Koch's Snowflake
Exploration Questions

The Koch Curve is the most recognized "line bender" fractal.

Directions: Draw several iterations of the Koch Curve, filling in the table below.

Iteration 1 2 3 4 5
Number of Segments per Side
Length of a Segment
Total Length of Curve

Answer the following questions:

  • What would the total length of the N-th iteration be? Look at the patterns made by the numbers both before and after simplifying.

  • What do you expect the Koch Curve to look like? In other words, what would you expect to happen if you repeated this infinitely many times?

  • What is the length of the Koch Curve?

  • Can you estimate the area at each stage? What is the area of the final snowflake?