< activated (and the *paper* theme)
> To know how to include MathJax in a *StrapDown*-flavored HTML page, you can read this [example 3](example3.html).
To discover an even nicer way to import MathJax, read [the last example](example5.html).
> These examples are directly imported from [the samples from the mathjax.org website](http://www.mathjax.org/demos/tex-samples/).
> The following equations are included in the HTML source code as **pure LaTeX code**.
***
### The [Lorenz Equations](https://en.wikipedia.org/wiki/Lorenz_system#Overview)
### $$\left\\\{\begin{aligned} \dot{x} & = \sigma(y-x) \\\\ \dot{y} & = \rho x - y - xz \\\\ \dot{z} & = -\beta z + xy \end{aligned}\right. $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page (*ie.* after the opening ``xmp`` tag and before its closing):
```latex
$$\left\\\{\begin{aligned}
\dot{x} & = \sigma(y-x) \\\\
\dot{y} & = \rho x - y - xz \\\\
\dot{z} & = -\beta z + xy
\end{aligned}\right. $$
```
### The [Cauchy-Schwarz Inequality](https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Rn) (in $\mathbb{R}^n$)
### $$ \left( \sum\_{k=1}^n a\_k b\_k \right)^2 \leq \left( \sum\_{k=1}^n a\_k^2 \right) \left( \sum\_{k=1}^n b\_k^2 \right) $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
```latex
$$ \left( \sum\_{k=1}^n a\_k b\_k \right)^2 \leq \left( \sum\_{k=1}^n a\_k^2 \right) \left( \sum\_{k=1}^n b\_k^2 \right) $$
```
### A [Cross Product](https://en.wikipedia.org/wiki/Cross_product#Coordinate_notation) Formula
### $$\mathbf{V}\_1 \times \mathbf{V}\_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\\\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
```latex
$$\mathbf{V}\_1 \times \mathbf{V}\_2 = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\\\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix} $$
```
### The probability of [getting $k$ heads when flipping $n$ coins](https://en.wikipedia.org/wiki/Bernoulli_process#Binomial_distribution) is
### $$P(E) = {n \choose k} p^k (1-p)^{n-k} $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
```latex
$$P(E) = {n \choose k} p^k (1-p)^{n-k} $$
```
### An Identity of Ramanujan (obviously)
### $$ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
```latex
$$ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } $$
```
### A [Rogers-Ramanujan Identity](https://en.wikipedia.org/wiki/Rogers%E2%80%93Ramanujan_identities)
### $$ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q|<1$}. $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
```latex
$$ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}. $$
```
### [Maxwell's Equations](https://en.wikipedia.org/wiki/Maxwell%27s_equations)
### $$ \left\\\{\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}\right. $$
> The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page:
```latex
$$ \left\\\{\begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\
\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}\right.
$$
```
As you can see, math environment (like ``aligned``) are supported by MathJax, even with the default configuration and no external plugin.
****
### Inline equations are also supported.
Finally, while **display equations** look good for a page of samples, the ability to mix math and text in a paragraph is also important.
This expression $\sqrt{3x-1}+(1+x)^2$ is an example of an **inline equation** (inserted with the code ``$\sqrt{3x-1}+(1+x)^2$``).
As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.
### End of the examples
That's all for today!
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