Prometheus (in ) said:

| But that's the extreme case- I know a lot of people who can't do
| long division, and don't care to know how because they have a
| calculator. But then when they don't have a calculator handy,
| they're lost. That would indicate to me that they don't understand
| the math, they just know how to operate a calculator.

Hmm. I studied math through an advanced course in partial differential
equations - and, when it comes to solving even simple trig problems,
I'm one of those who're lost without a calculator.

I suppose I could do a little (lot of?) review and calculate my own
trig function values:

sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...

[ Anyone who did this in their head for sin(18 degrees = pi/10
radians) to solve Burt's problem can pat themselves on the back and
disregard the remainder of this post. All of those who evaluated /pi/
with a series approximation have a surplus of brain cells and a
serious need to "get a life".]

Ah. Glad I'm not alone :-)

It's a Good Thing, IMO, to understand the math - but I don't think
it's bad to not understand the math. Mathematics *and* calculators are
both tools.

Burt has a formula and, presumably, a calculator - and can grind out
whatever chord lengths he wants. He doesn't /need/ to understand the
mathematics. It wouldn't hurt if he did, but all the understanding in
the world won't produce any better results.

--
Morris Dovey
DeSoto Solar
DeSoto, Iowa USA
http://www.iedu.com/DeSoto/solar.html