User:Neocapitalist

I am ...

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vrwc

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13377h15 u53r 15 31337.

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${\frac {d}{dx}}\int _{a}^{g(x)}f(t)dt$This user likes math.

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(…so where is my $200?)

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That which is not forbidden is compulsory. This is the law of human existence.

• User:Neocapitalist/How to pick your nose

  User:Neocapitalist/evolution debates

  User:Neocapitalist/SDnet

  http://en.wikipedia.org/wiki/Help:Formula

  Thats: Help:Formula

  User:Neocapitalist/He-man (Tribute to PA...)

  User:Neocapitalist/boxes

Math

other stuff

$\mathbf {v} \in \mathbb {R} ^{n}$

$\mathbf {v} =\langle v_{1},v_{2},v_{3},...,v_{n}\rangle$

points on a sphere

The volume of a sphere is given by

${\frac {4\pi }{3}}R^{3}$;

Then

${\frac {dV}{dt}}={\frac {4\pi }{3}}3r^{2}{\frac {dR}{dt}}=4\pi r^{2}{\frac {dr}{dt}}$.

Since the infinitesimal distance on the surface of the sphere is given by

$d\theta \ ^{2}+d\phi \ ^{2}=dr^{2}$,

differentiating gives

${\frac {d\theta }{dt}}d\theta +{\frac {d\phi }{dt}}d\phi ={\frac {dr}{dt}}dr=\left({\frac {1}{4\pi r^{2}}}\right){\frac {dV}{dt}}dr$

points on a hypersphere

The volume of a hypercube should be given by

$\int _{-R}^{R}\left(\int _{-y}^{y}\left({\sqrt {R^{2}-x^{2}-y^{2}}}\right)^{3}dx\right)dy$

Then, if I have my numbers right,

Proof there exists a number of the form $a^{n}$ s.t. a, n are irrational, and $a^{n}$ is rational

Let $k=n={\sqrt {2}}$. Then $k^{n}={\sqrt {2}}^{\sqrt {2}}$. Now, ${\sqrt {2}}^{\sqrt {2}}$ is either rational or irrational. If it is rational, then the theorem is proven. If it is irrational, then we can choose a new $a=({\sqrt {2}}^{\sqrt {2}})$. Then $({\sqrt {2}}^{\sqrt {2}})^{\sqrt {2}}={\sqrt {2}}^{2}=2$, which is rational.

Riemann

$\zeta (z)=\sum _{n=0}^{\infty }{\frac {1}{n^{z}}}$ $\zeta (z)=0\wedge z\neq -2n$$\Rightarrow Re(\zeta (z))={\frac {1}{2}}$

Wiggy

$\int \equiv$