The Budget of Paradox

Sophia,

Greenways Academy. How is it? I’m sure there’s a big story behind the switch. I hope you give me the chance to understand it all some day. I’d love to know what your day looks like. I mean, is it just rolling out of bed and getting a tablet in your hands?

As you can imagine, I have a few opinions about this, but I doubt it matters to anyone. I’m very unhappy that Lynchburg schools were such a disappointment for both you and your sister. What’s really tragic is that your mother specifically mentioned the high-quality schools in Lynchburg during our divorce as justification why she had to live there. She refused to move anywhere more convenient for me or somewhere with better job opportunities for her. Nope, it had to be Lynchburg because the schools were the best in the nation. She really said that.

And here we are, ten years later, and both of my daughters have essentially dropped-out. Morey told me she barely graduated. She certainly didn’t earn it.

The whole thing makes me sad. And I’m sure your mother will never admit she was wrong. I think she’s incapable of admitting she was ever wrong about anything. She insisted that you and Morey were much better off being raised by a single mom in Lynchburg. I think ANYTHING is better than the situation we have now.

But, whatever. I mean, everything is broken and no one cares.

I hope Greenways Academy is the answer to your problems.

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