Publishing Math On Web Pages

Figure 1: Sven Carrying On As Usual About Calculus

We used MathJax for publishing math on web pages. This is fairly easy to set up according to their instructions, and you can refer to their demos page for specific examples.

Another great tool to use along with this is MathEQ. This is a builder tool that allows you to visually set up your equations. Then you can simply copy and paste these onto your MathJax page as Latex code.

Just for testing and reference, we’re posting some math from one of their main example pages. Our research probably won’t get more complex than any of the equations shown below, but you never know. Our Latest Articles are listed in the right column if you’re using a Desktop monitor, or below the content section if you’re viewing this on a Smart Phone. Please share your questions or feedback in the Comments section!

The Quadratic Formula

When $a \ne 0$, there are two solutions to $ax^2 + bx + c = 0$ and they are

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

The Lorenz Equations

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

The Cauchy-Schwarz Inequality

\[
\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq
\left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\]

A Cross Product Formula

\[
\mathbf{V}_1 \times \mathbf{V}_2 =
\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\
\end{vmatrix}
\]

Probability of getting $k$ heads when flipping $n$ coins:

\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]

An Identity of Ramanujan

\[
\frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }
\]

A Rogers-Ramanujan Identity

\[
1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q| < 1$}.
\]

Maxwell’s Equations

\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}

In-line Mathematics

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.

Conclusion

Now that we have the math publishing tools set up and ready to go, we already have several new articles posted. So this is proving to be a surprisingly efficient way to archive our work! Even if this site was never made public, it would still be the most valuable tool you could ever have for researching topics like math and science. So much better than jotting ideas down in an old notebook, where it will never be as clean, illustrated, and well organized!

Follow Us On Social Media

Also be sure to follow our social networks where you can stay up to date on our latest research! And feel free to share your thoughts in the Comments section below.