Lim and Self-Similarity

Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar

Lim and Self-Similarity

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2004

Autor:innen

Peitgen, Heinz-Otto

Jürgens, Hartmut

Saupe, Dietmar

DOI (zitierfähiger Link)

https://doi.org/10.1007/0-387-21823-8_4

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Beitrag zu einem Sammelband

Publikationsstatus

Published

Erschienen in

PEITGEN, Heinz-Otto, ed., Hartmut JÜRGENS, ed., Dietmar SAUPE, ed.. Chaos and Fractals : New Frontiers of Science. 2. ed.. New York: Springer, 2004, pp. 129-172. ISBN 978-0-387-20229-7. Available under: doi: 10.1007/0-387-21823-8_4

Zusammenfassung

Dyson is referring to mathematicians, like G. Cantor, D. Hilbert, and W. Sierpinski, who have been justly credited with having helped to lead mathematics out of its crisis at the turn of the century by building marvelous abstract foundations on which modern mathematics can now flourish safely. Without question, mathematics has changed during this century. What we see is an ever-increasing dominance of the algebraic approach over the geometric. In their striving for absolute truth, mathematicians have developed new standards for determining the validity of mathematical arguments. In the process, many of the previously accepted methods have been abandoned as inappropriate. Geometric or visual arguments were increasingly forced out. While Newton’s Principia Mathematica, laying the fundamentals of modern mathematics, still made use of the strength of visual arguments, the new objectivity seems to require a dismissal of this approach. From this point of view, it is ironic that some of the constructions which Cantor, Hilbert, Sierpinski and others created to perfect their extremely abstract foundations simultaneously hold the clues to understanding the patterns of nature in a visual sense. The Cantor set, Hilbert curve, and Sierpinski gasket all give testimony to the delicacy and problems of modern set theory and at the same time, as Mandelbrot has taught us, are perfect models for the complexity of nature.

Fachgebiet (DDC)

004 Informatik

Zitieren

ISO 690

PEITGEN, Heinz-Otto, Hartmut JÜRGENS, Dietmar SAUPE, 2004. Lim and Self-Similarity. In: PEITGEN, Heinz-Otto, ed., Hartmut JÜRGENS, ed., Dietmar SAUPE, ed.. Chaos and Fractals : New Frontiers of Science. 2. ed.. New York: Springer, 2004, pp. 129-172. ISBN 978-0-387-20229-7. Available under: doi: 10.1007/0-387-21823-8_4

BibTex

@incollection{Peitgen2004SelfS-42199,
  year={2004},
  doi={10.1007/0-387-21823-8_4},
  title={Lim and Self-Similarity},
  edition={2. ed.},
  isbn={978-0-387-20229-7},
  publisher={Springer},
  address={New York},
  booktitle={Chaos and Fractals : New Frontiers of Science},
  pages={129--172},
  editor={Peitgen, Heinz-Otto and Jürgens, Hartmut and Saupe, Dietmar},
  author={Peitgen, Heinz-Otto and Jürgens, Hartmut and Saupe, Dietmar}
}

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