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On 24 Jan 2006, wrote:

> That's a good explanation. I can see even though it's well done by you
> I still had to stop for a moment to see what you were getting at. Not
> as simple reading as a good anecdote. So when I tried a formula, that
> probably is slowing things down. But okay, you fit 4 x 1" in a
> cross-section of a 2" pipe. That has a good feel to the explanation.

tee hee hee. I guess it is a good thing that I am not a Math teacher!
Since you already knew "the answer", I knew that you would be able to look
at (or envision) the circle and see the 4 sections so I wasn't as detailed
as I should have been.

I have to think "outside the box" when it comes to math. You see, it seems
logical to me that if you have a 1" pipe and you want twice as much water,
then you just go to a 2" pipe (like if you have 1 apple and you want 2
apples, you just get another apple because 1 + 1 = 2). So, if you have a
2" pipe and you cut it in half - lenghtwise - then you have 2 1" pipes.
Of course that is wrong - but that is beside the point (hahaha). That
"seems" logical and fits with other math principles (like the apple). So,
I, and people like I am, have to be able to forget or unlearn what we are
sure we know in order to allow another (contradicting) idea to take its
place. That's easier said than done. I always do better if I can "see" it.

When my dad drew the circle and drew the horizontal line through it, my
brain said, "ok, you divided 2" in half, so now we have 2 sections of one
inch each. done."

Wrong.

When I said, "why?" (which I say a lot!), he
pointed out that yes, from the center line to the top of the circle was,
indeed one inch (we had cut it in half), but the horizontal line was still
2 inches long (because we had not cut it in half), making
the area 1" high times 2" long for 2" of space. Then he drew the line down
the center and we had four equal pieces and each was 1" high and 1" wide.
Geez, go figure.

And how many one inch pipes does it take to move as much water as one 4"
pipe? (Dad never could quit while I was ahead! ha).

Why, 16, of course. geez. Draw a bigger circle (you'll need it to see all
the lines. sheesh) Then cut the circle in 4 equal pieces horizontally and
in 4 equal pieces vertically. (Kinda like cutting brownies! OB food <g>).

Then the time came when I had to figure out how many city blocks
were in a square mile. (256, BTW). Who knew that math class was easier
than life would be? sheesh!

I admire (and, ok, I'll say it, envy) people like you who are
"math-brained". The whole world works on math. I have been able to learn a
lot, but every step is a struggle. I don't have any propensity for it.

OB food: (kinda <g>) That's why I'm not a good baker. Cooking is an art.
Baking is a math-based science.

It all has to do with that Right Brain/Left Brain thing. I just struggle
not to be "No Brained".

>
> Slide rule? I am trying to recall the last time I even saw one. I used
> to have a real one, K&E? They were kind of neat. I could do simple
> stuff on it.

I never did learn to use the slide rules. I wish I had. They were very
common before calculators. My dad started using one in the 1950s. He had
the bar ones but he loved the circles. He had one the size of a dinner
plate and one the size of a cup's saucer. He was an industrial bearing and
power transmission specialist and he could figure drives, gear ratios,
lift, thrust, and torque, etc. like it was child's play. I have to have a
calculator to figure the tip for lunch! haha.

When I look back on the days before calculators - much less computers -
and see all the math that was done by hand, I'm amazed.
I remember working those formulas that took a half page of notebook paper
just to write down before we started any calculations. sheesh.

>
> About driving your teachers nuts. I recall in high school, I used to
> stare out the window. But every time I got called on in trigonometry
> class, I came up with the answer. I don't even know how I could do that
> since sine, cosine and tangents were tedious.

But see, you just had a propensity for that. Something in the brain just
connects with some things and they come easy. I was like that in English.
My Composition 1 teacher would ask a question. I would answer correctly
and then she would say, "Why is that correct?"

"I don't know." (Geez, Lady, isn't being right enough???? Do I have to
know "why", too????) This is where math beats English six ways to Sunday.
2 + 2 = 4 and you don't have to know "why".

One day, after weeks of this, that poor lady got so frustrated that she
balled her hands into little fists and stomped her foot on the floor as
she hissed at me, "You can't possible get these answers right every time
and not know why they are right!"

Geez, I had an A+ in her class and I was a criminal.

Come to find out, there are pages and pages of "rules" that teach you
English grammar. sheesh, go figure. I didn't know. The only rule I had
ever heard about identifying the parts of speech was, "if it ends in -ly,
it's probably an adverb". I didn't know that there were dozens and dozens
of such rules. But, I did learn a lot. Now I know "why" - for all the
good that does me! <g>

I never took trig. I was required to take algebra. After that, I ran as
hard I could from all things math.

I use math every day, but I have never needed algebra "out in the real
world".

Schools really do need to get their acts together and give kids things
that they actually can use in life.

The one thing about Academe, is that they want to take 50 steps getting
somewhere when 10 will do.

>But if you can simplify
> problems, that's good - a lot of difficult problems are really simple,
> like e = mc(squared) tee hee. Reminds me of that physicist who had
> humorous yet serious books, 'Surely You're Joking, Mr. Feynman!'
> (Adventures of a Curious Character): Richard P. Feynman. He always was
> simplifying problems so he could get the answers in his head.
>
>

I'm not familiar wth Mr. Feynman, but he sounds like my kind of guy.

I've always simplified whenever I could. It is just easier for me.

When I took Economics, we were back to those half-page formulas. sheesh.
I was headed into a test in a couple of days and I knew that I could never
finish using those long, complicated formulas. I was stressed.

While I was doing homework and studying for the test, I
noticed that, interestingly, when you got your answer to the long formula,
there was a formula (something akin to A + B = C [a little more
elaborate]) to use to check your answer.

So I deduced that if I could plug my answer into A + B = C to determine if
it was right, I could use the same formula - with a tad of adjustment - to
get the answer in the first place. Since, A + B = C, then C - A = B and so
forth. I took the answer checker formula, turned it around and solved for
the answer to the problem. It saved me on that test - and all the others.

Elaine, too