How to make the margins relative to the actual content rather than the baseline?

Question

I need to have small margins in my document. It seems that the margins are relative to the baselines rather than the content.

See this example, where the content is cut out of the page:

\documentclass{article}

\usepackage[paperwidth=10cm, 
            paperheight=3.2cm,
            margin=0mm]{geometry}

\begin{document}

We have
\[ A= 2^{N-2}  \]
\[ B= 2^{N-1}  \]
\[ C= 2^{N-2}-\frac{(1+i)^N+(1-i)^N}{4}  \]
\[ D= 2^{N-2}+\frac{(1+i)^N+(1-i)^N}{4}  \]

\end{document}

How to make the margins relative to the actual content rather than the baseline? Is it possible?

Answer 1

It's not clear what you want to get, but the explanation about the cropped part is easy: the last baseline sits at the bottom of the paper, because of margin=0pt; however, LaTeX allows the depth of the last line to be at most 5pt before taking countermeasures. The relevant parameter is \maxdepth.

\documentclass{article}

\usepackage[paperwidth=10cm,
            paperheight=3.2cm,
            margin=0mm]{geometry}

\setlength{\maxdepth}{0pt}

\begin{document}

We have
\[ A= 2^{N-2}  \]
\[ B= 2^{N-1}  \]
\[ C= 2^{N-2}-\frac{(1+i)^N+(1-i)^N}{4}  \]
\[ D= 2^{N-2}+\frac{(1+i)^N+(1-i)^N}{4}  \]

\end{document}

Answer 2

As typography goes this is bad practice, but I suspect it is precisely what you want.

\documentclass{article}
\usepackage[paperwidth=10cm,showframe,
            paperheight=3.2cm,
            margin=0mm,bottom=5pt]{geometry}
\lineskip 1pt plus 1pt minus 1pt
\begin{document}

We have
\[ A= 2^{N-2}  \]
\[ B= 2^{N-1}  \]
\[ C= 2^{N-2}-\frac{(1+i)^N+(1-i)^N}{4}  \]
\[ D= 2^{N-2}+\frac{(1+i)^N+(1-i)^N}{4}  \]

\end{document}

The 5pt bottom margin appears to be a magic number for any descenders (any font size), even using a default \lineskip.

---

Even more dramatic results can be obtained using:

\lineskip=0pt plus 1fil
\begin{document}
\baselineskip=0pt

---

The downside is that only descenders (anything below the baseline) will go below the bottom margin.

An alternative is to put the baseline at the very bottom of each equation using \raisebox, only you can't put display mode math inside a \raisebox (at least not without using a \parbox, which leads to too much vertical space). Anyway, the following fakes display mode math (without equation numbers).

\documentclass{article}
\usepackage[paperwidth=10cm,
            paperheight=3.2cm,
            margin=0pt]{geometry}

\newcommand{\mybox}[1]% #1 = contents
{\ifvmode\vskip\lineskip\else\newline\fi
 \centerline{\raisebox{\depth}{$\displaystyle #1$}}%
 \vskip\lineskip}

\lineskip=1pt plus 1fil

\begin{document}
We have
\mybox{ A= 2^{N-2}  }
\mybox{ B= 2^{N-1}  }
\mybox{ C= 2^{N-2}-\frac{(1+i)^N+(1-i)^N}{4}  }
\mybox{ D= 2^{N-2}+\frac{(1+i)^N+(1-i)^N}{4}  }
\end{document}