we can neither bracket the statement "This sentence is false" with either all true statements or all untrue statements. As indicated previously, like the song "row, row, row your boat" or an Escher painting, the sentence defies pidgeon holing owing to its recursive quality.

Back in 1931, Kurt Godel shocked the mathematics community with his assertion that mathematically consistent systems themselves necessarily produce formally undecideable propositions (the math equivalent of "This sentence is false"). At the time of presenting his paper, it was Godel's intent to demonstrate the unique nature of human intellect because if we can resolve undecideable propositions then there must be something unique to the process of human intellect.

While Godel certainly brought undeniable genius to the creation of his theorem, it doesn't follow that the theorem proves the uniqueness of human intellect. And the reason Godel's theorem doesn't prove the uniqueness of human intellect is because its logical limitations are our own.

Just as Godelian mathematics can't prove undecideable propositions, neither can we "prove" them.

However, we can "believe" undecideable propositions. (In this regard, two easy cases in point are Goldbach's conjecture -- that all even numbers are the sum of two primes -- and that parallel lines really are parallel.) In this way, Godel's theorem, in combination with modern research on artificial intelligence, shows that it is the emotive side of reason that defies the strict logical limitations of Godelian constructs.

These hard won discoveries have combined to make for some surprising findings.

Probably the first among these most observable to the general public through the misconception of science fiction is that emotion somehow stagnates the operation of intellect. In this way, it was HAL 9000's personality as much as the creepiness of that personality that was surprising to 1968 movie goers watching "2001: A Space Odessy." As demonstrated in the movie, it was the fact of HAL's emotive connections with the ongoing actions of his crew that prompted "him" to formulate and act on plans.

Second, modern research has shown that human intellect is not best characterized as being a "blank slate" but rather a delicate combination of various systems that survey reality in the own ways. An easy example is the human eye which uses a combination of three different light cones to measure redness, greenness and blueness. It is the relative comparisons of these cone findings that nudges your visual perception to observe the color of an object. At the intellectual level, one system is entirely devoted to our understanding of artifacts. How do they work? How can they be modified for use in a situation? Another system comprehends animate creatures. Yet another system recognizes faces. Still another system is devoted to language acquisition.

And significantly all these systems acquire information emotively. We see the face of a parent and emotively appreciate it (unless we suffer from a particular cognitive disorder that has disabled our ability to do so as for example discussed by Oliver Sacks in his great book "The man who mistook his wife for a hat"). We remember a concept learned and emotively evaluate it. In this way, freedom, communism, taxes are not just intellectual constructs but ideas that spark real feelings on our part.

In creating Godel, Escher, Bach, Douglas Hofstadter displayed true genius in linking three domains wherein recursiveness seems to play such a pivatol role. As he indicated, they are three shadows cast from the same source.

In re-concluding this book, however, I couldn't help but think of other possible titles that could be added to a Godel, Escher, Bach type encyclopedia: "Phi, Di Vinci, Bach" -- the story of the "golden ratio" of phi which plays a role in Di Vinci's art work and as it so happens also in the music of Bach; "Pascal, State Lotteries, Happy Birthday" -- the story of Pascal's wager and how an appreciation of statistics will make us understand why states will never lose money running a state lottery for reasons akin to why relatively small groupings of people will have at least two that share the same birthday; and "Klein, Carroll, Kubrick" -- the story of Oscar Klein's bottle which can resort to the fourth dimensionj to fill itself up and how speculations by the physicist J Richard Gott suggest that Alice and all of us may have originallyu gone down the rabbit hole for a real space odessy through time itself.

The point here is not that Hofstadter was incorrect but (no pun intended) merely incomplete in his survey when he said that Godel's proof, Escher's paintings and Bach's music were but three shadows cast from the same source. The point here is that -- properly examined -- those three shadows, together with the encyclopedia I've suggested, would direct us not only to the origins of consciousness but also the origin of origins itself.

Average customer rating:

Nice selection of some of Escher's most famous works.
Excellent Escher

M.C. Escher : 29 Master prints
Maurits Cornelis Escher
Manufacturer: Harry N. Abrams
ProductGroup: Book
Binding: Paperback

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Customer Reviews:

Nice selection of some of Escher's most famous works........2004-10-25

Nearly everyone will have seen some of the work of Dutch graphic artist Maurits Cornelis Escher (1898-1970). His woodcuts and lithographs are largely based in mathematics and geometry, and provide endless fascination. Many of the two dimensional images Escher created simply could not exist in the three dimenional world, yet on paper they LOOK entirely plausible at first glance (for instance, "Ascending and Descending" and "Belvedere"), and this alone gives the mind of the viewer plenty to ponder. Escher also incorporated tessellations - images composed of repeating, interlocking shapes - into many of his pieces (such as in "Reptiles" or "Fish"), and he played with the idea of having different figures in the same composition existing on different planes, despite sharing the same space. For instance, a surface which is the floor for one figure may be a wall for another (see "Relativity").

This particular book is a very nice collection of some of Escher's most well-known pieces, and is very afordable. There are certainly more detailed books on Escher's life and work available, such as J.L. Locker's 200-page "The Magic of M.C. Escher," but "29 Master Prints" is a great alternative for those who simply want something visually stimulating to put on their coffee table, without too much text. Each print covers a full page (and these are large pages - approximately 14.5 x 10.5 inches), and is accompanied by a small amount of text on the facing page, giving the piece's title, date of completion, medium, dimensions, and a short blurb offering insights about the print, written by either Escher himself or one of several other authors. The explanations written by the artist are often delightfully witty. At the beginning of the book there is a short essay by Escher, "On Being a Graphic Artist."

