View source for HandWiki:HelpMathEquations

HandWiki uses [https://www.mathjax.org/ MathJax] for rendering equations. You can show equations as this <math>F_2=\frac{H_1}{H^2}</math> inline. This is programmed as:

<pre>
You can show equations as this <math>F_2=\frac{H_1}{H^2}</math> inline. This is programmed as:
</pre>

You can show equations using the LaTeX syntax  "dollar sign": 

$F_2=\frac{H_1}{H^2}$ 

As you can see, it positions the equation at centre. This is programmed as:

<pre>
$F_2=\frac{H_1}{H^2}$ 
</pre>

Alternatively, you can do this formula <math inline>F_2=\frac{H_1}{H^2}</math> as:

<pre>
<math inline>F_2=\frac{H_1}{H^2}</math>
</pre>

== More examples ==

See more examples here (original source [https://en.wikipedia.org/wiki/User:Jmkim_dot_com/TeX_Samples|here].

<source lang='html5'>
<math>E=mc^2</math>
</source>
<math>E=mc^2</math>

<source lang='html5'>
<nowiki><math>E=mc^2</math></nowiki>
</source>
<nowiki><math>E=mc^2</math></nowiki>

== Inequality Sign Test ==
<source lang='html5'>
<math>1<2</math>
</source>
<math>1<2</math>

<source lang='html5'>
<math>2>1</math>
</source>
<math>2>1</math>

<source lang='html5'>
<math>1\lt 2</math>
</source>
<math>1\lt 2</math>

<source lang='html5'>
<math>2\gt 1</math>
</source>
<math>2\gt 1</math>

== Inequality Sign Test 2 ==
<source lang='html5'>
<math>a<b</math>
</source>
<math>a<b</math>

<source lang='html5'>
<math>a < b</math>
</source>
<math>a < b</math>

<source lang='html5'>
<math>a>b</math>
</source>
<math>a>b</math>

<source lang='html5'>
<math>a > b</math>
</source>
<math>a > b</math>

<math>f(x)=1
</math>

== UTF-8 Test ==
<source lang='html5'>
<math>전압 = 전류 \times 저항</math>
</source>
<math>전압 = 전류 \times 저항</math>

<source lang='html5'>
<math>저항 = \frac{전압}{전류}</math>
</source>
<math>저항 = \frac{전압}{전류}</math>

== The Lorenz Equations ==
<source lang='html5'>
<math>\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}</math>
</source>

<math>\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}</math>

== The Cauchy-Schwarz Inequality ==
<source lang='html5'>
<math>\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)</math>
</source>
<math>\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)</math>

== A Cross Product Formula ==
<source lang='html5'>
<math>\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix}</math>
</source>

<math>\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix}</math>

== The probability of getting k heads when flipping n coins is ==
<source lang='html5'>
<math>P(E)   = {n \choose k} p^k (1-p)^{ n-k}</math>
</source>

<math>P(E)   = {n \choose k} p^k (1-p)^{ n-k}</math>

== An Identity of Ramanujan ==
<source lang='html5'>
<math>\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }</math>
</source>

<math>\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }</math>

== A Rogers-Ramanujan Identity ==
<source lang='html5'>
<math>1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots
= \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad for\,|q|<1.</math>
</source>

<math>1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots
= \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad for\,|q|<1.</math>

== Maxwell’s Equations ==
<source lang='html5'>
<math>\begin{align}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}</math>
</source>

<math>\begin{align}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}</math>