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I've seen people using fancy equations in ham.SE. How can I do that?

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Short answer: use MathJax! There's a great cheat-sheet style tutorial and quick reference here! Also if you click "More" in the formatting tips near the edit box for any question or answer, you get taken to a web page that mentions MathJax and links to a site with TeX formatting help, but the cheat sheet is way better. By the way, you can see the MathJax syntax for any MathJax equation by right-clicking the equation, if you have a mouse. On an Android or iOS device, try long-pressing.

Long answer:
Ever since the creation of the world-wide web, there has been a need to easily put equations in web pages. The official stewards of internet standards such as HTML, the World Wide Web Consortium (W3C), have proposed a specification for a standard known as MathML. MathML is great, but it has two major shortcomings. First, it's based on XML, so its syntax is long and clumsy to work with. Second, actual progress in web standards like MathML entirely depends on the authors of browser applications, and a standard is not really a standard until the great majority of modern browsers support it. Unfortunately support for MathML has not reached that milestone yet.

But not to worry! Some clever programmers came up with an ingenious work-around that works in just about every browser! The work-around is called MathJax. It's a Javascript library. All modern browsers support Javascript, so any author can easily embed math into an HTML page by merely linking to the MathJax library.

In the browser, the MathJax library scans the HTML for MathJax syntax, and when it finds some it uses Javascript magic to translate that syntax into something your browser can display, whether that is MathML or just a rendered image of an equation. Problem solved! Ingenious! In my opinion, if there were a Nobel prize for computing, which there isn't, then the creators of MathJax should get it.

If you're wondering about the syntax used by MathJax, it's based on the syntax used by TeX and its derivative LaTeX, which is much easier to use than MathML syntax. LaTeX has been rendering equations in textbook quality for decades. To quote the web site, "LaTeX is the de facto standard for the communication and publication of scientific documents."

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