Optimizing a document to contain the least amount of white space/most amount of text

Question

I am currently composing a cheat sheet for an exam using latex base. A lot of space on the page is wasted.

Can anyone give me some tips about how to reduce the amount of white space?

I suspect that the main culprit is \documentclass[8pt]{article} in the preamble, maybe there is a better document class for writing chunky documents?

Edit: In case it isn't clear, a lot of space appears to be wasted on the vertical and horizontal margins. The document does however need to allow enough space such that it is printable.

Edit 2: here is the current code. Please ignore the foreign language contents.

\documentclass[8pt]{article} \usepackage{amsmath} \usepackage{graphicx} \usepackage{hyperref} \usepackage[latin1]{inputenc}

\title{Zettel zur Mathe 2} \author{Oscar}

\begin{document} \maketitle

\\ \textbf{Zettel zur Mathe 2} \\ Eulersche Phi-Funktion:  \\ Quotientenregel: $f(x) = \frac{g(x)}{}h(x), f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{h(x)^2}$ \\ Kettenregel: $f'(x) = u'(v(x)) \cdot v'(x)$ \\ Produktenregel: $(f(x) \cdot g(x))' = f'(x) \cdot g(x) + f(X) \cdot g'(x)$ \\ L'Hôpital: $\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$ if $\lim_{x \to c} f(x) \vee g(x) = 0 \vee \plusminus \infty$ \\ Differentialquotient: $f'(x_0) = \lim_{x\to\infty} \frac{f(x_0 + h) - f(x_0)}{h}$ \\ Bogenlaenge: $\int_{a}^{b} \sqrt{1 + (f'(x))^2} dx$ \\ Partielle Integration: $\int^b_a u(x) v'(x) dx = [u(x)v(x)]^b_a - \int^b_a u'(x) v(x) dx$ \\ Taylor: $T(x) = \sum\limits_{n = 0}^\infty {\frac{{{f^{\left( n \right)}}\left( a \right)}}{{n!}}{{\left( {x - a} \right)}^n}} = f(a)
+ f'(a)(x-a) + \frac{f''(a)}{2!} \cdot (x-a)^2 + \dots$ \\ \textbf{Integrals:} \\ $ \int \sin{(x)} dx = -\cos{(x)} + C, \int \cos{(x)} dx = \sin{(x)} + C, \int \sec^2{(x)} dx = \tan{(x)} + C$  \\ $\int \frac{1}{\sqrt{1 - x^2}} = \sin^{-1}(x) + C = \arcsin(x) + C$ \\ $\int \frac{1}{\sqrt{1 - x^2}} = -\cos^{-1}(x) + C = \arccos(x) + C$ \\ $\int \frac{1}{x^2 + 1} dx= \tan^{-1}(x) + C = \arctan(x) + C $ \\ Complex Integrals: $\tan(x), \ln(x)$ \\ $\int e^x dx = e^x + C, \int \frac{1}{x} = \ln{(|x|)} + C$



\end{document}

Answer 1

Here's an example that shows how tightly things can be crammed without using too many bells and whistles.

\documentclass{article}
\usepackage[landscape,margin=0.25cm]{geometry}
\usepackage{multicol}
\usepackage{lipsum}
\begin{document}
\begin{multicols}{4}
\footnotesize
\lipsum[1-19]
\end{document}

One thing to notice is how I've used the multicol package.

But, when it comes to cheatsheets, I would not just work it as any other document. I would take another approach of using minipages to compartmentalize the various details I want to keep on the sheet.

So, I would in addition to using multicol as in the above example, I would define an environment for each type of note you want to make: let's call it note. And then I'll define a command \notetitle. So each cheatsheet note would be of the form

\begin{note}
  \notetitle{Definite Integral}
  Everything I want to remember about definite integrals
  will be entered here.
\end{note}

which will create something like

So that gives you the basic idea. Here's how I'll define that environment:

\newsavebox\aebox
\newenvironment{note}
  {\begin{lrbox}\aebox
    \begin{minipage}[t]{\dimexpr\textwidth/5
                                -\columnsep
                                -2\fboxrule
                                -2\fboxsep}
      \setlength\parskip{0pt}%%
      \setlength\parindent{0pt}%% make everything very tight
      \small\raggedright
  }{%%
  \end{minipage}%%
  \end{lrbox}%%
  \noindent\fbox{\usebox{\aebox}}\newline}
\newcommand\notetitle[1]{\par\textbf{#1:}\newline}

There's no particular reason to frame the box, but I find that if I don't, then it'll be hard to find things. Your call. If you don't want to frame things, then remove the call to \fbox and remove -2\fboxrule-2\fboxsep to save more space.

