<ul class="pager"> <li class="previous"><a href="example3.html">← Previous example</a></li> <li><a href="index.html">Index</a></li> <li class="next"><a href="example5.html">Next example →</a></li> </ul> # A second example with [MathJax](http://www.mathjax.org/) 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) ### $$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for |q|&lt;1}.$$ > The previous equation corresponds to the following code, inserted *verbatim* in the Markdown part of this page: latex $$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod\_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for |q|&lt;1}.$$  ### [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! --- <ul class="pager"> <li class="previous"><a href="example3.html">← Previous example</a></li> <li><a href="index.html">Index</a></li> <li class="next"><a href="example5.html">Next example →</a></li> </ul>