Making an equation sheet for a 3'' x 5'' index card

As the title says I am trying to make a small cheat sheet for a 3"x5" index card in LaTeX. I'm using LaTeX so I can get a really small font and fit as much as possible. I've seen the flashcards package which is just to have front and back notecards, not necessarily made for equations. I also attempted to do a minipage with dimensions of 3x5 however the text did not seem to obey that either. I decided on the following which is a VERY messy solution to my problem

\documentclass[10pt]{book}
\usepackage[width=5in, height=3in]{geometry}
\usepackage{amsmath, amsfonts, amssymb}
\usepackage{physics}

\usepackage{lipsum}
\usepackage{multicol}
\pagestyle{empty}
\newcommand{unit}[1]{\mathrm{#1}}
\newcommand{\E}[2]{\times10^{#1}\,\unit{#2}}
\begin{document}
\begin{multicols}{3}
\begin{aligned} m_c&=9.11\E{-31}{Kg}\\ m_p&=1.67\E{-27}{Kg}\\ \mathrm{e}&=1.60\E{-19}{C}\\ \epsilon_0&=8.85\times10^{-19}\flatfrac{\unit C^2}{\unit N\cdot\unit m^2}\\ k_0&=8.99\times10^9\flatfrac{\unit N\cdot\unit m^2}{\unit C^2}\\ F&=k\frac{Q_1Q_2}{r^2}\\ \oint&\vec{E}\cdot\,\dd\vec{A}=\frac{Q}{\epsilon_0}\\ F&=qE\\ x&=v_0t+\frac12at^2\\ a&=\frac{v_f^2-v_0^2}{2x}\\ p&=\ell Q \end{aligned}\\ \begin{aligned} F&=qvB\sin\theta\\ V&=\ell vB\sin\theta\,\mathrm{(emf)}\\ \flatfrac{N_1}{N_2}&=\flatfrac{V_1}{V_2}\\ \end{aligned}
\lipsum[1-2]
\end{multicols}
\end{document}

I apologize for any sloppy code, my problem is that the equations in either the aligned nor align* don't automatically go over to the next column in multicols and it does not space properly. My other problem is that altering the margins in the way I did makes it so only one side of the card will appear on one page. I was wondering if there was a way to do this equation sheet to have all my equal signs aligned and spaced properly throughout 3 or more columns. There is also that overlap of the units and the rest of the text which does not look well.

• If you use aligned (or any math environment of that sort), the stuff will always run over the borders if it is too wide. Otherwise the minipage approach works. (Of course, if you were to use natural units, the stuff won't be that wide ;-) – marmot Aug 10 '18 at 0:33
• @marmot I want to do one card front and back, the problem with the mini page is that it doesn’t matter if I specify the dimension to be 3x5, the lipsum text runs over 3 inches long – Teh Rod Aug 10 '18 at 0:35
• You can't specify the vertical dimensions with minipage. You already load the geometry package, you can set them there, and multicols also work modulo the aligned stuff. – marmot Aug 10 '18 at 0:36
• @marmot even with the margins and a mini page it won’t automatically go into the next column in the align there as well – Teh Rod Aug 10 '18 at 0:53
• Yes, that's what I said. Even there are some attempts to automatize line breaks in equations, one often ends up doing them by hand. The main issue is that some of your relations like the one for \epsilon_0 are too wide. You could improve the situation by writing the fractions of units with \frac and replacing \times by \cdot, but I am afraid that won't fix all issues. If you were to give up on aligned you would save a bit more space but that won't solve all problems either. There is also adjustbox. None of these proposals will lead to a good-looking card, though. – marmot Aug 10 '18 at 1:00

Maybe this could help:

If everything fit in only one page you could you the use poster from tcolorbox:

\documentclass[10pt]{book}
\usepackage[width=5in, height=3in]{geometry}
\usepackage{amsmath, amsfonts, amssymb}
\usepackage{physics}

