math poetry?

While browsing around, I found a poem about irrational numbers that I believe rings true.

On Irrationality

Some judge quickly the crazies and budding neon spores
Painted in the run down studio with sloppy splotchéd floors.
My ears wilt when waves carry a sign of numerical distress
That the weak of mind have all my rules obsessed,
But what they can't see beyond the eaves and pies
Are the endless strings of digits stretching well into the sky

Fin.

polar freeze

While on a recent trip to Florida, I was messing around with polar coordinates. I made a few interesting discoveries, although nothing too fancy.

I guess a diagram would be useful here:

If you can read that you'll know I was trying to find angle Beta.

After multiple failures, I started thinking: if the tangent line was at the pole, then both angles (Theta and Beta) would be zero (sort of a stretch). The distance r would be zero, so only dy/dx and dr/d (Theta) would be positive. I know that at the pole if r=zero but r' does not equal zero, then tan (theta) is equal to the slope of the tangent line, and that the sine of beta was zero, so I started setting sin(Beta) equal to things that also equal zero, such as rand Theta. Theta doesn't really make much sense, since the sine of two different angles that don't have the same reference angle are never the same. Thus, for a while I assumed sin(Beta)=r. Then since sine and cosine never simultaneously equal zero, I set cos(Beta)=dr/d(Theta), since dy/dx doesn't make intuitive sense either, because it's more rectangular. So if you managed to get through the most complicated, incoherent paragraph I've ever written, then you realize that I realized:

So that was pretty cool, I guess. I found the angle just by taking the inverse tangent of the right side. That's when another cool idea hit me (nerdiest blog ever?). Since the sine of Beta was equal to r and the cosine to r'. I substituted them into the definition of the derivative in polar form. That's when the greatest part came. When you do that you can use the sine and cosine angle addition formulas to obtain that the sin(Theta + Beta)/cos(Theta + Beta) is equal to dy/dx. In other words:

Why's the first parenthesis so bad? I don't know, but this works like a charm if you remember Beta is between O and pi/2. This might be the first formula I've made that may be somewhat useful sometime, someday, somehow...if someone else didn't do it first.

It's called "polar freeze" because when I came back to my house, parts of me shriveled up.

on math, death, and digressions

naI ma I. So you hate math. Cool. I'm not an expert by any means, nor claim to be one. I'm not even so great at math myself, but I love it. Being fluent in math is being fluent in pure nature. Not everyone can appreciate math, as high schools around the world have pressed everything math isn't into everybody's head. It's not about formulas and equations and solving for x. It's about discovering fundamental truths and learning about yourself along the way. It's about expanding your mind so it doesn't grow dull. And above all, it's the story of human ingenuity. As I find things interesting, I'll post them. If you have found anything interesting as of late, please leave a comment. Let this be my disclaimer, and without further ado:

I always enjoy messing around with De Moivre's Theorem (Yes, I know there's a circumflex). Random identities, anyone?



That's supposed to be sin(3x), but my latex skills are lackluster. And while I'm here:

Please send me challenge problems, though I probably can't solve any worth sending!