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Author: Barry Mazur
Publisher: Macmillan + ORM
ISBN: 1429931469
Category : Mathematics
Languages : en
Pages : 290
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Book Description
How the elusive imaginary number was first imagined, and how to imagine it yourself Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers. With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.
Author: Barry Mazur
Publisher: Macmillan + ORM
ISBN: 1429931469
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
How the elusive imaginary number was first imagined, and how to imagine it yourself Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers. With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.
Author: Barry Mazur
Publisher: Penguin UK
ISBN: 0141931701
Category : Mathematics
Languages : en
Pages : 237
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Book Description
The book shows how the art of mathematical imagining is not as mysterious as it seems. Drawing on a variety of artistic resources the author reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.
Author: John H. Conway
Publisher: Springer Science & Business Media
ISBN: 1461240727
Category : Mathematics
Languages : en
Pages : 313
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Book Description
"...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL
Author: Brian Rotman
Publisher: Stanford University Press
ISBN: 9780804736848
Category : Mathematics
Languages : en
Pages : 188
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Book Description
In this book, Rotman argues that mathematics is a vast and unique man-made imagination machine controlled by writing. It addresses both aspects—mental and linguistic—of this machine. The essays in this volume offer an insight into Rotman's project, one that has been called "one of the most original and important recent contributions to the philosophy of mathematics."
Author: Chip Heath
Publisher: Simon and Schuster
ISBN: 1982165456
Category : Business & Economics
Languages : en
Pages : 208
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Book Description
A clear, practical, first-of-its-kind guide to communicating and understanding numbers and data—from bestselling business author Chip Heath. How much bigger is a billion than a million? Well, a million seconds is twelve days. A billion seconds is…thirty-two years. Understanding numbers is essential—but humans aren’t built to understand them. Until very recently, most languages had no words for numbers greater than five—anything from six to infinity was known as “lots.” While the numbers in our world have gotten increasingly complex, our brains are stuck in the past. How can we translate millions and billions and milliseconds and nanometers into things we can comprehend and use? Author Chip Heath has excelled at teaching others about making ideas stick and here, in Making Numbers Count, he outlines specific principles that reveal how to translate a number into our brain’s language. This book is filled with examples of extreme number makeovers, vivid before-and-after examples that take a dry number and present it in a way that people click in and say “Wow, now I get it!” You will learn principles such as: -SIMPLE PERSPECTIVE CUES: researchers at Microsoft found that adding one simple comparison sentence doubled how accurately users estimated statistics like population and area of countries. -VIVIDNESS: get perspective on the size of a nucleus by imagining a bee in a cathedral, or a pea in a racetrack, which are easier to envision than “1/100,000th of the size of an atom.” -CONVERT TO A PROCESS: capitalize on our intuitive sense of time (5 gigabytes of music storage turns into “2 months of commutes, without repeating a song”). -EMOTIONAL MEASURING STICKS: frame the number in a way that people already care about (“that medical protocol would save twice as many women as curing breast cancer”). Whether you’re interested in global problems like climate change, running a tech firm or a farm, or just explaining how many Cokes you’d have to drink if you burned calories like a hummingbird, this book will help math-lovers and math-haters alike translate the numbers that animate our world—allowing us to bring more data, more naturally, into decisions in our schools, our workplaces, and our society.
Author: Asok Kumar Mallik
Publisher: #N/A
ISBN: 9813222948
Category : Mathematics
Languages : en
Pages : 197
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Book Description
'… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.
Author: Alberto A. Martínez
Publisher: Princeton University Press
ISBN: 9780691123097
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Explores controversies in the history of numbers, especially the so-called negative and ''impossible'' numbers. This book uses history, puzzles, and lively debates to demonstrate how it is possible to devise new artificial systems of mathematical rules. It contends that departures from traditional rules can even be the basis for new applications.
Author: Georges De Schrijver
Publisher: Wipf and Stock Publishers
ISBN: 1532610157
Category : Science
Languages : en
Pages : 253
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Book Description
Ever since it was demonstrated in the 1920s that the universe, with its trillions of galaxies, is caught up in a process of steady expansion, it became evident that it must have originated from an "initial singularity," a "Big Bang," which gave rise to the formation of subatomic parts, atoms, molecules, clouds of gas, and finally, stars and galaxies. Running this expansion back in time, scientists began to reckon with the miracle of an evolving universe of which we are the outcome: the iron in our blood has been formed in the stars. This book gives an overview of the cosmologies that were in vogue in antiquity--the Jewish and Christian concepts of Creation, and the classical thinkers in Greek cosmology: Plato, Aristotle, and Ptolemy--and in modern times, Copernicus, Galileo, Kepler, and Newton. The book brings us right down to the present day with a careful and readable treatment of the scientific innovations inaugurated by Einstein and the specialists in quantum physics, and to recent developments in astrophysics. This path of exploration opens the avenue for imagining a Creator God who is so generous that he invites creation to share in his own creativity.
Author: Les Evans
Publisher: Aust Council for Ed Research
ISBN: 0864315325
Category : Electronic books
Languages : en
Pages : 178
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Book Description
Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries of complex numbers. The text includes historical and background material, discussion of key concepts, skills and processes, commentary on teaching and learning approaches, comprehensive illustrative examples with related tables, graphs and diagrams throughout, references for each chapter (text and web-based), student activities and sample solution notes, and an extensive bibliography.
Author: David P. Henige
Publisher: University of Oklahoma Press
ISBN: 9780806130446
Category : Social Science
Languages : en
Pages : 556
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Book Description
In the past forty years an entirely new paradigm has developed regarding the contact population of the New World. Proponents of this new theory argue that the American Indian population in 1492 was ten, even twenty, times greater than previous estimates. In Numbers From Nowhere David Henige argues that the data on which these high counts are based are meager and often demonstrably wrong. Drawing on a wide variety of primary and secondary sources, Henige illustrates the use and abuse of numerical data throughout history. He shows that extrapolation of numbers is entirely subjective, however masked it may be by arithmetic, and he questions what constitutes valid evidence in historical and scientific scholarship.
