Imagining Numbers: (particularly the square root of minus fifteen)

Farrar, Straus and Giroux, 1. feb. 2004 - 288 strani

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.

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LibraryThing Review

Uporabnikova ocena  - waltzmn - LibraryThing

I never thought I'd see a book about imaginary numbers that i didn't like. If you know your mathematics, you'll see that that is a carefully constructed sentence. When I say i, I am not referring to ... Celotno mnenje

LibraryThing Review

Uporabnikova ocena  - rcorfield - LibraryThing

This is an interesting little book and I thoroughly enjoyed it. It sets out to help the user understand and, more importantly, visualise, imaginary numbers (i.e. the square-root of -1). The author ... Celotno mnenje

Vsebina

 Title Page What is a square root? NOTES The problem of describing how we imagine Permission Forced conventions or definitions? What kind of law is the distributive law? ECONOMY OF EXPRESSION 23 Charting the plane
 Back to Bombellis puzzle Interviewing Bombelli PUTTING GEOMETRY INTO NUMBERS 45 Many hands Imagining the dynamics of multiplication by Writing and singing The power of notation A plane of numbers Thinking silently out loud

 The geometry of qualities The spareness of the inventory of the imagination JUSTIFYING LAWS 26 Laws and why we believe them 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 31 The argument between Cardano and Tartaglia Bombellis LAlgebra I have found another kind of cubic radical which is very different from the others Numbers as algorithms The name of the unknown Species and numbers STRETCHING THE IMAGE 37 The elasticity of the number line To imagine versus to picture The inventors of writing Arithmetic in the realm of imaginary numbers The absence of time in mathematics Questioning answers
 The complex plane of numbers Telling a straight story SEEING THE GEOMETRY IN THE NUMBERS 53 Critical moments in the story of discovery What are we doing when we identify one thing with another? Song and story Multiplying in the complex plane The geometry behind multiplication by by 1 + and by 1 +2 What is a number? So how can we visualize multiplication in the complex plane? PART III THE LITERATURE OF DISCOVERY OF GEOMETRY IN NUMBERS 60 These equations are of the same form as the equations for cosines though ... A few remarks on the literature of discovery and the literature of UNDERSTANDING ALGEBRA VIA GEOMETRY 62 Twins Dal Ferros expression as algorithm Form and content But THE QUADRATIC FORMULA BIBLIOGRAPHY PERMISSIONS ACKNOWLEDGMENTS Avtorske pravice

O avtorju (2004)

Barry Mazur does his mathematics at Harvard University and lives in Cambridge, Massachussetts, with the writer Grace Dane Mazur.