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Space-Filling Curves

Space-Filling Curves - 94 edition

ISBN13: 978-0387942650

Cover of Space-Filling Curves 94 (ISBN 978-0387942650)
ISBN13: 978-0387942650
ISBN10: 0387942653
Edition: 94
Copyright: 1994
Publisher: Springer-Verlag New York
Published: 1994
International: No

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Space-Filling Curves - 94 edition

ISBN13: 978-0387942650

Sagan hans

ISBN13: 978-0387942650
ISBN10: 0387942653
Edition: 94
Copyright: 1994
Publisher: Springer-Verlag New York
Published: 1994
International: No
Summary

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.

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