## Thursday, September 3, 2020

### Mathpix Snip

Originally Posted on  by

I came across this amazing tool that can convert images of math equations into LaTeX format. The tool can be found at https://mathpix.com/. I’ve tried it on a number of texts including some not so clear and it does a fantastic job of converting to LaTeX. Here is a screen showing part of a page from Paul’s Online Notes:

The way it works is you select the screen icon on the mathpix tool, the entire screen goes black and white, then we draw a square around the section we want to convert and that’s it. In this case, it generates the following latex

We’ll start with finding the derivative of the sine function. To do this we will need to use the definition of the derivative. It’s been a while since we’ve had to use this, but sometimes there just isn’t anything we can do about it. Here is the definition of the derivative for the sine function.
$$\frac{d}{d x}(\sin (x))=\lim _{h \rightarrow 0} \frac{\sin (x+h)-\sin (x)}{h}$$
since we can’t just plug in $h=0$ to evaluate the limit we will need to use the following trig formula on the first sine in the numerator.
$$\sin (x+h)=\sin (x) \cos (h)+\cos (x) \sin (h)$$
Doing this gives us,
\begin{aligned} \frac{d}{d x}(\sin (x)) &=\lim _{h \rightarrow 0} \frac{\sin (x) \cos (h)+\cos (x) \sin (h)-\sin (x)}{h} \\ &=\lim _{h \rightarrow 0} \frac{\sin (x)(\cos (h)-1)+\cos (x) \sin (h)}{h} \\ &=\lim _{h \rightarrow 0} \sin (x) \frac{\cos (h)-1}{h}+\lim _{h \rightarrow 0} \cos (x) \frac{\sin (h)}{h} \end{aligned}
As you can see upon using the trig formula we can combine the first and third term and then factor a sine out of that. We can then break up the fraction into two pieces, both of which can be dealt with separately.

Which when processed by LaTeX becomes:

This is rendered inside the mathpix tool but you’ll notice there isn’t a significant difference between the original and the converted image. I’ve converted some fairly rough images and it generally succeeds. It also gives you a confidence level on how well it thinks it’s done. It took under a second to generate the LaTeX.

As a harder test, I decided to attempt to translate a page from Jim Burns’ thesis. This is a thesis from the 1970s that was typed and the equations a combination of typed characters and hand drawn. The following image shows page 93 which is part of the proof for the connectivity theorem.

And here is the image analyzed by mathpix. Remarkably the conversion is almost perfect, the equations, in particular, are translated almost without error, even getting the subscripts on the subscripts correct. It got the delta F1 wrong at the start and it interpreted a mark on the paper as an apostrophe. I tried other pages that included derivatives and these converted without incident.