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Famous Problems and Other Monographs Second EditionPDF|Epub|txt|kindle电子书版本网盘下载
- 著
- 出版社： Chelsea Publishing Company
- ISBN：
- 出版时间：1962
- 标注页数：365页
- 文件大小：49MB
- 文件页数：378页
- 主题词：
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图书目录
INTRODUCTION1
PRACTICAL AND THEORETICAL CONSTRUCTIONS2
STATEMENT OF THE PROBLEM IN ALGEBRAIC FORM3
PART Ⅰ．The Possibility of the Construction of Algebraic Expressions5
CHAPTER Ⅰ．ALGEBRAIC EQUATIONS SOLVABLE BY SQUARE ROOTS5
1-4．Structure of the expression x to be constructed5
5，6．Normal form of x6
7，8．Conjugate values7
9．The corresponding equation F(x)=o8
10．Other rational equations f(x)=o8
11，12．The irreducible equation φ(x)=o10
13，14．The degree of the irreducible equation a power of 211
CHAPTER Ⅱ．THE DELIAN PROBLEM AND THE TRISECTION OF THE ANGLE13
1．The impossibility of solving the Delian problem with straight edge and compasses13
2．The general equation x3=λ13
3．The impossibility of trisecting an angle with straight edge and compasses14
CHAPTER Ⅲ．THE DIVISION OF THE CIRCLE INTO EQUAL PARTS16
1．History of the problem16
2-4．Gauss＇s prime numbers17
5．The cyclotomic equation19
6．Gauss＇s Lemma19
7，8．The irreducibility of the cyclotomic equation21
CHAPTER Ⅳ．THE CONSTRUCTION OF THE REGULAR POLYGON OF 17 SIDES24
1．Algebraic statement of the problem24
2-4．The periods formed from the roots25
5，6．The quadratic equations satisfied by the periods27
7．Historical account of constructions with straight edge and compasses32
8，9．Von Staudt＇s construction of the regular polygon of 17 sides34
CHAPTER Ⅴ．GENERAL CONSIDERATIONS ON ALGEBRAIC CONSTRUCTIONS42
1．Paper folding42
2．The conic sections42
3．The Cissoid of Diocles44
4．The Conchoid of Nicomedes45
5．Mechanical devices47
PART Ⅱ．Transcendental Numbers and the Quadrature of the Circle49
CHAPTER Ⅰ．CANTOR＇S DEMONSTRATION OF THE EXISTENCE OF TRANSCENDENTAL NUMBERS49
1．Definition of algebraic and of transcendental numbers49
2．Arrangement of algebraic numbers according to height50
3．Demonstration of the existence of transcendental numbers53
CHAPTER Ⅱ．HISTORICAL SURVEY OF THE ATTEMPTS AT THE COMPUTATION AND CONSTRUCTION OF π55
1．The empirical stage56
2．The Greek mathematicians56
3．Modern analysis from 1670 to 177058
4，5．Revival of critical rigor since 177059
CHAPTER Ⅲ．THE TRANSCENDENCE OF THE NUMBER e61
1．Outline of the demonstration61
2．The symbol hr and the function φ(x)62
3．Hermite＇s Theorem65
CHAPTER Ⅳ．THE TRANSCENDENCE OF THE NUMBER π68
1．Outline of the demonstration68
2．The function ψ(x)70
3．Lindemann＇s Theorem73
4．Lindemann＇s Corollary74
5．The transcendence of π76
6．The transcendence of y=ex77
7．The transcendence of y=sin-1x77
CHAPTER Ⅴ．THE INTEGRAPH AND THE GEOMETRIC CONSTRUCTION OF π78
1．The impossibility of the quadrature of the circle with straight edge and compasses78
2．Principle of the integraph78
3．Geometric construction of π79
NOTES81
INTRODUCTION99
DETERMINANTS101
Ⅰ．ORIGIN OF DETERMINANTS103
Ⅱ．PROPERTIES OF DETERMINANTS112
Ⅲ．SOLUTION OF SIMULTANEOUS EQUATIONS121
Ⅳ．PROPERTIES OF DETERMINANTS（continued）123
Ⅴ．THE TENSOR NOTATION131
SETS147
Ⅵ．SETS OF QUANTITIES149
Ⅶ．RELATED SETS OF VARIABLES164
Ⅷ．DIFFERENTIAL RELATIONS OF SETS177
Ⅸ．EXAMPLES FROM THE THEORY OF STATISTICS184
Ⅹ．TENSORS IN THEORY OF RELATIVITY207
APPENDIX：Product of Determinants214
INDEX OF SYMBOLS216
GENERAL INDEX217
Ⅰ305
Ⅱ314
Ⅲ330