\usepackage{lipsum}
\usepackage{multicol}
\pagestyle{empty}
\newcommand{\unit}[1]{\mathrm{#1}}
\newcommand{\E}[2]{\times10^{#1}\,\unit{#2}}

\usepackage{tcolorbox}
\tcbuselibrary{poster}

\begin{document}

\begin{tcbposter}[
poster = {%showframe,
columns=3,
rows=1,
spacing=1mm,
},
]

\posterbox[
top=1pt,
bottom=1pt,
left=1pt,
right=1pt,
tile,
colback=white,
]{
name=Col,
sequence = 1 between top and bottom then
2 between top and bottom then
3 between top and bottom,
}{
\footnotesize
\begin{aligned} m_c&=9.11\E{-31}{Kg}\\ m_p&=1.67\E{-27}{Kg}\\ \mathrm{e}&=1.60\E{-19}{C}\\ \epsilon_0&=8.85\times10^{-19}\flatfrac{\unit C^2}{\unit N\cdot\unit m^2}\\ k_0&=8.99\times10^9\flatfrac{\unit N\cdot\unit m^2}{\unit C^2}\\ F&=k\frac{Q_1Q_2}{r^2}\\ \oint&\vec{E}\cdot\,\dd\vec{A}=\frac{Q}{\epsilon_0}\\ F&=qE\\ x&=v_0t+\frac12at^2\\ a&=\frac{v_f^2-v_0^2}{2x}\\ p&=\ell Q F&=qvB\sin\theta\\ V&=\ell vB\sin\theta\,\mathrm{(emf)}\\ \end{aligned}
$\flatfrac{N_1}{N_2}&=\flatfrac{V_1}{V_2}\\$
\lipsum[1-2]
}
\end{tcbposter}

\end{document}

NOTE: I removed the equation $\flatfrac{N_1}{N_2}&=\flatfrac{V_1}{V_2}\\$ from the aligned block In order to prevent the overflow of the dielectric constant. But if you reduce the font size to \scriptnote and augment the spacing to 6mm You could obtain this:

\documentclass[10pt]{book}
\usepackage[width=5in, height=3in]{geometry}
\usepackage{amsmath, amsfonts, amssymb}
\usepackage{physics}

\usepackage{lipsum}
\usepackage{multicol}
\pagestyle{empty}
\newcommand{\unit}[1]{\mathrm{#1}}
\newcommand{\E}[2]{\times10^{#1}\,\unit{#2}}

\usepackage{tcolorbox}
\tcbuselibrary{poster}

\begin{document}

\begin{tcbposter}[
poster = {%showframe,
columns=3,
rows=1,
spacing=6mm,
},
]

\posterbox[
top=1pt,
bottom=1pt,
left=1pt,
right=1pt,
tile,
colback=white,
]{
name=Col,
sequence = 1 between top and bottom then
2 between top and bottom then
3 between top and bottom,
}{
\scriptsize
\begin{aligned} m_c&=9.11\E{-31}{Kg}\\ m_p&=1.67\E{-27}{Kg}\\ \mathrm{e}&=1.60\E{-19}{C}\\ \epsilon_0&=8.85\times10^{-19}\flatfrac{\unit C^2}{\unit N\cdot\unit m^2}\\ k_0&=8.99\times10^9\flatfrac{\unit N\cdot\unit m^2}{\unit C^2}\\ F&=k\frac{Q_1Q_2}{r^2}\\ \oint&\vec{E}\cdot\,\dd\vec{A}=\frac{Q}{\epsilon_0}\\ F&=qE\\ x&=v_0t+\frac12at^2\\ a&=\frac{v_f^2-v_0^2}{2x}\\ p&=\ell Q F&=qvB\sin\theta\\ V&=\ell vB\sin\theta\,\mathrm{(emf)}\\ \flatfrac{N_1}{N_2}&=\flatfrac{V_1}{V_2}\\ \end{aligned}
\lipsum[1-2]
}
\end{tcbposter}

\end{document}

If this is not the case, you should consider to reduce the font size to \scriptsize in your example.