Creative Thinking in Mathematics
In trying to better my participation in the MOOC I'm in I started thinking about what creative things I know about. Well, I'm a math major and just recently took History of Mathematics. In one of our discussions, one of my classmates introduced us to crocheting geometry.
Here's a (hopefully) brief explanation. There are two main forms of geometry: Euclidean and non-Euclidean. Euclidean geometry is what most of us are probably familiar with, and is comprised of the x, y, andz-axes. These axes extend infinitely in the form of planes (think of a plane as a sheet of paper, a two-dimensional flat surface). Pretty much, Euclidean geometry is what people call geometry.
Non-Euclidean geometry can be broken into two different forms. First, there's Riemann geometry, or the geometry of a circle. You can sort of think of this as the latitude and longitude lines on a globe. There's more to it than just that, but essentially Riemann geometry is concerned with arcs on a sphere.
Finally, there's hyperbolic geometry; this is considered the geometry of outer space. Hyperbolic geometry consists of a single, two-sided surface that continuously expands and grows. It's actually a rather interesting concept. But to get to my point: it's really easy to model and picture Euclidean geometry, and Riemann geometry is performed on a sphere which is also easy to model and picture. However, it's really quite difficult to model hyperbolic geometry. It can be done, but in the past any such model was very delicate and fragile and easily broken. That is, until 1997 when Daina Taimina of Cornell University realized she could crochet a model of hyperbolic space.
At the end of this post is a website showing how this creative take on mathematics can be "applied" to the real world. I encourage you to simply Google "crochet hyperbolic geometry" and see what all you can find. You can also Google how to do this, it's very simple and can be done by someone who has never crocheted in their life. (Not to mention if you just keep going with it, it's a really cool end product!)