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Staying in Shape Mathematically: A Summer Practice for Student Entering 7th Grade (facts, whole numbers, fractions, decimals, percents, order of operations, geometry, problem solving, logic puzzles and games) ... Read more

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When September arrives it can be really discouraging for parents and teachers and students to discover that hard-won academic skills have been forgotten, and weeks or months may be needed to restore those skills. This workbook is designed to balance computation, problem solving, and mathematical challenges that will develop or retain addition, subtraction, multiplication and division facts through 10's. If your child is still having difficulty with basic number facts, you may want to think about having her or him work on one number family at a time. ... Read more

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This book discusses how to designgoodgeometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs. It outlines major categories of geometric puzzles and provides examples, sometimes going into the history and philosophy of those examples.The author presents challenges and thoughtful questions, as well as practical design and woodworking tips to encourage the reader to build his own puzzles and experiment with his own designs. Aesthetics, phychology, and mathematical considerations all factor into the definition of the quality of a puzzle. ... Read more

Customer Reviews (6)

An outstanding collection of puzzles that will interest the puzzler and the woodworker
Puzzles made from high quality wood are not only challenging to solve, they also are works of art. Coffin is clearly a master of the wood tools and in this book he describes some of his most imaginative creations. He deliberately does not give detailed shop-style drawings of the puzzles; he leaves the understanding of the mode of their creation to the interested reader.
My perspective is that of someone interested in the mental challenge of puzzles, I am completely lacking in the ability to create fine structures from wood. Nevertheless, I was intrigued by his explanations of the woodworking tactics used to create the puzzles.
The enormous breadth of the puzzles is something that will fascinate both the woodworker as well as the puzzle aficionado. Most of the puzzles are complex three-dimensional structures made up of interconnected parts where a few are key to maintaining the integrity of the structure. The puzzles go both directions, from the pieces to the whole and from the whole down to the pieces. In page after page he demonstrates puzzles and often points out that children generally are able to (de)construct them.
It is a rare occasion when a book is written that can appeal just as much to the master woodworker as it can to the mathematician. This is such a case; teachers of mathematics from elementary through advanced college will find many educational tools in this book. Nothing could please me more than to find one of these puzzles in my Christmas stocking.

Geometric Puzzle Design
Book is well written.Theories are great.I would have prefered more instruction on making the puzzles rather than just the theory.

A Must for all puzzle interested people
as a long time collector and producer of wooden puzzles is this new puzzlebook an absolute Must for every puzzle interested people; although I have allCoffin`s former editions this new review about his designs is usefull for collectors as well as for producers of puzzles;

Classic book not to be missed
This book covers a large number of puzzle designs, most due to the author.Most of these puzzles have become sought-after classics.The puzzles are mostly 3D interlocking burrs, but there also included are 2D designs, sliding block puzzles, and non-interlocking 3D puzzles.The author also talks about how to build puzzles, characteristics of wood, etc.

I am not a puzzle builder, but enjoyed the book immesely.The author is an excellent writer and his musings about symmetry and general design considerations I found fascinating.Solutions in general are lacking and much is left to the ingenuity of the reader to keep the mystery of solving these puzzles fresh.

Although you can download the OLD EDITION of this book, I enjoy the physical copy for perusal.Highly recommended.Look for the old edition under the title "The Puzzling World of Polyhedral Dissections".

A "must-have" for intermediate to advanced woodworkers seeking to create truly brain-teasing gifts.
Written by veteran woodworker and expert wood puzzle designer Stewart Coffin, Geometric Puzzle Design is a one-of-a-kind guide to creating intriguing, three-dimensional wooden puzzles. Special techniques for creating oddly shaped small puzzle pieces accurately and safely, recommendations for drafting one's own original designs, mathematical concepts that can be applied as engineering tools, and much more fill this original craftsman's manual. A "must-have" for intermediate to advanced woodworkers seeking to create truly brain-teasing gifts. ... Read more

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Customer Reviews (1)

Pretty, but ultimately unsatisfying
(Note, I originally gave this 3 stars but now would call it 2, although the system won't let me change that. See Edit note at the end.) The book contains about 90 or so optical illusions. The illusions are mainly along the lines of things that look curved when they are actually straight, things like look different sizes when they are a really the same size if you measure them, and similar. Many of these illusions will be like ones you've seen before if you are into this sort of thing, but there are some new variations I hadn't run across before.

The book is nicely illustrated and pretty to look at. However, it gets only an "average" rating for two reasons:
1. There's not a single word of explanation in the entire book as to *why* the illusion occurs and why the eye is fooled. According to the "about the author" page, the author is "the world's leading authority of visual and other types of sensory illusions". Given that, I would've hoped for at least a little bit of explanation or discussion of the illusions. Instead, you get just the photos, each accompanied by one or two sentences along the lines of "Does the one thing look larger than the other? Check your answer."