One disappointment I found was that the print of "Metamorphosis III" is broken up into pieces to fit it all on one page, so you can't see it end-to-end. I would rather have seen this done as some sort of fold-out. Also, unfortunately, this book does not appear to be available in hardcover, so it is slightly less durable. Nevertheless, I would certainly recommend "29 Master Prints" to any fan of Escher's work.

Following is a list of the particular twenty-nine prints included:

"Rind" - on front cover
"Other World"
"Smaller and Smaller"
"Circle Limit III"
"Knots"
"Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror)"
"Balcony"
"Circle Limit IV (Heaven and Hell)"
"Ascending and Descending"
"Day and Night"
"Regular Division of the Plane III"
"Sky and Water I"
"Cycle"
"Metamorphosis III"
"Belvedere"
"Reptiles"
"Relativity"
"Fish" - 1942 woodcut
"Mobius Strip II (Red Ants)"
"Snakes"
"Fish" - 1941 woodcut
"Drawing Hands"
"Three Spheres I"
"Stars"
"Waterfall"
"Double Planetoid (Double Planet)"
"Dream (Mantis Religiosa)"
"Concentric Rinds (Concentric Space Filling / Regular Sphere Division)"
"Dragon"

Excellent Escher.......2000-05-24

This is a great "coffee table" picture book - full page prints of 29 of M.C. Escher's works. Not much text. The main drawback is that it is a paperback, so you can't use it too well as a "lap table" for other projects. And hey, the price is right, now! Just under 15 bucks, wow! We got our copy 15-20 years ago when the price was quite a bit higher! You can count on Amazon.Com to deliver it fast and cheap. Great book...

Average customer rating:

No other word for it: Amazing.
Excellent book
GEB - A must read for all aspiring thinkers
Must for Math Majors and Enlightened Individuals
One of the biggest influences in my life, and a classic.

Godel, Escher, Bach: An Eternal Golden Braid
Douglas Hofstadter
Manufacturer: Vintage
ProductGroup: Book
Binding: Paperback

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ASIN: 0394745027
Release Date: 1980-09-12

Customer Reviews:

No other word for it: Amazing........2006-07-23

It is quite likely that the hardest question I've ever been asked is, "What's that book about?" This book manages to discuss, coherently, cohesively, and interestingly, everything from molecular biology to quantum physics to computer science to music theory to philosophy to advanced mathematics to Elizabethan literature and beyond. Reading this will definitely change the way you see the world, and if you read one book this entire year, this should probably be it. VERY highly recommended.

Excellent book.......2006-04-26

As far as the layout and design of the book go, I find this piece to be particularly structured in a way that one studying abstract and modern mathematics might find appealing. It gives specific axioms for use with each topic and in doing so defines more than just what the topic might imply. As the content goes, for those taking an introduction course in abstract algebra, this book may be slightly heavy and unwieldy, however, for those well-learned in some of its background material, this book is enjoyable and pleasurable to read. The author even makes use of antecdotes to enforce his topics. Overall, this book has been one of the most pleasurable assigned readings I have endured.

GEB - A must read for all aspiring thinkers.......2004-06-15

The Atlanta Journal Constitution describes Gödel, Escher, Bach (GEB) as "A huge, sprawling literary marvel, a philosophy book, disguised as a book of entertainment, disguised as a book of instruction." That is the best one line description of this book that anybody could give. GEB is without a doubt the most interesting mathematical book that I have ever read, quickly making its place into the Top 5 books I have ever read.
The introduction of the book, "Introduction: A Musico-Logical Offering" begins by quickly discussing the three main participants in the book, Gödel, Escher, and Bach. Gödel was a mathematician who founded Gödel's Incompleteness Theorem, which states, as Hofstadter paraphrases, "All consistent axiomatic formulations of number theory include undecidable propositions." This is what Hofstadter calls the pearl. This is one example of one of the recurring themes in GEB, strange loops.
Strange loops occur when you move up or down in a hierarchical manner and eventually end up exactly where you started. The first example of a strange loop comes from Bach's Endlessly rising canon. This is a musical piece that continues to rise in key, modulating through the entire chromatic scale, ending at the same key with which he began. To emphasize the loop Bach wrote in the margin, "As the modulation rises, so may the King's Glory."
The third loop in the introduction comes from an artist, Escher. Escher is famous for his paintings of paradoxes. A good example is his Waterfall; Hofstadter gives many examples of Escher's work, which truly exemplify the strange loop phenomenon.
One feature of GEB, which I was particularly fond of, is the `little stories' in between each chapter of the book. These stories which star Achilles and the Tortoise of Lewis Carroll fame, are illustrations of the points which Hofstadter brings out in the chapters. They also serve as a guidepost to the careful reader who finds clues buried inside of these sections. Hofstadter introduces these stories by reproducing "What the Tortoise Said to Achilles" by Lewis Carroll. This illustrates Zeno's paradox, another example of a strange loop.
In GEB Hofstadter comments on the trouble author's have with people skipping to the end of the book and reading the ending. He suggests that a solution to this would be to print a series of blank pages at the end, but then the reader would turn through the blank pages and find the last one with text on it. So he says to print gibberish throughout those blank pages, again a human would be smart enough to find the end of the gibberish and read there. He finally suggests that authors need to write many pages more of text than the book requires just fooling the reader into having to read the entire book. Perhaps Hofstadter employs this technique.
GEB is in itself a strange loop. It talks about the interconnectedness of things always getting more and more in depth about the topic at hand. However you are frequently brought back to the same point, similarly to Escher's paintings, Bach's rising canon, and Gödel's Incompleteness theorem. A book, which is filled with puzzles and riddles for the reader to find and answer, GEB, is a magnificently captivating book.

