ENGLISH

Space-Filling Curves

By Hans Sagan

Book information

Publisher
Springer
Year
1994
ISBN
0387942653, 3540942653, 9780387942650
LCC
QA643 .S12 1994
Open Library ID
OL1077065M
Language
english
Format
DJVU
Filesize
3 MB (2882403 bytes)
Edition
1
Pages
208\208
DPI
600
Time added
2011-06-04 13:46:07

Description

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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