[TheForge] Re: lamp shade

[Mike Spencer]

> My question now is, do all these formulas give the same result? They
> look quite different.

Depends on what the letters in the formulas stand for.

Say you have a circular disk-shaped object. Area is pi times r-squared:

       a = pi r^2

but measuring the radius is hard while measuring the diameter is easy,
so you use a formula with diameter in it instead of radius. Area is pi
times (diameter divided by 2)-squared.

       a = pi (d / 2)^2

They're essentially the same formula but they look different.

*Proving* stuff like that, especially when each formula is half a page
of hentracks instead of a simple one-liner, makes my head spin.  So I
don't fully believe my own results until I go make a physical object
that uses the results and it comes out right. :-)

Yarn:

Math professor starts at the left of a whole wall of blackboard,
lecturing with his back to the class and filling the board with
algebra, integrals, differentials, tensor notation etc.  Twenty
minutes later, the board is full of hentracks with just a bit of clear
space way over on the right.  He says. "And so it's obvious that..."
and triumphantly chalks up a final equation.  Then he says, "...ummm",
ponders a moment, says, "ummmmm...", looks at his notes, looks at the
board, leaves the room and is gone for ten minutes.  Slams back into
the room and shouts, "Yes!  It *is* obvious!"

Some obvious things are more obvious than others. :-)


- Mike

-- 
Michael Spencer                  Nova Scotia, Canada       .~. 
                                                           /V\ 
mspencer at tallships.ca                                     /( )\
http://home.tallships.ca/mspencer/                        ^^-^^