Must for Math Majors and Enlightened Individuals.......2003-03-08

This book is a must for math majors (as well as many logic and philosophy majors). Anyone else in the hard sciences should also read this book, at least to be enlightened. Initially, it is easy reading, then becomes slightly foggy, but pushing through is rewarding. Of the three, my favorite is Godel and I always mention his Incompleteness Theorem whenever his name comes up. It his probably actually best mentioned by Rudy Rucker in his book "Infinity and the Mind". I think it is significant enough to mention here:

---
The proof of Gödel's Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows:

1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.

2. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.

3. Smiling a little, Gödel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Gödel. Note that G is equivalent to: "UTM will never say G is true."

4. Now Gödel laughs his high laugh and asks UTM whether G is true or not.

5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.

6. We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true").

7. "I know a truth that UTM can never utter," Gödel says. "I know that G is true. UTM is not truly universal."

Think about it - it grows on you ...

With his great mathematical and logical genius, Gödel was able to find a way (for any given P(UTM)) actually to write down a complicated polynomial equation that has a solution if and only if G is true. So G is not at all some vague or non-mathematical sentence. G is a specific mathematical problem that we know the answer to, even though UTM does not! So UTM does not, and cannot, embody a best and final theory of mathematics ...

Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth ... But, paradoxically, to understand Gödel's proof is to find a sort of liberation. For many logic students, the final breakthrough to full understanding of the Incompleteness Theorem is practically a conversion experience. This is partly a by-product of the potent mystique Gödel's name carries. But, more profoundly, to understand the essentially labyrinthine nature of the castle is, somehow, to be free of it.
---

This is the kind of mental freedom you will gain by reading this book. Highly recommended.

One of the biggest influences in my life, and a classic........2001-08-25

Douglas Hofstadter uses the art of M.C. Escher, the music of J.S. Bach, and Kurt Goedel's mathematics as the centerpieces for a magnificent inquiry into the nature of the mind. Along the way you will encounter Bertrand Russel, Carroll Lewis, particle physics, molecular biology, Magritte's paintings, and Zen koans. These are all used to probe recursion and the mystery of how we form thoughts. But the list of topics alone is not what makes this book great, it's the playful, joyful sense that characterize's Hofstadter's treatment of this. This sense of wonder is critical, as without it this highly challenging book would be very frustrating. The book's style itself is based on Bach's canons, and the chapters are interspersed with dialogues between the Tortois and the Hare, in the style of Carroll's Alice in Wonderland. The result is an artistic as well as scientific or philisophical masterpiece. I am currently a triple-major in molecular biology, physics, and philosophy, and much of my curriculum has been influenced by the beauty of Hofstadter's book. This will go down as one of the 20th Century's bests books.

Average customer rating:

stark, gigantic, modern, you need a table to read this book

M C Escher
Sandra Forty
Manufacturer: Book Sales
ProductGroup: Book
Binding: Hardcover

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Book Description

Maurits Cornelis Escher was a truly unique artist whose vision was quite unlike anyone else's. To enter his world is to set foot into unknown and unsettling territory.

His extraordinary pictures of logic and perspective fool the brain into believing the impossible- that staircases can climb forever, that fish can morph into birds, and that water can run uphill. Enter the world of MC Escher in this truly unique collection of his work, encompassing over 70 full-color pictures

Customer Reviews:

stark, gigantic, modern, you need a table to read this book.......2004-05-29

My appreciation of art has been so influenced by the power of photography to capture things as I see them that I fail to see the works of M. C. Escher as being very artistic. If art is supposed to show the power of human beings to capture the essence of objects as we see them, Escher seems to be trying to show us things we could never see, but that try to be art like cinnamon rolls that come from a refrigerated can of dough and icing might try to replace real cinnamon rolls in our lives. Of the eight small pictures shown around the weird building topped with stairs and a tiny tower on the cover of M C ESCHER by Sandra Forty published by TAJ BOOKS 2003, a square near the lower right corner looks like a swirling combination of reptiles cooked up from splotchy shapes as a pattern emerges from the 10 x 10 squares around the edges, the shape of which suggests a pan of something from the oven.

I was introduced to the work of M C Escher about 33 years ago, after I was an adult attempting to understand the ways in which highly educated people understand the world. Or, in the case of M C Escher, there seems to be real questions about what people are doing here at all. On the stairs at the top of the building on the cover, the outer 14 hooded walkers seem to be climbing, holding the outer railing in their left hands, while the 12 inner walkers pass them descending the stairs with their left hands on the inner railing. The inner courtyard does not appear to be square, because the front wall is so much longer than the back, but due to perspective, each step appears to be higher or lower than any other step.

