# Maths HL Kochs Snowflake

by sunscreen123 (student)

The Koch Snowflake

The koch snowflake is a fractal that was identified by Helge Von Koch in 1904. It is created by starting with an equilateral triangle, removing the centre third of each side and replacing it with another, smaller equilateral triangle.

Table 1.1: Table of Values For the Koch Snowflake

Finding the values of N was relatively easy as this was just a process of counting the sides. It was discovered that the Number of sides was equal to four times the previous amount of sides. Nn= Nn-1 x 4

The Length of the original iteration was given as 1 and with each iteration the fractal divides each side by three.  So the side length became a third of the previous.  Ln =

The Perimeter of the Koch snowflake was rather simple too. As the length of each side of the snowflake is the same, the perimeter is equal to the amount of sides multiplied by the length of the sides. Pn = Ln x Nn

The area of the Koch snowflake was the most challenging to find. Firstly the area of an equilateral triangle is equal to

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