Space-Filling Curves (Universitext)

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9780387942650: Space-Filling Curves (Universitext)
Reseña del editor:

The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space­ filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis.

Reseña del editor:

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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Hans Sagan
Editorial: Springer-Verlag New York Inc., United States (1994)
ISBN 10: 0387942653 ISBN 13: 9780387942650
Nuevos Paperback Cantidad: 10
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The Book Depository
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Descripción Springer-Verlag New York Inc., United States, 1994. Paperback. Estado de conservación: New. 229 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****.The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski s paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space- filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis. Softcover reprint of the original 1st ed. 1994. Nº de ref. de la librería AAV9780387942650

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Hans Sagan
Editorial: Springer-Verlag New York Inc., United States (1994)
ISBN 10: 0387942653 ISBN 13: 9780387942650
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Descripción Springer-Verlag New York Inc., United States, 1994. Paperback. Estado de conservación: New. 229 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski s paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space- filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis. Softcover reprint of the original 1st ed. 1994. Nº de ref. de la librería AAV9780387942650

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Descripción Springer-Verlag New York Inc., 1994. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9780387942650

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Descripción Springer, 1994. Paperback. Estado de conservación: NEW. 9780387942650 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0411158

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