Modeling Mathematics using Fractals

Factals are useful in many ways, For instance, a mathematical problem can be processed easier when thought about as fractals which makes it more conceptual. An example of this would be in attempting to sum \[\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...\] and so on with the denominator always being the next power of three all the way to infinity. Without a graph or a function or anything else to visually represent the problem stated, this can pose itself to be quite difficult. However, this can be visually represented by means of a fractal.

First, think of a string with length n. In order to get the first number of our sum, we need 1/3 the length of n. We then save the 1/3 pice and then take a third of a different 1/3 piece. This give us a 1/9 piece which will be added to the original saved 1/3 pieve. You could visually or mentally do this forever and come to the conclusion that you will never get more that 1/2 of the original n-lengthed string₂. Thus the answer to the original problem is 1/2. Now, you have just soved a mathematical problem that Calculus 2 students face with a fractal.

Now we get to watch the rest of this video! The presenter visually goes through this problem. Feel free to start at the beginning to review fractals.

Use the following links to explore more of the mathematics of Snowflakes and Fractals!