Tales Of Impossibility

A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.

This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990–2014. The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity — Is a Graviton Detectable? Various possible graviton-detectors are examined. This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.

Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

NATIONAL BESTSELLER • Inspired by the fantastic worlds of Star Trek, Star Wars, and Back to the Future, the renowned theoretical physicist and national bestselling author of The God Equation takes an informed, serious, and often surprising look at what our current understanding of the universe's physical laws may permit in the near and distant future. Teleportation, time machines, force fields, and interstellar space ships—the stuff of science fiction or potentially attainable future technologies? Entertaining, informative, and imaginative, Physics of the Impossible probes the very limits of human ingenuity and scientific possibility.

A forgotten Haudenosaunee social song beams into the cosmos like a homing beacon for interstellar visitors. A computer learns to feel sadness and grief from the history of atrocities committed against First Nations. A young Native man discovers the secret to time travel in ancient petroglyphs. Drawing inspiration from science fiction legends like Arthur C. Clarke, Isaac Asimov and Ray Bradbury, Drew Hayden Taylor frames classic science-fiction tropes in an Aboriginal perspective. The nine stories in this collection span all traditional topics of science fiction--from peaceful aliens to hostile invaders; from space travel to time travel; from government conspiracies to connections across generations. Yet Taylor's First Nations perspective draws fresh parallels, likening the cultural implications of alien contact to those of the arrival of Europeans in the Americas, or highlighting the impossibility of remaining a "good Native" in such an unnatural situation as a space mission. Infused with Native stories and variously mysterious, magical and humorous, Take Us to Your Chief is the perfect mesh of nostalgically 1950s-esque science fiction with modern First Nations discourse.

A chilling, wildly original novel from a major new voice from South Korea The Impossible Fairy Tale is the story of two unexceptional grade-school girls. Mia is “lucky”—she is spoiled by her mother and, as she explains, her two fathers. She gloats over her exotic imported color pencils and won’t be denied a coveted sweater. Then there is the Child who, by contrast, is neither lucky nor unlucky. She makes so little impression that she seems not even to merit a name. At school, their fellow students, whether lucky or luckless or unlucky, seem consumed by an almost murderous rage. Adults are nearly invisible, and the society the children create on their own is marked by cruelty and soul-crushing hierarchies. Then, one day, the Child sneaks into the classroom after hours and adds ominous sentences to her classmates’ notebooks. This sinister but initially inconsequential act unlocks a series of events that end in horrible violence. But that is not the end of this eerie, unpredictable novel. A teacher, who is also this book’s author, wakes from an intense dream. When she arrives at her next class, she recognizes a student: the Child, who knows about the events of the novel’s first half, which took place years earlier. Han Yujoo’s The Impossible Fairy Tale is a fresh and terrifying exploration of the ethics of art making and of the stinging consequences of neglect.

In these twelve modern myths and tales for the young and the young at heart, Jane Yolen transforms the impossible into the familiar and real. Among the outlandish wonders are an Alice grown tough in Wonderland, a dear—but dead—mother’s homecoming, a bridge that longs for a goat-eating troll, and a mutiny among Peter Pan’s troops.