Maurits Cornelis Escher lived from 1898 to 1972, about the span of life of my grandparents, and page 5, which contains that information, also shows "House of Stairs" (my favorite Escher design) in the center of that page, though a larger copy, Plate 40 on page 51, is the same picture at about 6 inches by 12 inches. There are only a few pages in this book that don't have pictures on them. At the top of the pages of text up to page 11, there is a thin strip reproducing a long mural called "Metamorphosis" that is mainly black and white with a little color where a sky full of flying birds transforms into a city by a waterfront with a little bridge to a castle sitting on a chessboard. Escher did a lot, he "left over 2,000 drawings and 448 lithographs, woodcuts, and engravings. . . . His legacy is carefully guarded by the M. C. Escher Foundation at Baarn, The Netherlands." (p. 5). It is not surprising that this book contains some pictures that I did not have before. In the case of Plate 47, "Plane Filling Motif With Fish and Bird," (p. 58) I quickly saw four fish with eyes like circles, but it took me awhile to see a bird in the center between them, with an eye that looked like the number "6" which first seemed to be a cartoonish swirl to depict motion in whatever the fish were swimming in. There is nothing realistic in that picture: it looks more like a ragged potholder than a photograph, but the page is so black it can't be anything but ink on a page, which is what it is.

Escher's work is not totally devoid of women. One in a white dress is walking into "Convex and Concave" in Plate 56 (p. 67). Plate 7 shows "Jetta (Escher's wife)" 1925 woodcut 49.2 x 27.8 cm, looking very proper, with a collar that extends from shoulder to shoulder, holding a flower in front of a dark outfit that shows nothing of her figure, with her eyes lowered so that she can only see the flower if she is seeing anything. Her hair is neatly parted, but a tiny curl is visible by one temple. The picture is so black and white, the impression is that only her face, the flower and her hand are white, while her collar, neck and aura are trying to reside somewhere in between the light and the mystery where the shadow of her nose meets the edge of her lips. People who have worked with wood and a gouge will be able to detect each cut in the wood, and the only thing which is stark about the picture is that his use of technique is so visible.

A famous design, Plate 51 "Gravity" 1952 Lithograph and watercolor (p. 62), shows orange, purple, green, yellow, red, blue creatures standing on star-shaped planes with a point over the back of each creature. One point is a bit off center, with the five points of the plane on which the yellow creature is standing close to the edges of the picture, though five more points offset in the background suggest that the shape continues around to the other side. The creatures are arranged so each is shown from a different angle, each facing in a unique direction, but each seems to reflect the same dull recognition: I Know, I know, i know, i . . .

M.C. Escher: Life and Complete Graphic Work
Average customer rating:

All one might want about M. C. Escher

Wonderful With Great Explanations

Essential for the Escher fan

M.C. Escher

A Complete look!

M.C. Escher: Life and Complete Graphic Work
J L Locher
Manufacturer: Harry N. Abrams
ProductGroup: Book
Binding: Hardcover

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M.C. Escher: Visions of Symmetry (New Edition)

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M.C. Escher : 29 Master prints

ASIN: 0810981130

Customer Reviews:

All one might want about M. C. Escher.......2007-05-14

This is a major compilation of the work of the intriguing graphic artist, M. C. Escher. Remember seeing depictions of events that seem plausible but, under closer analysis, involve impossibilities? That describes some of Escher's most interesting works.
The book provides just about everything Escher produced (appearing in the "Catalog" section of the book), including his earliest works compiled during his teens. Among the most well known (and fascinating) include "The Waterfall," "Ascending and Descending March," "Convex and Concave," "Liberation," "Synthesis," "House of Stairs," and so on. The catalog section is fun, for one thing, simply to trace the evolution of his art.

But there is more to this volume than the works themselves. The volume provides context, with a brief description of his father's life as well as a more detailed analysis of Escher's life, from his birth in 1898 to his death in 1972.

There is also a most useful chapter labeled "The Vision of a Mathematician" (featuring the thoughts of mathematics teacher Bruno Ernst). It begins by noting two periods in the work of Escher--(page 135): ". . .pre 1935, in which landscapes predominate, and post 1937, which is characterized by a marked mathematical tendency." Ernst describes the mathematical principles in some detail (for those interested in this, a fascinating discussion). The textual portion of the book concludes with an essay by Escher himself on "The Regular Division of the Plane," including his reflections on his art.

This book has been around a while, but it is a valuable backdrop to getting a sense of the art of M. C. Escher.

Wonderful With Great Explanations.......2007-05-13

I love everything Escher. I have several books, numerous calendars, as well as large jigsaw puzzles, T-shirts, magnets and mini jigsaw puzzles. Because of the detail in this book, I will never need to add another book to my collection. I especially appreciate the explanations. I am nowhere near smart enough to figure out what Escher was doing in each of his artworks. The detailed lesson on what each piece means is much appreciated by an art fan who is not an art scholar. I think this book would be great for any Escher fan, but I feel the need to tell you it is very large. Make sure you have room for it.

Essential for the Escher fan.......2006-08-13

And c'mon - if you've seen his work, you're a fan.

The great thing about this book is not just the extensive and readable biography, but the complete (so they say) catalog of his graphic works. Even people very familiar with Escher's ouvre will be surprised by some of the entries here. They go back to work he did at ages 18 and 19, and show the devleopment of the Escher that has become so famous. It's just a little disappointing that the catalog is printed only in black and white, when so many of his works used color. The catalog reproductions are just that - a listing of his work, not a gallery, so the quarter-page size of most pieces is adequate for recognizing a piece, if not for appreciating it fully.

