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

Valutazione media 3,44
( su 117 valutazioni fornite da Goodreads )
 
9780312421878: Imagining Numbers: (particularly the square root of minus fifteen)

Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

About the Author:

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

Excerpt. © Reprinted by permission. All rights reserved.:

PREFACE

1, 2, 3, . . . The "counting numbers" are part of us. We know them forward and backward. Babies as young as five months old, psychologists claim, are sensitive to the difference between 1 + 1 and 2 - 1. We sing numbers, counting up the days of Christmas and counting down to the poignant monotheism of "One is one and all alone and evermore shall be so." 

Our ancestors have added to this repertoire and reckoned with zero and the negative numbers, which were sometimes referred to as fictions (fictae) before they gained familiarity. 

All these together constitute what we call the whole numbers, . . . , -2, -1, 0, +1, +2, . . . 

More formally, they are called integers, from the Latin adjective meaning "whole, untouched, unharmed." 

"Whole," "untouched"; their very name hints that integers can be touched, or fractionated. Indeed they can be, and when they are, we get the larger array of numbers that are fractions, ratios of whole numbers. 

Fractions, as their notation vividly displays, also stand for proportions (think of 1/2 = 2/4 as "one is to two as two is to four and for actions (think of 1/2 as "halving," ready to cut in half anything that follows it). To bring fractions into line, we express them as decimals (1/2 = 0.5000000 . . . ). The modem world gives us much experience with decimals to a high degree of accuracy -- to "many decimal places"; mathematics, as always, goes all the way, happy to deal with numbers with complete accuracy -- to infinitely many decimal places. Numbers represented by infinitely many decimal places, whether they are fractions or not, are called real numbers. 

But the telltale adjective real suggests two things: that these numbers are somehow real to us and that, in contrast, there are unreal numbers in the offing. These are the imaginary numbers

The imaginary numbers are well named, for there is some imaginative work to do to make them as much a part of us as the real numbers we use all the time to measure for bookshelves. 

This book began as a letter to my friend Michel Chaouli. The two of us had been musing about whether or not one could "feel" the workings of the imagination in its various labors. Michel had also mentioned that he wanted to "imagine imaginary numbers." That very (rainy) evening, I tried to work up an explanation of the idea of these numbers, still in the mood of our conversation. 

The text of my letter was the welcome excuse for continued conversation with a number of friends, many of whom were humanists interested in understanding what it means to imagine the square root of negative numbers. The successive revisions and expansions of my letter were shaped by their questions, comments, critiques, and insights. This book, then, is written for people who have no training in mathematics and who may not have actively thought about mathematics since high school, or even during it, but who may wish to experience an act of mathematical imagining and to consider how such an experience compares with the imaginative work involved in reading and understanding a phrase in a poem. Of course, poetry and mathematics are far apart. All the more glorious, then, for people at home in the imaginative life of poetry to use their insight and sensibility to witness the imagination at work in mathematics. 

Although no particular mathematical knowledge is necessary, pencil and paper are good to have at hand, to make a few calculations (multiplying small numbers, mostly). The operation of multiplication itself is something we will be looking at. There are three standard ways of denoting the act of multiplication: by a cross ×, by a centered dot ·, or, when there is no ambiguity, by simple juxtaposition of the objects to be multiplied. Which notation we use reflects where we wish to direct our attention: the equation 

2 x 3 = 6 

emphasizes the act of multiplying 2 times 3, whereas 

2 · 3 = 6 

focuses on the result, 6, of that operation. Nevertheless, despite this difference in nuance, both equations, 2 x 3 = 6 and 2 · 3 = 6, are saying the same thing. When we deal with an unknown quantity X, here are three equivalent ways of denoting 5 times that unknown quantity: 

5 × X = 5·X= 5X

Again, we write 5 × X if we want to emphasize the act of multiplying and 5·X or 5X if we want to emphasize the result; and that last variant notation, juxtaposition, is used for visual conciseness. 

Copyright © 2003 Barry Mazur

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

I migliori risultati di ricerca su AbeBooks

1.

Mazur, Barry
Editore: PICADOR (2004)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Quantità: > 20
Print on Demand
Da
Pbshop
(Wood Dale, IL, U.S.A.)
Valutazione libreria
[?]

Descrizione libro PICADOR, 2004. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 11,08
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,42
In U.S.A.
Destinazione, tempi e costi

2.

Mazur, Barry
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: > 20
Print on Demand
Da
BargainBookStores
(Grand Rapids, MI, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Paperback. Condizione libro: New. This item is printed on demand. Item doesn't include CD/DVD. Codice libro della libreria 2094187

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 11,93
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,42
In U.S.A.
Destinazione, tempi e costi

3.

Barry Mazur
Editore: Picador USA, United States (2004)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 10
Print on Demand
Da
The Book Depository
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Picador USA, United States, 2004. Paperback. Condizione libro: New. Reprint. Language: English . Brand New Book ***** Print on Demand *****.Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves. Codice libro della libreria APC9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 15,48
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

4.

Barry Mazur
Editore: Picador USA, United States (2004)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 10
Da
Book Depository hard to find
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Picador USA, United States, 2004. Paperback. Condizione libro: New. Reprint. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves. Codice libro della libreria BZE9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 15,48
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

5.

Barry Mazur
Editore: Picador USA, United States (2004)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 10
Print on Demand
Da
The Book Depository US
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Picador USA, United States, 2004. Paperback. Condizione libro: New. Reprint. Language: English . Brand New Book ***** Print on Demand *****. Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves. Codice libro della libreria APC9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 15,49
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

6.

Barry Mazur
Editore: St. Martins Press-3pl
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 20
Da
BuySomeBooks
(Las Vegas, NV, U.S.A.)
Valutazione libreria
[?]

Descrizione libro St. Martins Press-3pl. Paperback. Condizione libro: New. Paperback. 288 pages. Dimensions: 8.4in. x 5.4in. x 0.9in.Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 13,21
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,39
In U.S.A.
Destinazione, tempi e costi

7.

Mazur, Barry
Editore: Picador
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi PAPERBACK Quantità: 3
Da
Lakeside Books
(Benton Harbor, MI, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Picador. PAPERBACK. Condizione libro: New. 0312421877 BRAND NEW, GIFT QUALITY! NOT OVERSTOCKS OR MARKED UP REMAINDERS! DIRECT FROM THE PUBLISHER!|0.85. Codice libro della libreria OTF-S-9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 13,65
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,42
In U.S.A.
Destinazione, tempi e costi

8.

Mazur, Barry
Editore: Picador (2017)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 10
Print on Demand
Da
Murray Media
(North Miami Beach, FL, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Picador, 2017. Paperback. Condizione libro: New. This item is printed on demand. Codice libro della libreria 0312421877

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 16,03
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 2,56
In U.S.A.
Destinazione, tempi e costi

9.

Mazur, Barry
Editore: Picador (2004)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 10
Da
Ergodebooks
(RICHMOND, TX, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Picador, 2004. Paperback. Condizione libro: New. Codice libro della libreria INGM9780312421878

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 16,87
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,42
In U.S.A.
Destinazione, tempi e costi

10.

Barry Mazur
Editore: Picador (2004)
ISBN 10: 0312421877 ISBN 13: 9780312421878
Nuovi Paperback Quantità: 1
Da
Ergodebooks
(RICHMOND, TX, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Picador, 2004. Paperback. Condizione libro: New. Reprint. Codice libro della libreria DADAX0312421877

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 17,43
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,42
In U.S.A.
Destinazione, tempi e costi

Vedi altre copie di questo libro

Vedi tutti i risultati per questo libro