The art of the infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. And as we go deeper into infinity, we explore the most profound mystery of mathematics: Are its principles eternal truths that we discover? Or ones that we invent? Used book in Good Condition.

Robert and ellen kaplan guide us through the “republic of Numbers, ” where we meet both its upstanding citizens and its more shadowy dwellers; and transport us across the plane of geometry into the unlikely realm where parallel lines meet. The journey is enriched by deft character studies of great mathematicians and equally colorful lesser ones.

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The Nothing that Is: A Natural History of Zero

Try multiplying CLXIV by XXIV. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. Remarkably, even the greeks, didn't have a zero--or did they? We follow the trail to the East where, mathematically brilliant as they were, a millennium or two ago, Indian mathematicians took another crucial step.

A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. For kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. Indeed, without zero mathematics as we know it would not exist.

The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists. The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.

Robert kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. And without mathematics our understanding of the universe would be vastly impoverished.

At first it was called "dangerous saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping.

Out of the Labyrinth: Setting Mathematics Free

For any reader who has felt the excitement of mathematical discovery-or tried to convey it to someone else-this volume will be a delightful and valued companion. Who hasn't feared the math Minotaur in its labyrinth of abstractions? The subject can seem convoluted and forbidding. Stocked with puzzles, out of the labyrinth is both an engaging and practical guide for parents and educators, and insights from the authors' own teaching experience, colorful anecdotes, and a treasure chest of mathematical discoveries.

Robert and ellen kaplan are founders of the Math Circle, a pioneering learning program begun at Harvard in 1994 and now spreading around the world. Yet to do mathematics is to wrestle with “accessible mysteries”-and Out of the Labyrinth shows how exhilarating the challenge can be. Used book in Good Condition.

In their classrooms students ages six to sixty have discovered mathematics as the highest form of intellectual play, while exploring topics that range from Roman numerals to quantum mechanics. Used book in Good Condition. The kaplans reveal the secrets of their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics.

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The Golden Ratio: The Story of PHI, the World's Most Astonishing Number

Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality.

Used book in Good Condition. Used book in Good Condition. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist. Since then it has shown a propensity to appear in the most astonishing variety of places, sunflower florets, from mollusk shells, and rose petals to the shape of the galaxy.

Broadway Books. It tells the human story of numerous phi-fixated individuals, cezanne, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Bartok, and physicist Roger Penrose.

It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. In this fascinating book, mario Livio tells the tale of a number at the heart of that mystery: phi, or 1. 6180339887.

Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

Xn + yn = zn, 4, where n represents 3, 5, . No solution"i have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain. With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as fermat's last theorem looked simple; proving it, became the Holy Grail of mathematics, however, baffling its finest minds for more than 350 years.

In fermat's enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, sacrificed for, and the lives that were devoted to, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

Used book in Good Condition. Used book in Good Condition. Broadway Books.

Gödel, Escher, Bach: An Eternal Golden Braid

Used book in Good Condition. Gödel, recursion, reduction, bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, Escher, and much more. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it.

Godel escher Bach An Eternal Golden Braid. Broadway Books. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Winner of the pulitzer prizea metaphorical fugue on minds and machines in the spirit of Lewis CarrollDouglas Hofstadter's book is concerned directly with the nature of "maps" or links between formal systems.

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The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics

Marcus du sautoy's enthusiasm shines through every line of this hymnto the joy of high intelligence, illuminating as it does so even the darkestcorners of his most arcane universe. Used book in Good Condition. Inthe tradition of fermat’s enigma and pi, marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematics—the formula to predict prime numbers.

Oliver sacks, author of the man who mistook His Wife for a Hat, calls TheMusic of the Primes “an amazing book. . . . I could not put it down once Ihad started. Simon winchester, “this fascinating account, writes, decoding the inscrutable language of themathematical priesthood, author of The Professor and the Madman, is written like the purest poetry.

Used book in Good Condition. Harper Perennial. Broadway Books. Godel escher Bach An Eternal Golden Braid.

An Awe-Inspiring Journey Through the World of Numbers - Here's Looking at Euclid: From Counting Ants to Games of Chance

In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. The world of mathematics is a remarkable place. Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, to the creations of the Zen master of origami, from the breakthroughs of Euclid, the greatest mathematician of all time, one of the hottest areas of mathematical work today.

Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize.

. Used book in Good Condition. Used book in Good Condition. Broadway Books. Whether writing about how algebra solved swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies.

Here’s looking at euclid is a rare gem that brings the beauty of math to life. Journeying to the bay of bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.

Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs.

The Problem of Poverty

Roger henderson's essay "How Abraham Kuyper Became a Kuyperian" is included in the appendix. Free Press. His words not only illuminate with stark simplicity many of the enduring problems of poverty, they also bring a strong and pointed biblical message that has outlived Kuyper's time and place. Used book in Good Condition.

The text, translated and introduced by james skillen, was originally a speech by Abraham Kuyper 1837-1920 that opened the first Christian Social Congress in The Netherlands on 9 November 1891. Used book in Good Condition. Harper Perennial. Condition: New. Notes: brand new from publisher! 100% satisfaction guarantee.

Godel escher Bach An Eternal Golden Braid. Buy with confidence! Millions of books sold! Tracking provided on most orders. Isbn13: 9780932914873. Broadway Books.