It is fascinating to see Escher's style develop though his (and the twentieth century's) twenties. Various influences early on suggest Beardsley (cat. 49, 67), Picasso (cat. 51, 58), or the pervasive Art Deco of his time (cat.34). Even then, some of Escher's later fascinations begin to emerge, including hands and reflective balls (cat. 88 and 80), symmetries and tilings (cat. 61, 65), and complex interactions of many figures in a repeating structure (cat. 90). The lesser-known parts of his work also start to emerge by the time he's 30, including delicate lithographs (cat. 129, 132). As much as I love his visual paradoxes and flirtation with the infinite, the lithos and mezzotints are the pieces that truly move me. "Snow" and "Blowball" (cat. 278 and 330) have an eloquent simplicity. "Eye" and "Drop" (cat. 344 and 356) demonstrate his classical sense and his perseverance with the demanding medium of mezzotint.

The text is also thorough and enjoyable - a good thing, since it takes up half of this heavy book, including its own set of illustrations. I admit that I have only skipped around this section, which starts by describing Escher's father. It's small wonder that his father was an engineer and that his son Arthur studied geology. Although an artist to the core, Escher had fruitful contact with mathematicians and crystallographers. He is one of very few artists that have successfully incorporated hard science into their artistic vision at such a visceral level, and the scientists appreciated that as much as anyone.

Although out of print, this book is available inexpensively on the used market. It's one of the best bargains around; if you've read this far, you'll probably find it well worth having.

//wiredweird

M.C. Escher.......2003-10-31

Definitely the first book every Escher fan should purchase. It's helpful in getting to know about the man himself as well as his brilliant artwork. It may seem pricey, but it's totally worth it, being hardcover (at least the one I got), and high quality photos of his work. It also shows his lesser known works (ones never released apparently), as well as photos of himself and his family. A very informative read and a quality edition.

A Complete look!.......2003-05-20

I haven't even had a chance to go through all of this remarkable book yet, but I am so impressed with it so far I cannot burble enough about how delighted I am with my purchase. This is a beautifully produced, designed, and wonderfully complete book. Many tales of the personal life an vision of the artist, countless, cleanly reproduced graphics, many works I have never seen or heard of before. Terrific! Can't recommend enough!!!

Average customer rating:

This Escher book is a Labor of Love
Magic of M.C. Escher
M-escher-merizing!
Outstanding!
Stunning

The Magic of M. C. Escher
J. L. Locker
Manufacturer: Harry N. Abrams
ProductGroup: Book
Binding: Hardcover

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M.C. Escher : 29 Master prints
M.C. Escher: Visions of Symmetry (New Edition)
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ASIN: 0810967200

Amazon.com

M.C. Escher, the artist who lived from 1898 to 1972, suffers from horrible overexposure. Who hasn't seen the college dorm room posters, postcards, T-shirts, and coffee mugs of such well-worn images as a hand drawing another hand or gothic buildings with never-ending staircases? The mass reproduction of these images has carved a firm place in our popular culture, yet made the work dismissible as modern art. Beyond the familiar images, though, is an immense body of work. The Magic of M.C. Escher covers in depth the graphic illustrations, woodcuts, and lithographs of Escher's career. The artist has always attracted the attention of scientists, mathematicians, and teenage boys everywhere; the popular 1980s game Dungeons & Dragons seems to borrow heavily from the systematic yet mystical quality of his drawing style. With his amazingly repetitive graphic illustration and unflinchingly control of size, shape, and shading, Escher draws like a human computer. One can only wonder what he might have done with today's graphic tools.

The book itself is creatively put together, with foldouts, seemingly endless images, and a loving introduction by the director of the Gemeentemuseum in the Hague. The minimal text selections that appear throughout are quotes from Escher himself, many taken from letters to family members. These personal musings give candid insight into what he thought about his peers, his career, and his work: "I really do feel these days like a kind of 'specialist,' and I don't want to 'depend' on my specialty alone, but I also feel it to be my duty to devote myself to that as much as possible." This remarkable book is a wonderful opportunity to enjoy the astounding work of the man who could create two-dimensional origami with a pencil. --J.P. Cohen

Customer Reviews:

This Escher book is a Labor of Love.......2005-04-22

Almost cinematic in design and construction, truly, "The Magic of M.C. Escher" is a breakthrough book on the works of this artist. Every page is filled with inspiration and surprise. Designed by a gifted art director named Erik The' and produced by Andreas Landshoff, this book flows together to form a loving catalogue of Mr. Escher's visions. It is unlike other books based on Escher which tend to be either tutorial or biographical in nature. Whereas these past books, more or less, deconstruct and analyze his works mainly through words, "The Magic of M.C. Escher" successfully accomplishes this through the images themselves, revelling in their sheer beauty, from his preliminary studies all the way to the finished prints. There are many double foldout pages to better impact Escher's mastery of his craft. Some of the pages are filled, corner to corner, with extremely detailed, magnified sections of specific works that allow the reader to closely experience what it's like to be "nose to nose" with the actual prints.

This book catapults the reader into Escher's world immediately. Before you even open the title page, you discover that the inside of the dust cover reproduces, in full color, of course, "Metamorphosis III" in three horizontal panels each measuring an astounding 39" across. This book brings us along on a visual journey ajoined by Escher's own words, as if he is personally giving us insights on a guided tour of his works. It thoughtfully limits itself to short excerpts from Escher's lectures and letters whose sole purpose is to compliment glorious, detailed photographs of original work. It's filled with Escher's never-before published pencil studies and sketches, extreme closeups of his prints, and detailed photographs of his original carved wood blocks. The pencil studies from his notebooks allow us to follow his thought processes and fully appreciate the endless hours he joyfully and dutifully spent on formulating the precise combination of graphic elements to arrive at his finished images.

