Matches in Harvard for { <http://id.lib.harvard.edu/aleph/007048791/catalog> ?p ?o. }
Showing items 1 to 28 of
28
with 100 items per page.
- catalog abstract "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.".
- catalog contributor b9767898.
- catalog created "c1994.".
- catalog date "1994".
- catalog date "c1994.".
- catalog dateCopyrighted "c1994.".
- catalog description "Includes bibliographical references (p. [177]-185) and index.".
- catalog description "Introduction -- Hillbert's space-filling curve -- Peano's space-filling curve -- Sierpinski's space-filling curve -- Lebesgue's space-filling curve -- Continuous images of a line segment -- Schoenberg's space-filling curve -- Jordan curves of positive Lebesgue measure -- Fractals.".
- catalog 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.".
- catalog extent "xv, 193 p. :".
- catalog hasFormat "Space-filling curves.".
- catalog identifier "0387942653 (New York : acid-free paper)".
- catalog identifier "3540942653 (Berlin : acid-free paper) :".
- catalog isFormatOf "Space-filling curves.".
- catalog isPartOf "Universitext".
- catalog issued "1994".
- catalog issued "c1994.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Space-filling curves.".
- catalog subject "516.3/62 20".
- catalog subject "Curves on surfaces.".
- catalog subject "Mathematics.".
- catalog subject "QA643 .S12 1994".
- catalog subject "Topology.".
- catalog tableOfContents "Introduction -- Hillbert's space-filling curve -- Peano's space-filling curve -- Sierpinski's space-filling curve -- Lebesgue's space-filling curve -- Continuous images of a line segment -- Schoenberg's space-filling curve -- Jordan curves of positive Lebesgue measure -- Fractals.".
- catalog title "Space-filling curves / Hans Sagan.".
- catalog type "text".