math 2015
Shodor > SUCCEED > Workshops > Archive > math 2015

The instructor began by describing the concept of a mathematical curve, showing Koch’s Snowflake (a Fractal) which is a great example of a mathematical curve. The Snowflake is a exponential sequence that when graphed, results in an infinite perimeter but a finite area. The instructor then went on to describe the concept behind this, and the function (at least the concept of the function) showing an interactive applet that showcases this (the tortoise and the hare, which is another exponential sequence). The lesson then covered Sierpinski’s Triangle, which is another fractal, a graphic of Pascal’s Triangle, and then a colored (blue) version with the numerical values in order to show the patterns (within the values) within the applet. She then allowed the students to experiment with the applet, gaining a better understanding of the patterns that are within Pascal’s triangle. Then the instructor demonstrated to the class the interactivate “Flake Maker”, an applet that enables the user to continue a pattern that they create, graphically, through the use of fractals. Shortly afterwards, the instructor showcased the Interactivate Applet called “Fractured Pictures that creates different fractals based upon the inputs (side number, side length, Scale Factor, and Depth of fractal). The lesson concluded with the students with the scale factors of fractals, deriving great structural differences from simplistic calculation changes.