The book makes side-by-side visual comparisons of earlier works that inspired Escher to create more self-satisfying images that better convey his "relative division of the plane" and other spacial concepts. Most of its visual content were supplied by two sources: The M.C.Escher Foundation and Michael Sachs, a private collector and print dealer from Connecticut.

Overall, this is book is a stunning, loving homage to this master of printmaking and genius to the graphic arts. Nothing is spared in this book's construction and design. If the adage is true that a picture is worth a thousand words, "The Magic of M.C.Escher" could fill a library.

Magic of M.C. Escher.......2003-07-19

Wonderful coffee-table book of Escher's best drawing illusions. Even the jackets is two-sided and imaginatively done with style.

M-escher-merizing!.......2002-10-06

Given as a gift by a special friend of mine, the book has always adorned the coffee table in the living room as a centerpiece that never fails to attract the attention of both art lovers and art dabblers alike. Perhaps it could be said that my interest in the two seemingly disparate field of mathematics and art motivated that friend of mine to purchase the book, as Escher himself apparently believed and proved that those two seemingly unrelated fields could be beautifully synthesized in a brilliant fusion of creativity. The result is more than convincing.

Outstanding!.......2002-06-30

Escher was a Dutch wanna-be mathematician, who expressed himself through incredibly intricate, creative works of art. This book contains hundreds of his drawing as well as his notebook sketches, which is interesting to look at because you get to see how he developed his drawings. Accompanying most of the pictures in this book are excerpts of letters that he wrote to various people. If you want a book on Escher's work, then this is the one to buy! Fantastic.

Stunning.......2002-06-02

High-quality reproductions of the amazing artworks. Minimalistic style of comments and excerpts from artist's letters gives you a focus on subtle details and motives, and lets images tell you the rest.

Average customer rating:

Not What I Thought It Was
The unusual world of M.C Escher
Just gives us what we need, and that's good
Eschers Graphic Work
Escher Is the World's Greatest

M. C. Escher
M. C. Escher , and Maurits Cornelis Escher
Manufacturer: Taschen
ProductGroup: Book
Binding: Paperback

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ASIN: 3822858641

Customer Reviews:

Not What I Thought It Was.......2006-10-28

I thought I was buying a wall calendar, and instead received this engagement book. However, it is a very nice item. It is spiral bound, with sturdy, cardboard type pages. It contains both weekly pages and monthly pages. The monthly pages have squares too small to write anything in except a word or two. The weekly pages have enough room to write down projects, assignments or reminders. I am not educated in art - the only thing I know of M.C. Escher is optical illusions, but this book contains drawings, wood engravings, watercolors, etc. The pictures are spectacular and Escher has a new fan. I bought this as a gift, and thought of returning it, but I think the teen artist I bought it for will like it more than a wall calendar.

The unusual world of M.C Escher.......2006-06-16

Many words come to mind when attempting to describe the work of Dutch artist M.C Escher: surreal, haunting, mysterious, dream-like.
Escher is best known for his exploration of the boundaries between art and reality ("Drawing Hands", "Reptiles", "Print Gallery"), and for his distortion of everday objects and mathematical experimentation with geometric shapes, patterns and perspectives (too many of his paintings to number). His best and most characteristic works, including "Depth" (1955), "Stars" (1948), and (naturally), "Other World" (1946) are highly imaginative, creating a fantastic and indescribable dream-universe all their own, one which must ultimately be experienced in order to be fully appreciated.

Just gives us what we need, and that's good.......2004-04-25

M.C. Escher is one of those artists that editors and art critics can't help but spew nonsense about. Taschen's collection of Escher's work is remarkably sparse on editorializing and allows the works to do what they have always done best: draw the viewer into the magical and hypnotic realm of M.C. Escher. The prints are extremely crisp and thoughtfully arranged, unlike other collections that throw works together in a hodge-podge fashion.

No other artist of the 20th century has had such wide approval and acclaim as M.C. Escher, and this slim volume perfectly expresses why that is so without resorting to pages upon pages of discussions on deconstruction, reality vs. illusion or image vs. icon, and all the other blah-blah-blah that you'll find in other collections. This collection just allows you to turn the pages and enjoy, which I did and you will too.

Eschers Graphic Work.......2004-03-27

Just as the title suggests this book contains The Graphic Work of M.C. Escher. In the beginning of the book there are short descriptional insights about each of the pieces. The rest is filled with Eschers work. If you're an artist and need inspiration or like Eschers work this is a great book. Out of about 90 pages, 70 contain full page prints of Eschers work.

Escher Is the World's Greatest.......2000-12-29

The copies of the prints in this calendar are magnificent. The detail and artistry that escher puts into his works is the most beautiful I have ever seen. Escher is the greatest artist of all time. I recommend this to everyone.

M.C. Escher: Visions of Symmetry (New Edition)

Average customer rating:

Not for the casual Escher fan.
A Most Comprehensive Study of M. C. Escher's Works.

M.C. Escher: Visions of Symmetry (New Edition)
Doris Schattschneider
Manufacturer: Harry N. Abrams
ProductGroup: Book
Binding: Hardcover

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ASIN: 0810943085

Book Description

Doris Schattschneider's classic M. C. Escher: Visions of Symmetry (1990) is the most penetrating study of Escher's work in existence, and the one most admired by mathematicians and scientists. It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzle-like interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by meticulously analyzing Escher's notebooks, and the New Scientist described the result as "a collection of detective stories whose plots are brilliantly organized patterns."

Like the first edition of the book, this new volume includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. It also features an illustrated epilogue by the author that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists. Visions of Symmetry is a trip into the mind of a creator who continues to captivate the world.

Customer Reviews:

Not for the casual Escher fan........2006-02-04

Make no mistake. This isn't a comprehensive book for the Escher fan who wants to look at all his pretty pictures. It is a highly academic (no problem there, unless you're looking for, like I said, pretty pictures) book that focuses on basic patterns. It doesn't have many of the drawings that introduced me to his work in the first place. It's not the coffee-table book I was looking for, but that's my problem. It does have volumes of text for the so-inclined.

A Most Comprehensive Study of M. C. Escher's Works........2005-06-30

It is most gratifying to note that at large, it is a professor of Mathematics who was inspired to collect the materials and compile this most penetrating study on the works of M. C. Escher. That professor is Dr. Doris Schattschneider and her latest publication "M. C. Escher : Visions of Symmetry" is a life's labour of love at collecting, classifying and indexing the works of M. C. Escher in a single volume. The book opens with a stunning photograph of M. C. Escher and a penetrating one-page foreword by Douglas R. Hofstadter.

Who then is M. C. Escher and what is his global appeal? Maurits Cornelis Escher (1898-1972) was a Dutch graphic and wood-cut artist, who for decades working in isolation, single handedly produced the most haunting, fascinating and intriguing works of tesselation, the kind, the world had not seen before. His obsession with visual patterns built by the intricate interlocking of shapes that repeat and repeat forever, filling every crack in the regular plane, made it almost into a visual poetry. What is remarkable is that an artist single handedly learned by himself, the mathematical laws of the plane symmetry group including all it's isometries (i.e. translations, rotations, reflections and glide reflections) as he produced year after year patterns with interlocking shapes of unmatched beauty and provocation. He saw symmetry and beauty where others saw only a senseless repetiton. One can spend hours describing the various feelings brought out by a single image, suffice to say it would require a multi volume encyclopedia to describe in detail all that is collected in this single tome. I am flabbergasted that this book sells on the internet for as low as US $11.00. It is worth it's weight in precious diamonds. Thanks a million Doris, for doing such amicable justice to a great artist, and for providing us such a timeless treasure.

Escher on Escher: Exploring the Infinite

Average customer rating:

Tiny pictures.
Escher in his own words
Not as interesting as one would expect
Casual Fan Book

Escher on Escher: Exploring the Infinite
Maurits Cornelis Escher
Manufacturer: Harry N. Abrams
ProductGroup: Book
Binding: Paperback

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M.C.Escher's Legacy: A Centennial Celebration

ASIN: 0810924145

Customer Reviews:

Tiny pictures........2007-02-13

I think I was under the impression that this was a bigger book or something, but I wish it had bigger, better pictures. This is a paperback with lots more writing than pictures. Small pictures and not a ton of them. Decent book from what I've skimmed.

Escher in his own words.......2004-10-03

Maurits Escher, as an artist, needs no introduction. As a writer, however, he is not nearly well known enough. This short book collects some of his early writings from rather obscure journals, and presents a lecture that was never actually given.

Escher is well known for his precise renderings, and we are blessed with writing in the same precise style. He wrote out the script for his lecture in full, before it was to be given. That means that, when a medical emergency forced its cancellation, the lecture was preserved in its entirety. Like his geometric woodcuts and his precise lithographs, the calm of the text belies the passion that lay behind it. Escher spent decades in poverty before his well-earned fame, and pursued visions for which he had no good words and certainly no companions. That same drive was what pushed his skill as a woodblock artist down to the limits of his hands and his materials, below the limit of his unaided eye.

Although not trained in math or the hard sciences, he puts a human face on subtle mathematical concepts. The infinite and unbounded is a common idea, the finite and bounded is part of everyday life. These aren't his words, but he pursued the finite and unbounded, in tiled patterns on the surface of a sphere. He also sought out the infinite and bounded, and found it in the Cirle Limit pieces and other works.

This book is the only inexpensive and easily accesible source of Escher's own thoughts on his work. It's not a catalog of his work - most of the reproductions so small that they only suggest the piece depicted, or remind a viewer already familiar with the work. It's not a biography, although it has a few biographical details. People with the wrong expectations are sure to be disappointed in this.

I'm happy with it. It is a very enjoyable look at his cool manner of presentation. Like his Three Worlds litho, it presents a surface of meaning, but shows reflections of distant ideas and hints at his hidden depths.

//wiredweird

Not as interesting as one would expect.......2003-07-29

I feel that this book seems, at first glance, to be much better than it really is. That is, when one picks up the book for the first time in a book store and flips through the pages, one gets the impression that it will actually be interesting to read, and will help in understanding Escher's genius. But really, the works themselves are the only things this book offers, the text is basically useless, shallow and uninteresting.

