The Book of Nothing: Vacuums, Voids, and the Latest Ideas About the Origins of the Univers
by John D. Barrow
What conceptual blind spot kept the ancient Greeks (unlike the Indians and the Mayans) from developing the concept of zero? Ranging through mathematics, theology, philosophy, literature, particle physics and cosmology, the book explores the enduring hold that vacuity has exercised on the human imagination.
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
by Mario Livio
Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It was discovered by Euclid more than 2,000 years ago. It seems that for any line divided into two unequal segments, the resultant lengths of the two segments and the original line can be formed into a ratio that equals phi. This curiosity of plane and solid geometry might have remained just an oddity had the ratio not cropped up in unusual places, from the structure of crystals to botany to the shape of spiral galaxies.
There's a whole mathematical community devoted to Fibonacci numbers, whose permutations produce phi again and again. Livio's encyclopedic selection of subjects, supported by dozens of illustrations, will snare anyone with a recreational interest in mathematics. This thoroughly enjoyable work vividly demonstrates to the general reader that, as Galileo put it, the universe is, indeed, written in the language of mathematics.
Imaginary Numbers : An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings
by William Frucht
Don't be fooled by the title. It isn't a book devoted to explicating the many mysteries of the square root of minus one. What he has done is far more impressive. Pursuing what he envisions as "a truly literary science fiction," Frucht has dared to collect an idiosyncratic company of writers--including such disparate names as Rudy Rucker, Italo Calvino, William Gibson, and Lewis Carroll--into one eclectic, accomplished anthology. The unifying theme of these writings, the short stories, essays, out-loud ponderings, even poetry, is the world of mathematics: every contributor is either "using mathematics to tell stories or using stories to explain mathematics," what Frucht describes as two sides of the same coin.
An Imaginary Tale: the Story of the Square Root of -1
by Paul J. Nahin
"This book will be most accessible to the million or so who each year complete a college course in freshman calculus." Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. "Dispelling many common myths about the origin of the mystic 'imaginary' unit, Nahin tells the story of i from a historic as well as human perspective. His enthusiasm and informal style easily catch on to the reader. The book is a must for anyone curious about the evolution of our number concept. Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. The author tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them.
Addressing readers with both a general and scholarly interest in mathematics, Nahin includes entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as a history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.
Islands of Truth: A Mathematical Mystery Cruise
by Ivars Peterson
Peterson , author of The Mathematical Tourist, explores topics at the frontier of mathematics research, among them: new developments in fractal geometry, applications of number theory, computer graphics, and artificial intelligence.
It Must Be Beautiful: Great Equations of Modern Science
by Graham Farmelo (editor)
"A fascinating history of science for educated nonmathematical readers. The power of equations can seem magical, writes MIT physics professor Frank Wilczek in an essay on the Dirac Equation, which describes the movement of quantum particles.
Like the brooms created by the Sorcerer's Apprentice, they can take on a life of their own, giving birth to consequences that their creator did not expect, cannot control, and may even find repugnant. Though it seems like an odd reversal of the scientific method to do the math first and then find the data that fit,
it has happened time and again. These 11 essays contributed by various scientists and science writers (e.g., Roger Penrose, Peter Galison, Oliver Morton, and Steven Weinberg) describe scientific advances that derived from mathematical theory such as Einstein's thought experiments on relativity, a game theory equation that predicted animal behavior, or the discovery that the mathematics of chaos describes the real-world phenomenon."
Just Six Numbers: The Deep Forces That Shape the Universe
by Martin Rees
Just six numbers govern the shape, size, and texture of our universe. If their values were only fractionally different, we would not exist: nor, in many cases, would matter have had a chance to form. If the numbers that govern our universe were elegant such as 1 or pi, or the Golden Mean, we would simply shrug and say that the universe was an elegant mathematical puzzle. But the numbers Martin Rees discusses are far from tidy. Rees is the Astronomer Royal of Great Britain.
Keys To Infinity
by Clifford A. Pickover
A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today. By most standards he is a mathematics geek (Ph.D. research scientist for IBM, associate editor for two computer journals), but he is the coolest math geek you might ever meet. For this book he has compiled 30 chapters of mathematical puzzles (and one short story), all having some connection to the concept of infinity. These problems are open-ended; in the event that the reader actually solves the main puzzle, there are enough digressions, diversions, and tangents to keep even the fastest computer running for hours. Computer modelers will be happy to find that instructive BASIC and C language has been provided for most of the problems. Many puzzles have been previously posted on the Internet, and the best or weirdest replies have been included in this book.
Mathematical Mystery Tour
The author asks the question: Did humans make up mathematics, or did mathematics make up everything, including humans? Beginning his journey in Miletus, the ancient home of Pythagoras and other deep thinkers, he meets the fictional Dr. Petros Pygonopolis, the first of his guides through space and time in search of mathematical meaning in history. His journey continues with stops in the Arabian desert, Venice, and England. Dewdney's style is accessible, his knowledge is thorough, and his sense of humor refreshing. It is not a difficult read, although the ideas are quite abstract. The fictional tour guides at each port of call are helpful in humanizing the subject matter.
Mathematical Sorcery: Revealing the Secrets of Numbers
by Calvin C. Clawson
A unique guide to the history of mathematics. An overview of the history of mathematics, this book explains how ancient scholars devised the rules of mathematics and illustrates the significance of these rules for modern life. Balancing the elusiveness of numbers with the rigor of mathematical theory, the author discusses the experiments that have defined the field and the results they have produced.
In his quest for pure knowledge, the author takes readers on a journey of discovery to divulge the wisdom of the ancient Greeks, Sumerians, Babylonians, and Egyptians, whose stunning revelations have deep meaning to this day.
The secret of constellations, the enigma of the golden mean, and the brilliance of a proof; these are just some of the wonders the author explores in this recreational math book.
Mathematics: From the Birth of Numbers
by Jan Gullberg & Peter Hilton
This book is an enthusiastic and utterly amazing popularization that promises to be in print for decades. It is a book for school or home library, where there are people eager to learn or in need of an in-depth understanding of algebra, calculus, trigonometry, topology, or more advanced studies. It is an important reference and a book that is plain fun to dip into. If a family is to have only one mathematics book on the reference shelf, then this is the one. It is worth the price and will not quickly become obsolete like so many other scientific texts.
Nothing That Is: A Natural History of Zero
by Robert & Ellen Kaplan
Usually the invention (or discovery) of zero is given as occurring in India in about the year 600 CE. The author goes back further to Sumerian, Babylonian, and Greek experiments with abacuses, counting boards, positional notation, and abstract thought. He makes the story very interesting with a wonderful combination of literature, history and philosophy. Even if the reader does not particularly care much for math, if you enjoy literature and philosophy you'll learn something.
On Beyond a Million : An Amazing Math Journey
by David M. Schwartz and Paul Meisel
Amazing facts about millions, trillions, and much bigger numbers are explained in picture-book cartoon scenarios, contributed by Paul Meisel. They show kids in the classroom, at the seashore, in the rain forest, and all over the place, learning how to count by powers of 10. The sheer numbers are astounding, whether they refer to the population of the U.S. or the number of stars in the Milky Way; and the explanation of exponents gives kids a way to count what seems unimaginable. In a funny gag, one kid keeps asking, "Have we reached infinity yet?" and the answers make math awesome and yet accessible--even for those of us who are scared of all those zeros.