Classics On FractalsGerald A. Edgar Fractals have recently become an important topic of discussion in such varied branches of science as mathematics, computer science, and physics. Accordingly, there is an interest in the mathematical underpinnings for a (yet to be realized) theory of fractals. Classics on Fractals collects for the first time the historic seminal papers on fractal geometry, dealing with such topics as non-differentiable functions, self-similarity, and fractional dimension. This compendium is an invaluable reference for all researchers and students of fractal geometry. Of particular value are the twelve papers that have never before been translated into English. Commentaries by Professor Edgar are included to aid the modern student of mathematics in reading the papers, and to place them in their historical perspective. The volume contains papers from the following notables: 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. |
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A₁ angle approach arc arbitrary belongs Besicovitch Borel set bounded set C₁ Cantor closed sets compact compact space condition consider construction contains continuous function converges convex corresponding countable cover cube defined definition denote diameter disjoint endpoints equal equation Euclidean space example exists F₁ Figure finite follows fractal fractional dimensions given Hausdorff dimension Hausdorff measure homeomorphic homothety inequality infinite number integer interior points intersection interval Koch curve Lebesgue Lebesgue measure Lemma length limit linear sets m₁ Math Mathematical measurable point sets metric space n-dimensional n₁ neighborhood obtained open set outer measure P₁ plane points in common polygonal line polyhedra polyhedron positive number proof proved ratio region retreat arc S₁ satisfying segment sequence set of points sides similar similitude spheres subset symmetric t₁ tangent Theorem theory topological topological dimension triangle values vertex vertices zero г₁