Casual Fan Book.......1999-12-21

This is a nice collection of Esher work for the casual fan not looking to spend a lot of dead presidents. THe book also has biographical information,ect

M. C. Escher ® Kaleidocycles: An Illustrated Book and 17 Fun-to-Assemble Three-Dimensional Models

Average customer rating:

Fun and educational
Teachers Alert! Parents Alert!
best kaleidocycles
Adds a whole new dimension to the wonders of M.C.Escher
From the Publisher

M. C. Escher ® Kaleidocycles: An Illustrated Book and 17 Fun-to-Assemble Three-Dimensional Models
Maurits Cornelis Escher
Manufacturer: Pomegranate
ProductGroup: Book
Binding: Paperback

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ASIN: 0764931105

Book Description

A Kaliedocycle is a three-dimensional ring made from a chain of solid figures enclosed or bonded by four triangles. These kaleidocycles are adaptations of Escher's two-dimensional images of fish, angels, flowers, people, etc., transformed into uniform, interlocking, three-dimensional objects whose patters wrap endlessly. Kaleidocycles contains a 48-page book with over 80 reproductions and diagrams, assembly instructions, and a fascinating discussion of the geometric principles and artistic challenges underlying Escher's designs and their transformation to three-dimensional models; and seventeen die-cut, scored, three-dimensional models (11 kaleidocycles and 6 geometric solids) Cigar box-style packaging, size: 9 1/2 x 12 1/4 x 1 1/2".

Customer Reviews:

Fun and educational.......2007-01-15

My 9-year-old son and I had tremendous fun assembling the models in this kit. Each of the models in the kit contains an adaptation of Escher's periodic design in a way that the geometric solid is continously covered with it. Though a unique personal experience, my son learned what tetrahedron, octahedron, dodecahedron, cuboctahedron and kaleidocycle look like. This is the best project we ever worked on.

Teachers Alert! Parents Alert!.......2006-12-26

Want to get your kids or students interested in math? Let them put together a geometric solid covered with interlocking trolls or other tesselated designs, then hang them from the playroom ceiling! Your kids will never get over it!

Beautifully colored, easily put together. and very, very neat...

best kaleidocycles.......2006-10-31

This is the bet presentation and best manufactured kaleidocycles that I had bought. Sent in a very good and fast way.

Adds a whole new dimension to the wonders of M.C.Escher.......2006-06-28

If you are as fascinated with the graphics of Escher as I am; you'll be entertained,amazed and engrossed with this 'kit' which allows you to assemble and hold these wonderful models of intrigueing mathematics , coupled with the graphic art and figures of the master himself; M.C.Escher.
It is one thing to look at Escher's magnificient work in 2-dimension; but it is another experience entirely, to hold these 3-dimensional models and view the figures and patterns as you turn as fold these models on themselves,
One of the other reviewers talked about creating additional models; and that is obviously possible ,because there is all the information needed to do that; right here in the book.
I have had this kit for some time ; but hadn't actually constructed any of the models. I recently was told about a man who constructed ball and stick models. I contacted him,and visited him to see his models. I brought along with me a book ,
"Polyhedron Models" by Magnus Wenninger .This is an outstanding book covering the subject as well as 119 models. The man I was visiting ,had the book and even knew its author. This book deals with models whose surfaces are flat and made of cardboard or if desired ,other materials. To see what these fascinating models look like, look them up on the net under "Magnus Wenninger".
The man I visited constructs similar models;but uses only wooden balls and sticks. Think of those chemistry models of compounds,and you can imagine how beautiful and interesting they can be. All models begin with one of the known uniform polyhedra and from them the stellated models are formed. The variations are in the many millions.
Anyone who has much interest in this sort of stuff will find an excellent chapter ,Polyhedra,in "Mathematical Recreations and Essays" by W.W. Rouse Ball,a real classic in the subject of Mathematical Recreations.
The man I went to visit has been working on these models for many,many years. He has created his own techniques and even an intrigueing appratus to make the holes in the balls. The exactness is so critical,that making them by hand would be terribly difficult. To date he has made about 500 0f these ball and stick models.
So, after my visit,it was a real joy to cit down and construct some models.

From the Publisher.......2005-12-01

"A kaleidocycle is a closed chain of tetrahedra that can cycle endlessly through a center hole. ? Best known for his strangely realistic depictions of things that defy the laws of physics, Maurits Cornelis Escher became interested in problems of repetition and symmetry after traveling to the Alhambra, a 14th century Moorish castle in Granada, Spain. Fascinated by the periodic (i.e. regularly recurrent) designs of the castle's mosaics, he began to pursue the idea that a plane can be divided into uniform, interlocking figures, forming a pattern that repeats itself at set intervals, theoretically to infinity. Instead of simply combining abstract shapes to produce a pattern, however, Escher decided to use more meaningful figures--shells and starfish, angels and devils, for example--images that could be connected not just graphically but also conceptually. Kaleidocycles, created by mathematician Doris Schattschneider and graphic designer Wallace Walker, explores the three-dimensional implications of Escher's two-dimensional periodic designs. With a little glue, you can easily assemble the enclosed models--all printed with repeating patterns derived from the artist's original drawings--into various kaleidocycles and geometric solids. In doing so, you will transform Escher's beautiful designs into true examples of infinite repetition: the interlocking images will wrap endlessly over the surfaces of the three-dimensional objects. ? Kaleidocycles contains a 48-page book with over 80 reproductions and diagrams, assembly instructions, and a fascinating discussion of the geometric principles and artistic challenges underlying Escher's designs and their transformation to three-dimensional models; and seventeen die-cut, scored, three-dimensional models (11 kaleidocycles and 6 geometric solids) Cigar box-style packaging, size: 9-1/2 x 12-1/4 x 1-1/2". [Refers to revised edition:] ISBN: 0-7649-3110-5

KALEIDOCYCLES 3-D MODELS ONLY
"Purchase an extra set of the 17 models for each additional participant. Assembly instructions are not included. ISBN: 0-7649-3207-1."--? Pomegranate

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