Posted: September 27, 2016, 7:53pm
Since this is a blog on an engineering university’s website, I’ll never apologize for a nerdy post (sorry, not sorry). I was recently reminded of the days when I got my first graphing calculator, back in high school calculus. It’s useful for graphing functions and it even had a tiny black-and-white screen to see what various functions looked like. When we learned about polar coordinates, I remember my brain practically melted, what is this new coordinate system?? To add fuel to that fire, our teacher showed us how to graph “flowers” on a polar coordinate. It’s quite simple:
r = cos(k*theta)
The independent variable, theta, is the angle, and the dependent variable, r, is the radius as a function of the angle. This sinusoidal will look like a flower, depending on your selection of k. Splitting the parameter into two controlling parameters (k = n/m), we find that for integer values of n and m, it will complete a perfect loop.
Published on July 25th, 2017
Last updated on March 22nd, 2021