Chief Delphi - Crazy Math Formulas

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Quote:

Originally posted by Scott England
-d(a(du/dx))/dx+(d^2(b*(du^2/dx^2)/dx^2))+co*u+c1*(du/dt)+c2*(du^2/dt^2)=f(x,t)

this equation represents unsteady heat transfer in a fin

Actually, I think the c1*(du/dt) term is irrelevant. c1 will always be zero because the derivative is taken twice (with no intermediary steps in between) of the governing law (which is a function of t^2 only, not t), thus integration is guaranteed that the constant must equal zero. For comparison, consider an example of a sinusoid that is translated vertically in the y direction:

f(t) = sin(t) + 2

Then:

f'(t) = cos(t)
f''(t) = -sin(t)

Integrating twice yields:
f''(t) = sin(t) + C1t + C2

However, we are guaranteed that the sinusoid is translated, and should have no t term, thus C1 MUST be zero. With your above equation it's the same idea. c1 must be zero.

Seriously, putting aside my lame and incorrect argument above that has no validity at all, heat transfer equations (specifically fin analysis) are without any doubt in my mind the absolute worst equations I have ever come across. I'm actually impressed you found an equation for fins that is so simple... probably because it's in it's most generic form. Anyway, if you really like I can post the most obscene equation I can find in my heat transfer book. I remember it being very long, and containing many variables that took other equations to define what those variables mean, and so on and so on several times.

- Patrick

Lol, well Pat, according to a materials engineer like my dad, those "aren't hard at are to know by heart." Pfft. :P

I don't know about crazy, but I've always enjoyed this:

Quote:

(12+144+20+3*(4)^1/2)/7 +5*11 = 9^2 + 0

That is:

A dozen, a gross, and a score,
Plus three times the square root of four,
Divided by seven,
Plus five times eleven,
Equals nine squared and not a bit more

-John Saxon

George

Re: Crazy Math Formulas

Not much of a challenge but definatly a time filler.

pi/2 = 2/1 + 2/3 + 4/3 + 4/5 + 6/5 + 6/7 + 8/7 + 8/9 + 10/9...

It just repeats on and on.

Re: Crazy Math Formulas

Quote:

-d(a(du/dx))/dx+(d^2(b*(du^2/dx^2)/dx^2))+co*u+c1*(du/dt)+c2*(du^2/dt^2)=f(x,t)

This reminds me of an equation that my friend showed me that related to trebuceuts. The thing was a page long differential equation.

Re: Crazy Math Formulas

Quote:

Originally Posted by echos

Not much of a challenge but definatly a time filler.

pi/2 = 2/1 + 2/3 + 4/3 + 4/5 + 6/5 + 6/7 + 8/7 + 8/9 + 10/9...

It just repeats on and on.

i dont get it...
pi/2 is ~1.57, the first number on the other side of the = is a 2. and you keep adding more?
hm..

Re: Crazy Math Formulas

Quote:

Originally Posted by echos

Not much of a challenge but definatly a time filler.

pi/2 = 2/1 + 2/3 + 4/3 + 4/5 + 6/5 + 6/7 + 8/7 + 8/9 + 10/9...

It just repeats on and on.

How does this one work? As swando said, 1.57 =/= 2. I'm thinking that that pi/2 is supposed to be something else, but I have no idea what...

Re: Crazy Math Formulas

it give exactly half the value of pi thats all the pi/2 means. it means pi divided by 2 = 2/1 ...

Re: Crazy Math Formulas

Quote:

Originally Posted by echos

it give exactly half the value of pi thats all the pi/2 means. it means pi divided by 2 = 2/1 ...

but pi/2 > 2/1 + 2/3 already.
after a quick google i found the real formula:
pi/2 = 2/1 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * 8/7...

echos just made a symbol error :)

Re: Crazy Math Formulas

Thanks for the correction it was a little fuzzy in my mind. I found that one on google a while back ago and made a c program out of it. but i lost the source code.

Code:

 unsigned double float pi;

 unsigned int top;

 unsigned int bottem;

 unsigned int count;

 

 int main()

 {

 top = 2;

 bottem = 1;

 pi = top/bottem;

 

 while(count < 10000)

 {

 pi *= top/bottem;

 bottem += 2;

 

 pi *= top/bottem;

 top += 2;

 

 count++

 }

 

 printf ("pi = %f", pi*2);

 }

Re: Crazy Math Formulas

Try solving problem #2 in this thread:

http://www.chiefdelphi.com/forums/sh...ad.php?t=27647

Aside from that, I recommend looking at Olympiad problem books with inequalities in them, you can get some crazy formulas in there.

Talk to me on AIM or send me a PM if you want me to suggest some good books... I know quite a few.