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Classics on Fractals (Studies in Nonlinearity)

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Fractals are an important topic in such varied branches of science as mathematics, computer science, and physics. Classics on Fractals collects for the first time the historic papers on fractal geometry, dealing with such topics as non-differentiable functions, self-similarity, and fractional dimension. Of particular value are the twelve papers that have never before been translated into English. Commentaries by Professor Edgar are included to aid the student of mathematics in reading the papers, and to place them in their historical perspective. The volume contains papers from the following: Cantor, Weierstrass, von Koch, Hausdorff, Caratheodory, Menger, Bouligand, Pontrjagin and Schnirelmann, Besicovitch, Ursell, Levy, Moran, Marstrand, Taylor, de Rahm, Kolmogorov and Tihomirov, Kiesswetter, and of course, Mandelbrot.

Author(s): Gerald A. Edgar
Publisher: Westview Press
Year: 2003

Language: English
Pages: 384
Tags: Математика;Высшая геометрия;

Cover......Page 0000_0001.djvu
Title......Page 0001_0001.djvu
Contents......Page 0003_0001.djvu
Introduction......Page 0007_0001.djvu
J. D. MEMORY Blake and Fractals......Page 0011_0001.djvu
1 KARL WEIERSTRASS (1872)......Page 0013_0001.djvu
2 GEORG CANTOR (1884)......Page 0021_0001.djvu
3 HELGE VON KOCH (1904)......Page 0035_0001.djvu
4 CONSTANTIN CARATHÉODORY (1914)......Page 0057_0001.djvu
5 FELIX HAUSDORFF (1918)......Page 0085_0001.djvu
6 KARL MENGER (1926)......Page 0113_0001.djvu
7 GEORGES BOULIGAND (1928)......Page 0129_0001.djvu
8 L. PONTRJAGIN AND L. SCHNIRELMANN (1932)......Page 0143_0001.djvu
9 A. S. BESICOVITCH (1934)......Page 0155_0001.djvu
10 A. S. BESICOVITCH (1934)......Page 0171_0001.djvu
11 A. S. BESICOVITCH AND H. D. URSELL (1937)......Page 0181_0001.djvu
12 PAUL LÉVY (1938)......Page 0191_0001.djvu
13 P. A. P. MORAN (1946)......Page 0251_0001.djvu
14 J. M. MARSTRAND (1954)......Page 0269_0001.djvu
15 A. S. BESICOVITCHAND S. J. TAYLOR (1954)......Page 0279_0001.djvu
16 GEORGES DE RHAM (1957)......Page 0295_0001.djvu
17 A. N. KOLMOGOROV AND V. M. TIHOMIROV (1959)......Page 0309_0001.djvu
18 KARL KIESSWETIER (1966)......Page 0351_0001.djvu
19 BENOIT MANDELBROT (1967)......Page 0361_0001.djvu
Index......Page 0369_0001.djvu
Permissions and Acknowledgments......Page 0373_0001.djvu