Classics On Fractals

Gerald A. Edgar

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429711237
• Edition: 1
• Topic: Ciencias biológicas
• Subtopic: Biología

Read the masters! Experience has shown that this is good advice for the serious mathematics student. This book contains a selection of the classical mathematical papers related to fractal geometry. For the convenience of the student or scholar wishing to learn about fractal geometry, nineteen of these papers are collected here in one place. Twelve of the nineteen have been translated into English from German, French, or Russian. In many branches of science, the work of previous generations is of interest only for historical reasons. This is much less so in mathematics.1 Modern-day mathematicians can learn (and even find good ideas) by reading the best of the papers of bygone years. In preparing this volume, I was surprised by many of the ideas that come up.

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Table of contents

• Cover
• Half Title
• Series Page
• Title
• Copyright
• Contents
• Introduction
• Blake and Fractals
• 1 On Continuous Functions of a Real Argument that do not have a Well-Defined Differential Quotient
• 2 On the Power of Perfect Sets of Points
• 3 On a Continuous Curve without Tangent Constructible from Elementary Geometry
• 4 On the linear Measure of Point Sets–a Generalization of the Concept of Length
• 5 Dimension and Outer Measure
• 6 General Spaces and Cartesian Spaces
• 7 Improper Sets and Dimension Numbers (excerpt)
• 8 On a Metric Property of Dimension
• 9 On the Sum of Digits of Real Numbers Represented in the Dyadic System (1934)
• 10 On Rational Approximations to Real Numbers (1934)
• 11 On Dimensional Numbers of Some Continuous Curves (1937)
• 12 Plane or Space Curves and Surfaces Consisting of Parts Sirililar to the Whole
• 13 Additive Functions of Intervals and Hausdorff Measure (1946)
• 14 The Dimension of Cartesian Product Sets (1954)
• 15 On the Complementary Intervals of a Linear Gosed Set of Zero Lebesgue Measure (1954)
• 16 On Some Curves Defined by Functional Equations
• 17 ε-Entropy and ε-Capacity of Sets in Functional Spaces (exerpt)
• 18 A Simple Example of a Function which is Everywhere Continuous and Nowhere Differentiable
• 19 How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension (1967)
• Index
• Permissions and Acknowledgments