Since I'm going to use five columns across the page, I will divide the total \textwidth by 5. I need to take into consideration the space between the columns, hence -\columnsep.

You can then cram a lot into one page:

Obviously, I'm just repeating one of your notes. But, I wanted to populate the entire page so you can see how much information can potential fit on to a page.

Here's the full code:

\documentclass{article}
\usepackage{amsmath}
\usepackage[landscape,margin=0.125in]{geometry}
\usepackage{multicol}
\setlength\columnsep{1pt}
\setlength\fboxsep{2pt}
\newsavebox\aebox
\newenvironment{note}
  {\begin{lrbox}\aebox
    \begin{minipage}[t]{\dimexpr\textwidth/5
                                -1\columnsep
                                -2\fboxrule
                                -2\fboxsep}
      \setlength\parskip{0pt}%%
      \setlength\parindent{0pt}%% make everything very tight
      \small\raggedright
  }{%%
  \end{minipage}%%
  \end{lrbox}%%
  \noindent\fbox{\usebox{\aebox}}\newline}
\newcommand\notetitle[1]{\par\textbf{#1:}\newline}

\begin{document}

\begin{multicols}{5}

\begin{note}
  \notetitle{Quotientenregel $f(x) = \frac{g(x)}{h(x)}$}
  \footnotesize
  $f'(x) = \frac{g'(x)h(x) -
  g(x)h'(x)}{h(x)^2}$
\end{note}
\begin{note}
  \notetitle{Kettenregel:}
    $f'(x) = u'(v(x)) \cdot v'(x)$ \\ 
\end{note}
\begin{note}
  \notetitle{Produktenregel:} $(f(x) \cdot g(x))' = f'(x)
\cdot g(x) + f(X) \cdot g'(x)$ \\ 
\end{note}
\begin{note}
  \notetitle{L'Hôpital} 
    $\lim_{x \to c} \frac{f(x)}{g(x)} = 
     \lim_{x \to c} \frac{f'(x)}{g'(x)}$ 
  if $\lim_{x \to c} f(x) \vee g(x) = 0 \vee \pm \infty$
  \notetitle{Differentialquotient} 
    $f'(x_0) = \lim_{x\to\infty} \frac{f(x_0 + h) - f(x_0)}{h}$ 
  \notetitle{Bogenlaenge} 
    $\int_{a}^{b} \sqrt{1 + (f'(x))^2} dx$ 
  \notetitle{Partielle Integration} 
    $\int^b_a u(x) v'(x) dx = [u(x)v(x)]^b_a - \int^b_a u'(x) v(x) dx$ 
  \notetitle{Taylor} 
    $T(x) = \sum\limits_{n = 0}^\infty {\frac{{{f^{\left( n \right)}}\left( a \right)}}{{n!}}{{\left( {x - a} \right)}^n}} 
          = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!} \cdot (x-a)^2 + \dots$ 
\end{note}
\begin{note}
  \textbf{Integrals:} \\ $ \int \sin{(x)} dx = -\cos{(x)} + C, \int \cos{(x)} dx = \sin{(x)} + C, \int \sec^2{(x)} dx = \tan{(x)} + C$  \\ $\int \frac{1}{\sqrt{1 - x^2}} = \sin^{-1}(x) + C = \arcsin(x) + C$ \\ $\int \frac{1}{\sqrt{1 - x^2}} = -\cos^{-1}(x) + C = \arccos(x) + C$ \\ $\int \frac{1}{x^2 + 1} dx= \tan^{-1}(x) + C = \arctan(x) + C $ \\ Complex Integrals: $\tan(x), \ln(x)$ \\ $\int e^x dx = e^x + C, \int \frac{1}{x} = \ln{(|x|)} + C$
\end{note}
%%
.... no need to show all the repeated notes ....    
\end{multicols}
\end{document}

There's no reason to bother with nuisances like \title, \author, \maketitle. This isn't an actual article. Why waste space with such nonsense (unless you're publishing and it's not nonsense).

Avoid any formatting that likes to embellish things with whitespace. Don't use \\ unless you're presenting a table of values. Avoid using \newline except where absolutely necessary. I've whittled down the paragraph formatting by setting both \parskip and \parindent to 0pt. That'll save more space.