What Your Character has in Common with . . . Math?

To me (and I think that a lot of you agree), characters are what make or break a novel. The plot can be wonderfully paced, the concept can be incredible, but if the people aren't either of those at the least, a dimension (the best dimension!) of the story is lost.

So for this topic, I went to my bookshelves and notebooks to find characters who exponentially enrich the books they live in. The ones that immediately came to mind: 
- Kathy from Mrs. Mike. I'll limit my (nearly unending) praise of this book here to this: This is a true story, so it's not  like the authors or the MC had any control over events, but the way they make her change and grow her is inspiring to behold. (Homesickness --> Belonging)

- Ponyboy from The Outsiders. His unknown mission is to find his feet and conquer his fears, but he doesn't realize that until the end of the book. By then, he has a pretty solid grasp on to go on. (Fear --> Purpose)

- Symone from The White Darkness. She becomes so strong over the course of the novel and has such a good voice that I could feet the heart-pounding, ice cold gravity of her circumstances.(Desire --> Satisfaction)

- The narrator from A Separate Peace. I honestly cannot remember his name, but I do remember the way he started out as a shaky, rambunctious schoolboy and ended as a shaky, bleakly-inclined young man. That was interesting.(Youth --> Wisdom)

My favorite way of thinking of these goings-on is as their arc.

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It's like a function that has a power of 2 in algebra. You chose a number for x, plug it into the equation, subject it to the trials of being stretched and shifted however called for, and, if your professor is like mine, graph it. And because it's x², you'll get a lovely parabola - an arc. All of that gritty math happened to make x (aka your character) change and grow.

(I had a math test today, if you were wondering.)

Good writers yank the reader into their character's lives so subtly that she didn't even notice. The fun I have experimenting with this is the best part of mylifeasawriter. *mushy grin*

I'd love to hear your takes on the characters I mentioned above, or tell about others who fit the nicely-developed bill.

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Ps - The copy of Leviathan that I finally ordered arrived today! So next time Mr. Westerfeld is in town, maybe another autograph outing is in order? ;)