I went to the author's website (he is associated with Harvard and formerly associated with Caltech) in the hopes of more info. But that is mostly an extended resume for the author and list of his books, speaking engagements, etc. (Although there's a somewhat interesting section devoted to several Escher-like artists, with some movies of interviews of some of the artists.)

2. Many of the illusions are just very small variations on the exact same illusion, rather than being something new and different as I had hoped.

Overall, certainly not a worthless book and quite pretty. But probably a lot more interesting to someone who's never seen these types of illusions at all before (or to a child) than to any adult who has any previous familiarity with the topic.

Edit: Also, there is at least one of what appears to be an out and out mistake. One page shows what is supposed to be the "Wundt Illusion". It pictures two seemingly identical profile views of the drawing of a woman's head and torso, and asks "Does the figure on the left appear to be smaller than the figure on the right?". Well, the answer is "No, they appear to be the same size and they actually are the same size when measured." Not only that, but even if they appeared to be different this wouldn't be an example of what is normally called the "Wundt" illusion (I looked it up), which has to do with lines looking bowed when they are really straight.

Yikes, make that 2 errors so far. One page asks "Do all 3 squares appear to be the same size?" Well, the answer is "Yes, they do (and they are when measured) and they also aren't squares- they are clearly rectangles (both in perception and when measured."

For mistakes/ poor editing, I would call this a 2 instead of a 3 if I was able to change the # of stars.

... Read more

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The Math Machine Tangram Puzzles teaches copying, matching,problem solving, and logical thinking skills. It has everything you needin the box! Includes over 48 challenging puzzles, two sets of plastictangrams (seven per set), and 24

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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". ... Read more

Customer Reviews (9)

Fun and educational
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. Through 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!
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
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
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 sit down and construct some models.

From the Publisher
"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 ... Read more

Product Description
"aha! Gotcha"and "aha! Insight" are here combined as a single volume. The aha! books, as they are referred to by fans of the author Martin Gardner, contain 144 wonderful puzzles from the reigning king of recreational mathematics. In this combined volume, you will find puzzles ranging over geometry, logic, probability, statistics, number,time, combinatorics, and word play. Gardner calls these puzzles aha! problems. He explains that aha! problems "seem difficult, and indeed are difficult if you go about trying to solve them in traditional ways. But if you can free your mind from standard problem solving techniques, you may be receptive to an aha! reaction that leads immediately to a solution. Don't be discouraged if, at first, you have difficulty with these problems. Try your best to solve each one before you read the answer. After a while you will begin to catch the spirit of offbeat , nonlinear thinking, and you may be surprised to find your aha! ability improving."Studies show that persons who possess a high aha! ability are all intelligent to a moderate level, but beyond that level there seems to be no correlation between high intelligence and aha! thinking. So dig into some of the puzzles in this book, and prepare yourself for an aha! experience. ... Read more

Customer Reviews (1)

Gardner at his best
This book contains the complete texts of the two classic Gardner productions, Aha! Gotcha and Aha! Insight. If you have not read both of these books, then you are mathematically deprived, as they contain some of the best mathematical puzzles ever created. Many people in the business world tout the concept of "lateral thinking", which is a way to approach problems by attacking them from unusual and non-obvious directions. That is certainly the way to approach the problems in this collection, and the benefit to the reader is a good deal more than the solution to a problem. You cannot help but learn some mathematics.
The title of the second book is an accurate reflection of the consequences of solving these problems. When the solution is presented, the very demonstration gives you some significant insight into how problems are solved in general, as well as the specifics of math problems. Many of the puzzles have applications to the problems that occur in real life, such as how housework should be divided between two people to minimize the frustrations.
Martin Gardner has done more than anyone else to advance the general interest in mathematics and you can see why when you read each problem in this combined collection. He is a master at making the complex simple and disguising the simple as complex.

Published in Journal of Recreational Mathematics, reprinted with permission ... Read more

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Uses a variety of picture puzzles to teach the basic geometric concept of shape. ... Read more

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A collection of puzzles challenging the reader to make shapes and designs out of toothpicks, coins, or buttons and then change the shapes in various ways. ... Read more

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Twelfth edition of classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" — The Mathematics Teacher. Index. References for Further Study. 150 black-and-white line illustrations.
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Customer Reviews (3)

the best there is
Any fan of mathematical puzzles will go ape over this thoroughly researched, timeless classic. Even for jaded scientists in their forties (such as me) and beyond, there's always some new gem to be discovered at the turn of a page. The scope of the book is immense, ranging from all manner of "classical" recreations to the puzzles of antiquity (e.g., squaring the circle) to the history of pi to the structure and functionality of the kaleidoscope. It's all here!

