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

### Mnenja - Napišite recenzijo

#### LibraryThing Review

Uporabnikova ocena - rcorfield - LibraryThingThis 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

#### LibraryThing Review

Uporabnikova ocena - fpagan - LibraryThingLiterally a case of "mathematics for poets." The gentlest of intros to imaginary and complex numbers. It certainly doesn't explain things like raising one complex number to the power of another. Celotno mnenje

### Vsebina

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 | |

### Druge izdaje - Prikaži vse

Imagining Numbers: (Particularly the Square Root of Minus Fifteen) Barry Mazur Omejen predogled - 2004 |

Imagining Numbers: (particularly the Square Root of Minus Fifteen) Barry Mazur Omejen predogled - 2003 |

Imagining Numbers: (particularly the Square Root of Minus Fifteen) Barry Mazur Omejen predogled - 2004 |