How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. A proof shows that it is possible to design a series of jointed bars moving only in a flat plane that can sign a name or trace any other algebraic curve. One remarkable algorithm shows you can fold any straight-line drawing on paper so that the complete drawing can be cut out with one straight scissors cut. Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.

When it comes to mathematics, paper isn't just for pen and pencil any more! Origami, the art and science of paper folding, can be used to explain concepts and solve problems in mathematics-and not just in the field of geometry. The origami activities collected here also relate to topics in calculus, abstract algebra, discrete mathematics, topology, and more.

Using origami, learn about:

Solving Cubic Equations

Bucky Balls and PHiZZ units

Matrix models for folds

Gaussian Curvature and much more!

This encyclopedia contains trigonometric identity proofs for some three hundred identities. The book is presented in the form of mathematical games for the reader s enjoyment and includes a concordance of trigonometric identities, enabling easy reference.

This collection is a tribute to Martin Gardner by mathematicians, puzzle masters, and magicians. It was conceived and initiated in honor of his 90th birthday and is finally published as he celebrates his 94th year, maintaining the inspiring creativity that has motivated so many professional mathematicians and amateurs, who are all dedicated to his unique amalgamation of rational thought and magic. Some of the contributions celebrate the life of Martin Gardner; some tell about his influence on individuals or on the field of recreational mathematics in general; some are puzzles or tricks inspired by Martin Gardner and his work. Martin Gardner stands at the intersection of magic and mathematics. Mathematical magic, like chess, has its own curious charms, he says. [It] combines the beauty of mathematical structure with the entertainment value of a trick . Martin Gardner has been writing about magic and contributing new effects for nearly seventy years. Today, he keeps in contact with magicians like Penn and Teller by phone and receives occasional visits from magicians who come to trade notes with him. In 1999 he was named one of MAGIC Magazine s 100 most influential magicians of the twentieth century.

The properties of functions should be explored and discovered rather than taught and drilled. Students can explore various types of functions on the TI-84 Plus in cooperative groups or on their own as you facilitate their learning. Keying sequences guide them through the variety of menus on the TI-84 Plus without the need to page through the calculator manual. Detailed solutions at the back of the book help students over obstacles to their learning and the operation of the menus and submenus are absorbed with minimal effort as the mathematics is learned. Deeper investigations are included to challenge the more capable student, and historical vignettes are introduced to add a human dimension to the mathematical excursions. This new publication has been expanded to include a more detailed treatment of linear and quadratic functions and the law of sines and cosines found in most state and provincial guidelines. The topics include finding zeros, domain and range, extrema, and singularities of polynomial and rational functions. Properties of the trigonometric, exponential and logarithmic functions are also explored. Topics also include the study of limits and asymptotic behavior, polar coordinates, parametric equations and conics.

Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into ten languages. The Times called it "elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf" and The Philadelphia Inquirer praised it as "absolutely scintillating." In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the "Republic of Numbers," where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. "Less than All," wrote William Blake, "cannot satisfy Man." The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

What's more fun than a crossword puzzle and more addictive than Sudoku? It's Kakuro of course - the latest puzzle craze to sweep the nation. Puzzle Master Timothy E. Parker, known in the Guinness Book of World Records as "the world's most syndicated puzzle compiler," offers 150 brand new puzzles to tickle your brain and transform you from a number-stumbling novice into Kakuro Master.

*Easy, Medium, and Hard puzzles
*Five extra-large Bonus Puzzles
*Rules, Tips and Strategies
*A list of "unique sums" which are the key to unlocking the logic of Kakuro
*A "Complete Sum Chart" listing every possible answer (Kakuro's answer to the crossword puzzle dictionary)

HOW TO PLAY: Kakuro is a crossword with numbers that serve as the clues. The numbers you are given in the black cells represent the sum of that row or column. The goal is to enter digits 1 - 9 in the white cells to add up to the number stated. You cannot enter any number more than once.

Warning: Kakuro may cause you to forget reality, lose all sense of time, miss your bus stop, and wear out all erasers in a three mile radius. Use with caution!

70 Quick-and-Easy Games to Build Math Skills
Hands-on games to help you reinforce key math skills including addition, subtraction, multiplication, division, fractions, probability, and factors. All games are easy to make and play. Includes reproducibles.

"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.