Must have for any recreational mathematician.
This is a timeless classic and a primary reference
for recreational mathematicians. And the price
is unbeatable.

A Classic Compendium...
This is a classic collection of mathematical recreations.Originallywritten by W.W. Rouse Ball around 1900, this edition has been updated bythe great geometer H.S.M. Coxeter.It is a comprehensive first source forinformation about magic squares, Platonic and Archimedian solids,"Knight's Tours" and other chessboard recreations, and just aboutany other variety of math-related puzzle you could name.

For amathematician, Coxeter is an excellent writer, and the book is quiteaccessible, even to relative math novices.Fans of Martin Gardner's books,of his "Scientific American" Mathematical Games columns, willwant to own this.And because it's published by Dover, the price is right,too. ... Read more

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Uses a variety of picture puzzles to teach the basic geometric concept of repeating shapes to create patterns. ... Read more

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This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes. ... Read more

Customer Reviews (2)

Ultimate book on polyominoes by the inventor.
Polyominoes is an entire sub-domain of geometrical puzzles and
this book is the epitomie of the subject. Packed full of
results and puzzles old and new. An extensive bibliography
is provided. Another one for the bookshelf of all mathematical puzzlers.

Even better the second time through
One of the most eagerly anticipated second editions in the history of mathematics, the wait was worth it. Literally defining a whole new area of recreational mathematics, the problems and proof techniques introduced inthe first edition have kept an entire generation of mathematical thinkersbusy. Although easily understood, some of the problems have defied solutionfor decades after the publication of the first edition in 1965. It nowappears that all of the problems listed as unsolved in the first editionhave been resolved, the last succumbing in 1993. As befits the enormousinterest in these problems, three people announced solutionssimultaneously, this reviewer being one of them.
While there is not alot of material that was not part of the first book, it still stirs themathematical heart. For these problems and proofs are timeless things ofbeauty. Even a child can understand how to put polyominoes together - mytwo-year-old daughter is an existence proof of that. And the proofs aresometimes so clever in their simplicity that one is tempted to use thephrase attributed to Paul Erdos, "That one is from God's little book." Whoamong us fails to appreciate some of the proofs of placing pentominoes on acheckerboard that relies on nothing more than the number of spaces coloredblack versus red. Even the proofs of the problems that took decades toresolve can be understood by those with only a rudimentary knowledge ofmathematics. Sometimes, if you can count to 60, you can understand theproof.
Truly a jewel in the crown of mathematical royalty, this bookdeserves to be a runaway bestseller.

Published in Journal ofRecreational Mathematics, reprinted with permission ... Read more

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A dissection involves cutting a polygon into pieces in such a way that those pieces form another polygon; for a hinged dissection, the pieces must be attached by hinges. A piano hinge isa long narrow hinge with a pin running the entire length of its joint.So, unlike regular hinged dissections, which swing or twist (around single point of hinge), piano-hinged dissections fold along an edge. This book discusses the history, methods, and variations of these dissections and is rich with illustrations that clearly depict the cuts of the dissections and three-dimensional simulations of the dissections in the process of being folded.A CD that includes video recordings of select dissections being transformed accompanies the book. ... Read more

Customer Reviews (1)

Complex, yet fascinating dissections with a flip
While the dissection of a geometric object is generally easy to follow after the fact, the dissections in this book at times are very difficult to understand. A piano hinge dissection is one where a hinge runs the full length of a joint. The analogy is to the hinge that allows the top of a grand piano to be opened although in this case the hinge can allow the two pieces to be folded in either of the two directions. Add in multiple hinges and the potential for the pieces to overlap and the additional degrees of freedom can make for a complicated structure. I often found myself wondering how the dissection had been discovered.
While Frederickson uses very detailed and multiple diagrams with different styles of hashing of the lines to describe the dissections in the book, they are often hard to follow. That is not meant to be a criticism; much of the difficulty is due to the complexity and originality of the dissections. A good deal of this is solved by the videos on the CD that accompanies the book. In them, Frederickson uses paper and wooden models to illustrate the folding that allows you to transform one figure into another. Seeing the transformation by executing one active fold after another makes it so much clearer. Quite honestly, I am not sure if I would have completely grasped some of the more complex transformations without the video.
The use of one or more piano hinges in a dissection creates a significantly higher level of complexity. However, in complexity there is joy and while I had difficulty in the explanations, the wonder of seeing it work made the time of difficulty well spent.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more