|
|
Download this torrent!
Downloads via DownloadProvider - Give it a try!
Secure download| Category: | Books |
| Added: | 3 months ago |
| Size: | 9 Megabyte |
| Peers: | 75 Seeders & 18 Leechers  [ Update ]updated '3 months ago' |
| Tracker: | http://www.h33t.com:3310 |
| Infohash: | 52bd178986a19d1e226026390a023ad6f7316820 |
Retrieving torrent peers info from tracker, please wait...Description:
*******************************************************************************
E: The Story of a Number
*******************************************************************************
-------------------------------------------------------------------------------
General Information
-------------------------------------------------------------------------------
Type.................: Ebook
Part Size............: 9,049,551 bytes
-------------------------------------------------------------------------------
Post Information
-------------------------------------------------------------------------------
Posted by............: ~tqw~
-------------------------------------------------------------------------------
Release Notes
-------------------------------------------------------------------------------
The story of [pi] has been told many times, both in scholarly works and in
popular books. But its close relative, the number e, has fared less well:
despite the central role it plays in mathematics, its history has never before
been written for a general audience. The present work fills this gap. Geared to
the reader with only a modest background in mathematics, the book describes the
story of e from a human as well as a mathematical perspective. In a sense, it is
the story of an entire period in the history of mathematics, from the early
seventeenth to the late nineteenth century, with the invention of calculus at
its center. Many of the players who took part in this story are here brought to
life. Among them are John Napier, the eccentric religious activist who invented
logarithms and - unknowingly - came within a hair's breadth of discovering e;
William Oughtred, the inventor of the slide rule, who lived a frugal and
unhealthful life and died at the age of 86, reportedly of joy when hearing of
the restoration of King Charles II to the throne of England; Newton and his
bitter priority dispute with Leibniz over the invention of the calculus, a
conflict that impeded British mathematics for more than a century; and Jacob
Bernoulli, who asked that a logarithmic spiral be engraved on his tombstone -
but a linear spiral was engraved instead! The unifying theme throughout the book
is the idea that a single number can tie together so many different aspects of
mathematics - from the law of compound interest to the shape of a hanging chain,
from the area under a hyperbola to Euler's famous formula e[superscript i[pi]] =
-1, from the inner structure of a nautilus shell to Bach's equal-tempered scale
and to the art of M. C. Escher. The book ends with an account of the discovery
of transcendental numbers, an event that paved the way for Cantor's
revolutionary ideas about infinity.
Table of Contents
Preface
1 John Napier, 1614 3
2 Recognition 11
3 Financial Matters 23
4 To the Limit, If It Exists 28
5 Forefathers of the Calculus 40
6 Prelude to Breakthrough 49
7 Squaring the Hyperbola 58
8 The Birth of a New Science 70
9 The Great Controversy 83
10 e[superscript x]: The Function That Equals its Own Derivative 98
11 e[superscript theta]: Spira Mirabilis 114
12 (e[superscript x] + e[superscript -x])/2: The Hanging Chain 140
13 e[superscript ix]: "The Most Famous of All Formulas" 153
14 e[superscript x + iy]: The Imaginary Becomes Real 164
15 But What Kind of Number Is It? 183
App. 1. Some Additional Remarks on Napier's Logarithms 195
App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches]
[infinity] 197
App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus
200
App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1
and lim (1 + h)[superscript 1/h] = b as h [approaches] 0 202
App. 5. An Alternative Definition of the Logarithmic Function 203
App. 6. Two Properties of the Logarithmic Spiral 205
App. 7. Interpretation of the Parameter [phi] in the Hyperbolic
Functions 208
App. 8. e to One Hundred Decimal Places 211
Bibliography 213
Index 217
Product Details
* ISBN: 0691033900
* ISBN-13: 9780691033907
* Format: Hardcover, 232pp
* Publisher: Princeton University Press
* Pub. Date: November 1993
-------------------------------------------------------------------------------
Install Notes
-------------------------------------------------------------------------------
PDF Reader
*******************************************************************************
E: The Story of a Number
*******************************************************************************
-------------------------------------------------------------------------------
General Information
-------------------------------------------------------------------------------
Type.................: Ebook
Part Size............: 9,049,551 bytes
-------------------------------------------------------------------------------
Post Information
-------------------------------------------------------------------------------
Posted by............: ~tqw~
-------------------------------------------------------------------------------
Release Notes
-------------------------------------------------------------------------------
The story of [pi] has been told many times, both in scholarly works and in
popular books. But its close relative, the number e, has fared less well:
despite the central role it plays in mathematics, its history has never before
been written for a general audience. The present work fills this gap. Geared to
the reader with only a modest background in mathematics, the book describes the
story of e from a human as well as a mathematical perspective. In a sense, it is
the story of an entire period in the history of mathematics, from the early
seventeenth to the late nineteenth century, with the invention of calculus at
its center. Many of the players who took part in this story are here brought to
life. Among them are John Napier, the eccentric religious activist who invented
logarithms and - unknowingly - came within a hair's breadth of discovering e;
William Oughtred, the inventor of the slide rule, who lived a frugal and
unhealthful life and died at the age of 86, reportedly of joy when hearing of
the restoration of King Charles II to the throne of England; Newton and his
bitter priority dispute with Leibniz over the invention of the calculus, a
conflict that impeded British mathematics for more than a century; and Jacob
Bernoulli, who asked that a logarithmic spiral be engraved on his tombstone -
but a linear spiral was engraved instead! The unifying theme throughout the book
is the idea that a single number can tie together so many different aspects of
mathematics - from the law of compound interest to the shape of a hanging chain,
from the area under a hyperbola to Euler's famous formula e[superscript i[pi]] =
-1, from the inner structure of a nautilus shell to Bach's equal-tempered scale
and to the art of M. C. Escher. The book ends with an account of the discovery
of transcendental numbers, an event that paved the way for Cantor's
revolutionary ideas about infinity.
Table of Contents
Preface
1 John Napier, 1614 3
2 Recognition 11
3 Financial Matters 23
4 To the Limit, If It Exists 28
5 Forefathers of the Calculus 40
6 Prelude to Breakthrough 49
7 Squaring the Hyperbola 58
8 The Birth of a New Science 70
9 The Great Controversy 83
10 e[superscript x]: The Function That Equals its Own Derivative 98
11 e[superscript theta]: Spira Mirabilis 114
12 (e[superscript x] + e[superscript -x])/2: The Hanging Chain 140
13 e[superscript ix]: "The Most Famous of All Formulas" 153
14 e[superscript x + iy]: The Imaginary Becomes Real 164
15 But What Kind of Number Is It? 183
App. 1. Some Additional Remarks on Napier's Logarithms 195
App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches]
[infinity] 197
App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus
200
App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1
and lim (1 + h)[superscript 1/h] = b as h [approaches] 0 202
App. 5. An Alternative Definition of the Logarithmic Function 203
App. 6. Two Properties of the Logarithmic Spiral 205
App. 7. Interpretation of the Parameter [phi] in the Hyperbolic
Functions 208
App. 8. e to One Hundred Decimal Places 211
Bibliography 213
Index 217
Product Details
* ISBN: 0691033900
* ISBN-13: 9780691033907
* Format: Hardcover, 232pp
* Publisher: Princeton University Press
* Pub. Date: November 1993
-------------------------------------------------------------------------------
Install Notes
-------------------------------------------------------------------------------
PDF Reader