[Tex/LaTex] Making an equation sheet for a 3” x 5” index card

geometrymath-modespacingvertical alignment

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 3×5 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}

enter image description here

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.

Best Answer

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}

enter image description here

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 increase 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}

enter image description here

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

Related Question