Favorite Equation: Quadratic Formula - Solving for X

[OmCheeto]

y=x-sin(x)

(solve for x)

because after 20 years of scratching my head, some smarty said he was going to re-invent math to solve the problem.

I warned him...



(I finally found a "mathematician" that could explain the silliness to me)

 

[Char. Limit]

y=x-sin(x)

(solve for x)

because after 20 years of scratching my head, some smarty said he was going to re-invent math to solve the problem.

I warned him...



(I finally found a "mathematician" that could explain the silliness to me)

But that's easy to solve. $$x=Om(y)$$, where Om(y) is defined as the inverse of x-sin(x)

 

[OmCheeto]

But that's easy to solve. $$x=Om(y)$$, where Om(y) is defined as the inverse of x-sin(x)

Gulp. Did you know for the last 15 years I've been offering a $100 to anyone who could either solve the equation, or explain why it could not be solved.

I've never mentioned that at this forum as:
a. There are just way too many smart people here
b. It's a sign of a crackpot

I don't know why people can offer a million dollars for such things(Millennium Prize), but I get a bad label for doing such things.

Maybe I should have called it the "OmCheeto Prize"?

 

[Char. Limit]

Well, I believe you know me on Facebook, so you probably have my address. I expect my $100 within two weeks.

 

[dydxforsn]

I think I have two favorites, first, the infamous Fourier Series:

$f(x) = A_o + \sum_{n=1}^{\infty} A_n\cos{\frac{n\pi x}{L}} + \sum_{n=1}^{\infty} B_n\sin{\frac{n\pi x}{L}}$

which I think is one of the more interesting ideas in all of mathematics, and obviously one of the more applicable mathematical tools we use in everyday life. Joseph Fourier was truly brilliant to think along these lines (every function can be represented as an infinite series of sine and cosine, well, when you do a Fourier Transform anyway..), though I don't exactly know how much exactly he contributed to the theory of Fourier Series, I'm giving him the benefit of the doubt of total creativity :DSecond, I always liked the simple weighted average:

$\bar{x} = \sum_{i=1}^{n} P_i x_i$

I guess simply because it's extremely useful and just aesthetic to me, it's just always been on of my favorites, from quantum theory (expectation values) to statistical mechanics (with partition functions, Boltzmanm factors, etc.) it just always takes a conceptual center stage.

 

[Mike_Bson]

Ah, here we go:

$$\lim_{x\to0}\zeta(1 + ix)=\gamma$$

 

[Char. Limit]

Ah, here we go:

$$\lim_{x\to0}\zeta(1 + ix)=\gamma$$

But I get something different...

Actually, after the addition of $$\frac{i}{x}$$, I get the E-M constant.

 

[Sniperman724]

Mine is definitely v=v₀+at

 

[TylerH]

Distance along a curve is my favorite.
$$\int \sqrt{1-({{dy} \over {dx}})^2}dx$$

 

[Yayness]

I'm not sure what my favorite is, and I would probably keep switching favorite formula anyway.
I kind of like this one: $$\pi=\lim_{n\rightarrow\infty}2^n\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\cdots+\sqrt 2}}}}}_{n}$$
I like it because it goes quicker towards pi than what many other formulas do, but also because I managed to prove it 2 days ago, using regular 2ⁿ-gons.

 

[djosey]

$$e^{i\theta}=\cos\theta + i \sin\theta$$

This has already been mentioned but I thought it was the coolest thing ever when using series to show it.

For all of you talking about Euler's formula, i'd recommend looking at:
http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

Which gives what to me is a very good explanation, kinda breaks the wonder in a way but deepens the understanding.

I don't have a favorite formula, though the one posted by yayness is very interesting!

 

[MorallyObtuse]

Polar Inertial Momentum Inequality

 

[Yayness]

I don't have a favorite formula, though the one posted by yayness is very interesting!

It is, but it's not recommended if you want to calculate really large amounts of decimals in π. Even though it goes quickly towards π, you need to calculate a lot more decimals in $$\sqrt 2$$ than what the number of correct decimals in π will be.
Let's say you calculate k decimals in $$\sqrt 2$$, then you'll have k/2 correct decimals in $$\sqrt{2+\sqrt 2}$$ and k/4 correct decimals in $$\sqrt{2+\sqrt{2+\sqrt 2}}$$, and then k/8, k/16 and so on. I still like the formula though. It is simple and easy to remember.

 

[RichardParker]

$$n! \approx\sqrt{2 \pi n}(\frac{n}{e})^{n}$$

Stirling's Approximation. Haha.

 

[micromass]

My favorite equation is

$$e^\pi-\pi=20$$

It's a good way to check whether your computer is experiencing rounding errors

http://xkcd.com/217/

 

[eddybob123]

my favourite equation actually, is 1=1, cause it holds the fabric of math together

 

[Char. Limit]

my favourite equation actually, is 1=1, cause it holds the fabric of math together

But that's not true.

 

[eddybob123]

im not talking about beauty, I am talkingg about my favourite equation

 

[Char. Limit]

The equation 1=1, it's not true.

 

[TylerH]

Explain.

 

[Jabberwocky]

Euler's equation is beautiful, but I think my favorite is Stokes' Theorem:

Given a $k$-chain, $M$ in $\mathbb{R}^n$ and a $k-1$ form, $\omega \in \Omega^{k-1}\mathbb{R}^n$,
$$\int_{M}d\omega=\int_{\partial M}\omega.$$

All the classical theorems of div, grad, and curl, follow from this one elegant equation.