Imagining Numbers: (particularly the square root of minus fifteen) (Google eBook)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 sixteenthcentury 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. 
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Review: Imagining Numbers
User Review  Ginnz  GoodreadsOk so the book was billed as an explanation of imagery numbers, which it was. A brief history of imaginary numbers from then they were first encountered through to the nineteenth century. The issue I ... Read full review
Review: Imagining Numbers
User Review  Rishiyur Nikhil  GoodreadsWith many excursions into visualization in poetry, goes into the history of how imaginary numbers (square roots of negative numbers) were initially deemed "impossible", and slowly evolved into the ... Read full review
Contents
IMAGINATION  
The problem of describing how we imagine  
Permission  
Charting the plane  
The geometry of qualities  
The spareness of the inventory of the imagination  
JUSTIFYING LAWS  
To imagine versus to picture  
The inventors of writing  
Arithmetic in the realm of imaginary numbers  
The absence of time in mathematics  
Questioning answers  
Back to Bombellis puzzle  
Interviewing Bombelli  
PUTTING GEOMETRY INTO NUMBERS  
Defining the operation of multiplication  
The distributive law and its momentum  
Virtuous circles versus vicious circles  
So why does minus times minus equal plus?  
PART II  
BOMBELLIS PUZZLE  
BombellisLAlgebra 33 I have found another kind of cubic radical  
Numbers as algorithms  
The name of the unknown  
Species and numbers  
STRETCHING THE IMAGE  
algebra and geometry mixed  
Writing and singing  
The power of notation  
A plane of numbers  
NUMBERS  
THE LITERATURE OF DISCOVERY  
UNDERSTANDING ALGEBRA  
THE QUADRATIC FORMULA  
BIBLIOGRAPHY  
PERMISSIONS ACKNOWLEDGMENTS  
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Common terms and phrases
90 degrees algebra algorithm Analytic Art André Weil angle answer Ashbery Ashbery’s axis Bháskara Bombelli Bombelli’s puzzle Brann called Cardano Cartesian coordinates Chuquet complex numbers complex plane conjugate cosine cube roots cubic equations cubic radicals decimal expansions definition discussion distributive law equal Euclidean plane example Ferro’s formula Français Français’s geometric Gergonne give given horizontal imaginary numbers imagination John Ashbery Kafka L’Algebra Magna magnitude mathematicians mathematics method minus times minus Moivre Moivre’s negative numbers notation number line operation of multiplication Oresme phrase Plato’s poem poetry Poincaré conjecture positive number positive whole numbers Press problem prose quadratic formula quantities question ratio of whole real numbers realnumber referred rotation Scarry sect Servois Shakespeare’s Sonnets solutions solve specific square root Stendhal subtraction Tartaglia things Thomas Lux three cube roots trans transformation translation treatise tulip Univ unknown Viète Viète’s visualize word writing yellow zero