The Budget of Paradox

Sophia,
Yes, I know. I bitch and moan all the time about lawyers and judges. I’m sure you’re sick of reading about it. Yesterday, some of my thoughts came to a point. So I had to vent.

I was always a math weenie. Maybe your mother told you so at some point. Your father isn’t completely worthless. I really do like math. I like scribbling some fetish on the backs of napkins. Prime numbers. Integer factorization. Abundant numbers. Parlor tricks. Dumb stuff like that.

Right now, I’m writing some flight planning software. I ran into a situation I hadn’t ever considered before. How do you calculate where two circles intersect?

I’m sure you have had at least SOME geometry. Maybe even some trigonometry (side note: I learned trig in 8th grade; I’d love to teach you). Hopefully, you’ve had a class that had you drawing circles on graph paper given their center and radius. Circles are normally defined trigonometrically by sine and cosine.

Anyway, I wondered how I could find where two different circles intersected. And I was shocked to learn that the solution is entirely linear. That is, there is no trigonometry involved at all. No sines or cosines. No tangents. Just a straight-forward linear equation. I think this is fascinating. I know it’s not something most people ever think about, or get excited about. But I was truly surprised.

Number theory is full of surprises.

I’m going to guess that you were never very interested in math. Or inspired by it. But, for me, the purity of math is beautiful. It’s the poetry of logical ideas; the music of reason. In math, “obviously” is a dangerous word. If you ever get to study calculus, note that the Catholic Church banned the idea of the “infinitesimal” 400 years ago. And legend says that Pythagoras kept his discovery of irrational numbers a secret because he feared people would lose their faith in God if they knew the truth. People really do get serious about this.

And, if you learned nothing else today, you learned that the intersection of two circles can be computed without trigonometry.

Yours,
Mathgeek Dad