This blog is still alive, just in semi-hibernation. When I want to write something longer than a tweet about something other than math or sci-fi, here is where I'll write it.
Wednesday, September 29, 2010
Wednesday Math, Vol. 129: The trouble with trigonometry
Here's the thing about trig. With a tiny amount of information, you can figure out a whole passel of stuff. Let's assume that this is the unit circle, which means it all the points where x² + y² = 1. The x coordinate is the cosine of the angle and the y coordinate is the sine. There are four other trig functions, but once you've got sine and cosine, they can be derived as follows.
Confused yet? So are my students. It's a lot of stuff to grasp, but it's that first glimpse into symmetry, the most important concept in mathematics. Just a little information and the assumption of symmetry can unlock so many tricky puzzles if your mind works that way.
I am completely convinced not every mind works that way, and to have a mind that works that way and thinks this is kind of cool... an even smaller set.