-with geometry software
Objective::
Students will use algorithms to perform recursion in geometric settings and be introduced to the concept of self similarity. Students will be exposed to the use of algorithms in creating fractals with computer software.
Materials :
Lesson:
Students will follow an algorithm to create a portion of the Koch curve. If recursion of depth 5 or higher is selected, some computer processors will freeze. Encourage students to experiment, but you may want to be sure of a depth limit for your particular system. While they are following the algorithm, they will be creating a script for the Koch curve.
When they are finished, and have teseted their script on two points they should then attempt to create the Koch snowflake by applying their script to each side of an equilateral triangle.
Finally, students should create an algorithm and script for themselves for the construction of an equilateral triangle and the midpoints of each side. The script will involve a loop on the midpoints.
Assignment:
Investigate several basic figures and their properties, discuss the self-similarity you see in each of them. Can you create a construction to model this similarity in the form of an algorithm? Write at least one algorithm involvoing self similarity and a loop that can be tested using geometry software.
Handouts: