The Koch Snowflake Curve References

The Koch Snowflake Curve
Monica Agana
Boise State University
Abstract
A fractal is a fascinating type of curve. One example in particular is the Koch
Snowflake fractal, whose construction was first introduced in 1904 by a Swedish mathematician by the name of Helge Von Koch. As an introduction we provide the reader
with it’s construction [1]:
Begin with an equilateral triangle. Then divide each side into three equal parts, and
remove the middle third side, and replace it with a smaller equilateral triangle, without the base; this is the first iteration. Now we have 12 line segments. For each line
segment, again erase the middle third and replace it with a smaller equilateral triangle,
while removing the base; this is the second iteration. Repeat this procedure up to n
times.
The construction of the curve is quite simple, and in fact stems directly from the
construction of the Koch Curve. In this presentation we will introduce the audience
with these topics, as well as briefly discuss some of the curve’s properties such as,
having an infinite perimeter and finite area, and the notion that it can be used to
illustrate a continuous but nowhere differentiable function [2].
References
[1] H. von Koch, Une méthode géométrique élémentaire pour l’étude de certaines questions
de la théorie des curves plane, Acta Math. 30. (1906) 145-174.
[2] Ungar, Sime. “The Koch Curve: A Geometric Proof.” The American Mathematical
Monthly 114.1 (2007): 61-66. JSTOR. Web. 11 Dec. 2014.
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