MARC Record from marc_columbia

LEADER: 02989mam a2200385 a 4500
001 1530130
005 20220608182423.0
008 940121t19941994nyua b 001 0 eng
010 $a 94000246
020 $a0387942653 (New York : acid-free paper)
020 $a3540942653 (Berlin : acid-free paper) :$cDM59.90
035 $a(OCoLC)ocm29791898
035 $9AJZ4848CU
035 $a(NNC)1530130
035 $a1530130
040 $aDLC$cDLC$dNNC
050 00 $aQA643$b.S12 1994
082 00 $a516.3/62$220
100 1 $aSagan, Hans.$0http://id.loc.gov/authorities/names/n80004017
245 10 $aSpace-filling curves /$cHans Sagan.
260 $aNew York :$bSpringer-Verlag,$c[1994], ©1994.
300 $axv, 193 pages :$billustrations ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aUniversitext
504 $aIncludes bibliographical references (p. [177]-185) and index.
505 0 $aCh. 1. Introduction -- Ch. 2. Hilbert's Space-Filling Curve -- Ch. 3. Peano's Space-Filling Curve -- Ch. 4. Sierpinski's Space-Filling Curve -- Ch. 5. Lebesgue's Space-Filling Curve -- Ch. 6. Continuous Images of a Line Segment -- Ch. 7. Schoenberg's Space-Filling Curve -- Ch. 8. Jordan Curves of Positive Lebesgue Measure -- Ch. 9. Fractals.
520 $aThe subject of space-filling curves has generated a great deal of interest since the first such curve was discovered by Peano over a century ago. Hilbert, Lebesque, and Sierpinski were among the prominent mathematicians who made significant contributions to the field in its early stages of development.
520 8 $aCantor showed in 1878 that there is a one-to-one correspondence between an interval and a square (or cube, or any finite-dimensional manifold) and Netto demonstrated that such a correspondence cannot be continuous. Dropping the requirement that the mapping be one-to-one, Peano found a continuous map from the interval onto the square (or cube) in 1890. In other words: He found a continuous curve that passes through every point of the square (or cube).
520 8 $aThis book discusses generalizations and modifications of Peano's constructions, the properties of such curves, and their relationship to fractals.
520 8 $aSurprisingly, there has not been a comprehensive treatment of space-filling curves since Sierpinski's in 1912, when the subject was still in its infancy. The author, who has established his credentials through a series of publications on space-filling curves, provides a rigorous and comprehensive treatment, but also reflects on the subject's historical development and the personalities involved. The only prerequisite is a solid knowledge of Advanced Calculus.
650 0 $aCurves on surfaces.$0http://id.loc.gov/authorities/subjects/sh85034933
650 0 $aTopology.$0http://id.loc.gov/authorities/subjects/sh85136089
830 0 $aUniversitext.$0http://id.loc.gov/authorities/names/n42025686
852 00 $bmat$hQA643$i.S12 1994