Space-filling Curves - Universitext - Hans Sagan - Books - Springer-Verlag New York Inc. - 9780387942650 - September 2, 1994
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Hans Sagan
Space-filling Curves - Universitext Softcover Reprint of the Original 1st Ed. 1994 edition

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The subject of space-filling curves has generated a great deal of interest in the 100 years since the first such curve was discovered by Peano. Cantor, Hilbert, Moore, Knopp, Lebesgue, and Polya are among the prominent mathematicians who have contributed to the field. However, there have been no comprehensive treatments of the subject since Siepinsky's in 1912. Cantor showed in 1878 that the number of points on an interval is the same as the number of points in a square (or cube, or whatever), and in 1890 Peano showed that there is indeed a continuous curve that continuously maps all points of a line onto all points of a square, though the curve exists only as a limit of very convoluted curves. This book discusses generalizations of Peano's solution and the properties that such curves must possess and discusses fractals in this context. The only prerequisite is a knowledge of advanced calculus.

209 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released September 2, 1994
ISBN13 9780387942650
Publishers Springer-Verlag New York Inc.
Pages 209
Dimensions 155 × 235 × 11 mm   ·   303 g
Language English  

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