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Written by the award winning authors of Chaos and Fractals
(0-387-97903-4), this work introduces the reader to iterated
function systems through a lively, interactive approach. This
well-written, clearly illustrated book explores the history and the
unlimited potential of fractals, while developing a basic
mathematical understanding and appreciation for the topics.
There are many reasons for writing this first volume of strategic
activities on fractals. The most pervasive is the compelling desire
to provide students of mathematics with a set of accessible,
hands-on experiences with fractals and their underlying
mathematical principles and characteristics. Another is to show how
fractals connect to many different aspects of mathematics and how
the study of fractals can bring these ideas together. A third is to
share the beauty of their structure and shape both through what the
eye sees and what the mind visualizes. Fractals have captured the
attention, enthusiasm, and interest of many people around the
world. To the casual observer, their color, beauty, and geometric
structure captivates the visual senses like few other things they
have ever experienced in mathematics. To the computer scientist,
fractals offer a rich environment in which to explore, create, and
build a new visual world as an artist creating a new work. To the
student, fractals bring mathematics out of past history and into
the twenty-first century. To the mathematics teacher, fractals
offer a unique, new opportunity to illustrate both the dynamics of
mathematics and its many connecting links.
The same factors that motivated the writing of our first volume of
strategic activities on fractals continued to encourage the
assembly of additional activities for this second volume. Fractals
provide a setting wherein students can enjoy hands-on experiences
that involve important mathematical content connected to a wide
range of physical and social phenomena. The striking graphic
images, unexpected geometric properties, and fascinating numerical
processes offer unparalleled opportunity for enthusiastic student
inquiry. Students sense the vigor present in the growing and highly
integrative discipline of fractal geom etry as they are introduced
to mathematical developments that have occurred during the last
half of the twentieth century. Few branches of mathematics and
computer science offer such a contem porary portrayal of the
wonderment available in careful analysis, in the amazing dialogue
between numeric and geometric processes, and in the energetic
interaction between mathematics and other disciplines. Fractals
continue to supply an uncommon setting for animated teaching and
learn ing activities that focus upon fundamental mathematical
concepts, connections, problem-solving techniques, and many other
major topics of elementary and advanced mathematics. It remains our
hope that, through this second volume of strategic activities,
readers will find their enjoyment of mathematics heightened and
their appreciation for the dynamics of the world in creased. We
want experiences with fractals to enliven curiosity and to stretch
the imagination."
Das vorliegende Arbeitsbuch ist Teil eines Paketes von
verschiedenen Materialien, die das Ziel haben, das Thema Chaos und
Fraktale in den mathematisch-naturwissenschaftlichen Unterricht
einzufuhren. Ein weiteres Anliegen besteht darin, das mentale Bild
von Mathematik im Bewusstsein der Schuler attraktiver zu gestalten.
Mathematik ist die Antwort des Menschen auf die Komplexitat der
Welt. Mathematik ist die Ordnungsmacht im Dschungel der Phanomene.
Deshalb ist Mathematik le bendig, frisch und aktuell. Deshalb gibt
es zwischen einzelnen Teilgebieten und Ergebnissen der Mathematik
immer wieder uberraschende Querverbindungen, die oft das
Verstandnis einer Sache erst wirklich erhellen. Und deshalb bietet
es sich an, durch entdeckendes, explorierendes Lernen die
Anziehungskraft dieser Eigenschaften der Mathematik im Unterricht
auszunutzen. Chaos und Fraktale bieten hierfur eine besondere neue
Chance. Beide sind jung und aktuell und belegen so ohne weiteres,
dass Mathematik lebt. Fur beide gilt, dass einige ihrer
schrittmachenden Entdeckungen nicht ohne Hilfe von Computern
moeglich gewesen waren. Damit rucken faszinie rende
Computerexperimente naturlich in den Mittelpunkt. Beide sind
hochgradig interdisziplinar. Dieses heisst, dass gehaltvolle
Anwendungen nicht erst muhsam konstruiert werden mussen. Beide
behandeln Themen, die von sich aus wirken. Tatsachlich durchlaufen
seit Ende der siebziger Jahre Mathematik und Naturwissenschaften
eine Welle, die in ihrer Kraft, Kreativitat und Weitraumigkeit
langst ein interdisziplinares Ereignis er sten Ranges geworden ist.
Das andauernde Interesse innerhalb und ausserhalb der
Wissenschaften ist in einer aufruttelnden Betroffenheit begrundet,
die eine radikale Wende in dem uberkommenen naturwissenschaftlichen
Weltbild und manchen uberdehnten Interpretationen ankundigt.
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