Name: Name
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993

Question:
What is the length of the boundary of a fractal? If it is
infinite, then how can it enclose a region of finite area?

Replies:
There are many mathematical situations like this that are related
(as are fractals) in a process continuing to infinity. Another example of a
finite area formed by a line that goes to infinity is simple. The area between
the x-axis between 0 and 10 and the function 1/square root(x) (the reciprocal
of the square root of x) is finite, while the function itself goes to infinity
when x gets close to zero. These interesting occurrences will be clearer when
you study calculus. Math and science have a lot of non-intuitive situations
like this, making it fun.

Samuel B. Bowen
Some fractals are "curves". The Koch Snowflake curve is an
example. The ordinary curves such as circles, parabolas, etc. which are
normally studied in school mathematics are "locally straight". Draw such a
curve with your graphing calculator and then zoom in on a point of the curve
several times (i.e. put it under a high-powered microscope, so to speak) the
portion that you are viewing will eventually come to look like a straight
line. A fractal curve, on the other hand, will not look straight, no matter
how much you zoom in. A great book on the subject is Fractals for the
Classroom by Peitgen et. al. It is published by Springer-Verlag with the
cooperation of the National Council of Teachers of Mathematics.

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