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I'm looking for free software to create equations, and then be able to export to formats such as .jpg, .pdf, or maybe even MathML.

Open source is nice but not required, internet based would be great but a local installed application would work as well.

Being able to create graphs would be a positive, but I know of decent software for that so that's not a requirement.

I have used the equation creator and Word and that is workable, but not free and easy to distribute.

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    @Yrogirg - Thanks, not something I would recommend to my users, but looks like a lot of fun for personal use.2012-05-25

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The choice of tool is very dependent on what you are going to use it for. If you are going to include the equation in an e-mail for example, use an online tool to produce an image.

If the equation is for an article/report, then you should not use an online tool, but rather the build-in tools in Word (maybe look at MathType) or $\LaTeX$.

Examples of online tools who all use the $\LaTeX$-syntax are:

Edit: I have just discovered this page, which lists a lot of MathML editors.

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    @mrf - thanks for the feedback! I want a resource to prov$i$de to math teachers that I w$i$ll link to from a web application. Some teachers work at computers where they may not have the rights to install an app, or the app may be uninstalled later. A web link would work in all situations I expect to encounter. A really good installed app though would work for some users and I appreciate those recommendations too.2012-05-17
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The best online equation editor I found is Formula Sheet's: http://formulasheet.com/#r|ed

Exports to: PNG, PDF, TEX, MS Word 2007 or higher (using MathML)

The editor uses LaTeX, including buttons for symbols, and features many customization options like font, text color, background color, etc. If you click the 'Copy to Word' button at the bottom right, it will copy the equation's MathML to your clipboard, which can also be pasted into MS Word 2007 or higher. You can also use this site to store all your equations for later use.

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I have made an open source latex editor Latex Equation Toolbox - Github

That has a graphical Microsoft Word like equation editor, and a LaTeX math code editor.

It can convert LaTeX math to PNG, SVG and ASCII Math.

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There is also LaTeXiT, which comes with MacTeX.