Chapter 11.4, Problem 1E

Interpretation Introduction

Interpretation:

To find the dimension of the von Koch snowflake.

Concept Introduction:

• The Koch curve starts with a straight line that is divided up into three equal parts. Using the middle segment as a base, an equilateral triangle is created. Finally, the base of the triangle is removed, leaving us with the first iteration of the Koch curve.

• From the Koch curve comes the Koch Snowflake. Instead of one line, the snowflake begins with an equilateral triangle. The steps in creating the Koch Curve are then repeatedly applied to each side of the equilateral triangle, creating a snowflake shape.

• The Koch snowflake is an example of a figure that is self-similar, meaning it looks the same on any scale.

• The formula for the number of sides in the Koch snowflake is: $\text{N}\left(\text{ε}\right){\text{ = 3(4}}^{\text{n}})$.