Sequences & Series Fractal Project
2-D Data
2-D Model Recursive Definition-Begin with a 3x3 square. Attach a square that is 1/3 the size of the previous square to each side of the previous cube. Each square will be 1/3 the length of the previous iteration.
3-D Data
3-D Model Recursive Definition-Begin with a 3x3 cube. Attach a cube that is 1/3 the size of the previous cube onto each face of the older cube. Each side length will be 1/3 the length of the cube from the previous iteration.
Sequences & Series Project Reflection
I thought that it was interesting that these complex models had a pattern to them that you could find an equation to represent. The information that we used in order to find out those equations was also interesting, especially when considering the 3-D model. The hardest part about this project was definitely finding these equations, because although there was a pattern to the series, you had to take so much into account, including areas added on, perimeter of one vs. perimeter of all, etc. On top of it all, you had to be able to interpret all of these different things and be able to plug it into an equation, so there were several ways you could go wrong, and it generally took several trials and errors before we found the right equation.
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."
When I reflect upon what we have done so far in math, I think that the most beautiful thing we have done so far are the Strange Attractors. It was incredible to me how a series of numbers could be graphed several times, and form an image that we see in nature commonly, such as a fern. Although, when Cathy exclaims, "Math is beautiful!" I can't say I necessarily agree, especially when I'm trying to understand a new concept.