On approximations

Approximations are cool. Really. I'm gaining a whole new appreciation for them this semester. For one thing, I'm in my first ever 'engineering' class, and really, all of engineering is based on approximating. Approximate a woodpecker as a mass spring system (no, seriously, see this link. In particular, check out the diagram on page 5). Approximate a spring as linear. Approximate, approximate, approximate.
Or take my theoretical mechanics class. We find crazy systems of differential equations and then approximate to solve them. Or solve them numerically, which involves approximating every step of the way (no pun intended).
Anyhow, the reason I was inspired to post after all this time was a combination of two quotes. The first:
"How fast is this rocket going? Just a general guess."
"Erm ... very fast."
"No, I want one sig. fig., not zero!"

And the second:
"It turns out 4 is a really lousy approximation for pi"

I will admit to being the speaker for the second quote. I was trying to create a wire binding for a small handmade book, and needed this coiled wire to be a circle with a given radius. Not being one for measuring sticks, I needed to figure out how long I needed to coil the wire before tying off. Since I wanted a circle of at least that given radius, I figured I'd round pi up a bit, but ... well, as the quote says, 4 is a pretty lousy approximation for pi.

Ah, the adventures of life.

:-)