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Playing with Infinity: Mathematical Explorations and Excursions
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General Information
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Type.................: Ebook
Part Size............: 7,960,515 bytes
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Post Information
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Posted by............: ~tqw~
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Release Notes
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Popular account ranges from counting to mathematical logic and covers the many
mathematical concepts that relate to infinity: graphic representation of
functions; pairings and other combinations; prime numbers; logarithms and
circular functions; formulas, analytical geometry; infinite lines, complex
numbers, expansion in the power series; metamathematics; more. 216
illustrations.
Table Of Contents
INTRODUCTION
PART I THE SORCERER'S APPRENTICE
PLAYING WITH FINGERS
2 THE 'TEMPERATURE CHARTS' OF THE OPERATIONS 6
3 THE PARCELLING OUT OF THE INFINITE NUMBER SERIES 14
4 THE SORCERER'S APPRENTICE 21
5 VARIATIONS ON A FUNDAMENTAL THEME 29
POSTSCRIPT ON GEOMETRY WITHOUT MEASUREMENTS 33
6 WE GO THROUGH ALL POSSIBILITIES 42
7 COLOURING THE GREY NUMBER SERIES 56
8 'I HAVE THOUGHT OF A NUMBER' 66
PART II THE CREATIVE ROLE OF FORM
9 DIVERGING NUMBERS 77
10 LIMITLESS DENSITY 88
11 WE CATCH INFINITY AGAIN 99
12 THE LINE IS FILLED UP 112
13 THE CHARTS GET SMOOTHED OUT 126
14 MATHEMATICS IS ONE 140
POSTSCRIPT ABOUT WAVES AND SHADOWS 152
15 'WRITE IT DOWN' ELEMENTS 160
16 SOME WORKSHOP SECRETS 177
17 'MANY SMALL MAKE A GREAT' 196
PART III THE SELF-CRITIQUE OF PURE REASON
18 AND STILL THERE ARE DIFFERENT KINDS OF
MATHEMATICS 211
POSTSCRIPT ABOUT THE FOURTH DIMENSION 222
19 THE BUILDING ROCKS 225
20 FORM BECOMES INDEPENDENT 233
21 AWAITING JUDGEMENT BY METAMATHEMATICS 243
POSTSCRIPT ON PERCEPTION PROJECTED TO INFINITY 251
22 WHAT IS MATHEMATICS NOT CAPABLE OF? 255
AFTER USE 267
Product Details
* ISBN: 0486232654
* ISBN-13: 9780486232652
* Format: Paperback, 268pp
* Publisher: Dover Publications
* Pub. Date: June 1976
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Install Notes
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PDF Reader
*******************************************************************************
Playing with Infinity: Mathematical Explorations and Excursions
*******************************************************************************
-------------------------------------------------------------------------------
General Information
-------------------------------------------------------------------------------
Type.................: Ebook
Part Size............: 7,960,515 bytes
-------------------------------------------------------------------------------
Post Information
-------------------------------------------------------------------------------
Posted by............: ~tqw~
-------------------------------------------------------------------------------
Release Notes
-------------------------------------------------------------------------------
Popular account ranges from counting to mathematical logic and covers the many
mathematical concepts that relate to infinity: graphic representation of
functions; pairings and other combinations; prime numbers; logarithms and
circular functions; formulas, analytical geometry; infinite lines, complex
numbers, expansion in the power series; metamathematics; more. 216
illustrations.
Table Of Contents
INTRODUCTION
PART I THE SORCERER'S APPRENTICE
PLAYING WITH FINGERS
2 THE 'TEMPERATURE CHARTS' OF THE OPERATIONS 6
3 THE PARCELLING OUT OF THE INFINITE NUMBER SERIES 14
4 THE SORCERER'S APPRENTICE 21
5 VARIATIONS ON A FUNDAMENTAL THEME 29
POSTSCRIPT ON GEOMETRY WITHOUT MEASUREMENTS 33
6 WE GO THROUGH ALL POSSIBILITIES 42
7 COLOURING THE GREY NUMBER SERIES 56
8 'I HAVE THOUGHT OF A NUMBER' 66
PART II THE CREATIVE ROLE OF FORM
9 DIVERGING NUMBERS 77
10 LIMITLESS DENSITY 88
11 WE CATCH INFINITY AGAIN 99
12 THE LINE IS FILLED UP 112
13 THE CHARTS GET SMOOTHED OUT 126
14 MATHEMATICS IS ONE 140
POSTSCRIPT ABOUT WAVES AND SHADOWS 152
15 'WRITE IT DOWN' ELEMENTS 160
16 SOME WORKSHOP SECRETS 177
17 'MANY SMALL MAKE A GREAT' 196
PART III THE SELF-CRITIQUE OF PURE REASON
18 AND STILL THERE ARE DIFFERENT KINDS OF
MATHEMATICS 211
POSTSCRIPT ABOUT THE FOURTH DIMENSION 222
19 THE BUILDING ROCKS 225
20 FORM BECOMES INDEPENDENT 233
21 AWAITING JUDGEMENT BY METAMATHEMATICS 243
POSTSCRIPT ON PERCEPTION PROJECTED TO INFINITY 251
22 WHAT IS MATHEMATICS NOT CAPABLE OF? 255
AFTER USE 267
Product Details
* ISBN: 0486232654
* ISBN-13: 9780486232652
* Format: Paperback, 268pp
* Publisher: Dover Publications
* Pub. Date: June 1976
-------------------------------------------------------------------------------
Install Notes
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PDF Reader