Sandbox

Sandbox

Here's just a play page, so I can try to work out what wiki is all about. Bit of luck, I might work it out one day.

Lists

All I want is:

• easy editing.
• traceability.
• simple formating.
• good linking.
• good searchability.
• ability to include graphics, easily.

Numbered lists work like this:

1. item
2. item
   1. nested, too!

Definition lists look like this:

CPU

Central Processing Unit.

RAM

Random Access Memory.

ROM

Read Only Memory.

Tables

Table label

		colspan
		coltitle1	coltitle2	coltitle3
rowspan	rowtitle1	1	2	3
	rowtitle2	1	2	3

subsection

And good old <pre> tag stuff like this:

# ls -l
total 3826
-rw-r--r--  1 stix  wheel  1413137 Nov 12 10:35 231323.pdf
-rw-r--r--  1 stix  pc      524288 Sep 24 21:20 P4P800-E.ROM
drwxr-xr-x  3 root  wheel      512 Nov  2 00:08 screens

How does that look?

Math Test

See Displaying a formula at meta for more info on formulas.

[math]\displaystyle{ \sum_{n=0}^\infty \frac{x^n}{n!} }[/math]

Surprising π, Basel Problem

[math]\displaystyle{ \sum_{n=1}^\infty \frac 1{n^2} = \frac1{1^2} + \frac1{2^2} + \frac1{3^2} + \frac1{4^2} + \cdots = \frac{\pi^2}6 }[/math]

Sum of a divergent series

[math]\displaystyle{ \sum_{n=1}^\infty n={-\frac 1{12}} }[/math]

Stirlings Approximation (factorial)

[math]\displaystyle{ n! \sim \sqrt{2\pi n}\left(\frac{n}{e}\right)^n }[/math]

Surprising Factorial

[math]\displaystyle{ ^1/_2!=\frac{\sqrt\pi}2 }[/math]

Gamma Function

[math]\displaystyle{ \Gamma(z) = (z-1)! = \int_0^\infty x^{z-1} e^{-x}dx }[/math]

Windschitl approximation

[math]\displaystyle{ \Gamma(z) \approx \sqrt{\frac{2\pi}z} {\left(\frac ze \sqrt{z \sinh \frac 1z + \frac 1{810 z^6}}\right)}^z }[/math]

[math]\displaystyle{ 2\ln\Gamma(z) \approx \ln\left({2\pi}\right) - \ln{z} + z\left(2\ln z + \ln\left(z\sinh\frac 1z + \frac 1{810z^6}\right)-2\right) }[/math]

Nemes approximation

[math]\displaystyle{ \Gamma(z) \approx \sqrt{\frac{2\pi}z} \left({\frac 1e \left(z+\frac 1{12z-\frac1{10z}}\right)}\right)^z }[/math]

Fibonacci Sequence

[math]\displaystyle{ F_{n} = F_{n-1} + F_{n-2} }[/math]

[math]\displaystyle{ F_{n} = {\frac {\varphi ^{n}-\psi ^{n}}{\varphi -\psi }} = {\frac {\varphi ^{n}-\psi ^{n}}{\sqrt {5}}} }[/math]

[math]\displaystyle{ F_{n} = \frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{2}{1+\sqrt{5}}\right)^n\cos\left(n\pi\right)\right) }[/math]

where:

[math]\displaystyle{ \varphi = \frac{1+\sqrt{5}}{2} \approx 1.61803398875\cdots }[/math]

and:

[math]\displaystyle{ \psi = {\frac {1-{\sqrt {5}}}{2}} = 1-\varphi = {-1 \over \varphi } \approx -0.61803398875\cdots }[/math]

[math]\displaystyle{ \Phi = -{\frac {1-{\sqrt {5}}}{2}} = \varphi-1 ={1 \over \varphi } \approx 0.61803398875\cdots }[/math]

Quadratic

[math]\displaystyle{ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} }[/math]

Euler's Identity

[math]\displaystyle{ e^{i\pi}+1=0 }[/math]

which is a special case of the more general Euler's formula:

[math]\displaystyle{ e^{i\theta}=\cos \theta+{i}\sin \theta }[/math]

for [math]\displaystyle{ \theta=\pi }[/math]

Alternately, for tau fans:

[math]\displaystyle{ e^{i\tau}=1 }[/math]

e Limit Representation

[math]\displaystyle{ e = \lim_{n\rightarrow\infty}{\left({1+\frac 1n}\right)^n} }[/math]

[math]\displaystyle{ e = \lim_{n\rightarrow 0}{(1+n)}^{\frac{1}{n}} }[/math]

[math]\displaystyle{ e = \sum_{n=1}^{\infty}{\frac 1{n!}} }[/math]

[math]\displaystyle{ e^x = \sum_{n=1}^{\infty}{\frac {x^n}{n!}} }[/math]

Willans formula for Primes

[math]\displaystyle{ n\mathrm{th\,prime} = 1 + \sum_{i=1}^{2^n}\left[\left(\frac n{\displaystyle\sum_{j=1}^i\left[\left(\cos \pi \frac{(j-1)!+1}j\right)^2\right]}\right)^\frac 1n\right] }[/math]

Law of Cosines

[math]\displaystyle{ c^2=a^2+b^2-2ab\cos{C} }[/math]

Force

[math]\displaystyle{ F=ma=ma_c=\frac{mv^2}r=mr\omega^2=\frac{Gm_1 m_2}{r^2} }[/math]

Tetrahedral angle

Also the bond angle of methane!

[math]\displaystyle{ \arccos\frac{-1}3=90^\circ+\arcsin\frac 13=2\arccos\sqrt\frac{1}{3}=2\arctan\sqrt 2\approx{109.47}^\circ }[/math]

Dihedral angle

[math]\displaystyle{ \cos\theta=\frac{\cos(\angle{APB})-\cos(\angle{APC})\cos(\angle{BPC})}{\sin(\angle{APC})\sin(\angle{BPC})} }[/math]

e.g. for C60, aka Buckminsterfullerene (buckyballs):

[math]\displaystyle{ \arccos\frac{\cos{120^\circ}-\cos{108^\circ}\cos{120^\circ}}{\sin{108^\circ}\sin{120^\circ}} \approx {142.623}^\circ }[/math]

Where 120° is the angle between the vertices of a hexagon, and 108° is the angle in a pentagon.

Lorentz gamma

[math]\displaystyle{ \gamma=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}} }[/math]