Crazy Math Formulas

[jon virgi]

does anyone know any crazy math formulas or sites for them?

[srjjs]

Just what do you mean by crazy?

[Etbitmydog]

If you're going into engineering as a major, you'll come accross this. This is a dynamics formula that relates acceleration of one point, to the acceleration of another point, to the angular acceleration of the object, and angular velocity of the object and a velocity relavie to another point. the parentasies are added because that means that the vector is such relative to such. All the following are vectors.

Since i don't have all the proper symbols,
I'll use % for angular velocity
$ for angular acceleration

a(B)=a(a) + $Xr(B/A) + %X[%Xr(B/A)] + 2%X(v(B/A)+a(B/A)

X stands for cross product
r is a vector and (B/A) means that the vector at point B is relative to A.

This is math.. Isn't it?

[Jim]

http://antigravitypower.tripod.com/M...ems/index.html

[jon virgi]

I mean either like really tough problems, or even better, really weird, or odd formulas. Ive seen one before that was able to tell the amount of miles a tornado would last based upon its wind speed. Do you know any odd or weird formulas?

[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 is tough to type in without an equation editor, (du/dx) denotes the partial derivative of u with respect to x, (du^2/dt^2) denotes the second partial derivative of u with respect to t, etc.
anyways, this is a model equation from my finite element analysis class
When b=0, c2=0, co=0, c1=rho*A, a=kA
this equation represents unsteady heat transfer in a fin

When a=0, b=E*I, co=k, c1=0, c2=rho*A
this equation represents transverse vibrations in a beam

When a=E*A, b=0, c1=0, c2=rho*A, co=0
it represents longitudinal motion(vibration or wave propogation) of a slender rod

all of these require initial conditions and boundary conditions to be specified, but that would have been alot more typing and i think it looks intimidating enough already

[jon virgi]

sweet, does that formula have a name or something, so i could find more out about what it does and such? what is rho*A? Is kA supposed to be a an acid equilibria constant(im obviously thinking chem)? Thanks for the formula.

[Scott England]

we just call this equation the model equation, since by varying the coefficients you can model tons of stuff, from vibrations in any which direction, heat transfer through conduction or convection, probably lots more stuff but that's the bulk of what we focus on.
Its just a good overall exercise since it includes second and fourth order spatial derivatives and first and second time derivatives.

k can be any number of things, but my major is ESM(engineering science and mechanics), some places call it Applied Mechanics, in either case, i haven't touched most forms of chemistry since freshman year. So no, kA is not a chemical property. In heat transfer problems, k*A would be thermal conductivity of the material*cross sectional area. In solid mechanics and dynamics, k would be a spring constant, or a radius of gyration (neither of those showed up in the examples i typed in)In solid mechanics problems, rho*A would be density of the material times area, E*A would be Young's Modulus * area. Etc.

There's lots more about the Finite Element method than i can ever write in a CD post, i'd highly recommend taking a course in it in college. I believe most companies use it fairly extensively as a more realistic way of modeling things that don't perfectly match text books (hopefully any of the Professional Engineers in here can back me up on that) I just took the Fundamentals of Engineering exam (all 8 hours of it) on saturday, so i've got at least 5 years to go before I can be Scott England, P.E. and now at least 2 years of grad school before i'll ever hit a real company extensively.

[srjjs]

Einstein+Pythagoras:
E= m c^2= m ( a^2 + b^2)

The limit as n goes to infinity of sin (x) /n is 6.
Cancel the n in the numerator and denominator.

[jon virgi]

your einstein + pythagoras does not work. c in the einstein equation is the speed of light (constant )(3x10^8). Einsteins equation can be used to calculate stuff like bond energies and crap like that in MeV (mega electron volts).

now with the limit you posted , Lim n->infinity (sin(x))\n = 0, and not 6. there's no n in numerator, so denominator gets infinitely large, hence, it equals 0.

If you had something like Lim x->0 (sin(x))/x , then the answer is 1. since lim x->0 sinx/x = 0/0 , then we can use L'Hopitals rule, take derivative, get Lim x->0 (cos(x))/1 = 1/1=1

I put that in case u were unsure of limits, b/c the one u gave did not make sense.

[srjjs]

They are meant to be jokes.

The first is obviously replacing the c^2 in einstein's equation with the a^2+b^2 it equals according to the pythagorean theorem.

In the second, the top says sin x, and the bottom is n. Rearrange to get (six n)/n. Limit as n goes to infinity is therefore six.

[Jared Russell]

e ^ (pi * i) + 1 = 0

My Calculus teacher gave the above as proof that God exists...

[Raven_Writer]

http://mathworld.wolfram.com/

I'm not sure if it's got "crazy" formulas, but it does have many I never knew existed (even though I'm only in year 3 of integraded math)

[Pat Bogard]

This one is used to show enzyme kinetics, its actually derived through about 20 equations

Variables and Explanation of symbols used:
{} = subscripts
[] = concentration
E = enzyme
S = substrate
ES = enzyme-substrate bonded together
[S] = concentration of substrate
K{M} = (k{-1} + k{2})/k{1}
where k{1}, K{-1}, and k{2} are rate constants for the reaction these are dependant on the substrate and enzyme
V{max}= k{2}*[E]{T}
[E]{T} = [ES]

and the equation
Michaelis - Menten Model:
V{0} = V{max}*([S]/[S] +K{M}

[Gadget470]

Originally posted by Abwehr
e ^ (pi * i) + 1 = 0

My Calculus teacher gave the above as proof that God exists...

Care to explain how?