A length is a measure of distance. Many LaTeX commands take a length as an argument.
Lengths come in two types. A rigid length such as 10pt
does not contain a plus or minus component. (Plain
TeX calls this a dimen.) A rubber length (what plain
TeX calls a skip or glue) such as with 1cm
plus0.05cm minus0.01cm can contain either or both of those
components. In that rubber length, the 1cm is the natural
length while the other two, the plus and minus
components, allow TeX to stretch or shrink the length to optimize
placement.
The illustrations below use these two commands.
% make a black bar 10pt tall and #1 wide
\newcommand{\blackbar}[1]{\rule{#1}{10pt}}
% Make a box around #2 that is #1 wide (excluding the border)
\newcommand{\showhbox}[2]{%
\fboxsep=0pt\fbox{\hbox to #1{#2}}}
This next example uses those commands to show a black bar 100 points long between ‘ABC’ and ‘XYZ’. This length is rigid.
ABC\showhbox{100pt}{\blackbar{100pt}}XYZ
As for rubber lengths, shrinking is simpler one: with 1cm minus
0.05cm, the natural length is 1cm but TeX can shrink it down
as far as 0.95cm. Beyond that, TeX refuses to shrink any more.
Thus, below the first one works fine, producing a space of
98 points between the two bars.
ABC\showhbox{300pt}{%
\blackbar{101pt}\hspace{100pt minus 2pt}\blackbar{101pt}}YYY
ABC\showhbox{300pt}{%
\blackbar{105pt}\hspace{100pt minus 1pt}\blackbar{105pt}}YYY
But the second one gets a warning like ‘Overfull \hbox (1.0pt too wide) detected at line 17’. In the output the first ‘Y’ is overwritten by the end of the black bar, because the box’s material is wider than the 300pt allocated, as TeX has refused to shrink the total to less than 309 points.
Stretching is like shrinking except that if TeX is asked to stretch beyond the given amount, it will do it. Here the first line is fine, producing a space of 110 points between the bars.
ABC\showhbox{300pt}{%
\blackbar{95pt}\hspace{100pt plus 10pt}\blackbar{95pt}}YYY
ABC\showhbox{300pt}{%
\blackbar{95pt}\hspace{100pt plus 1pt}\blackbar{95pt}}YYY
In the second line TeX needs a stretch of 10 points and only 1 point was specified. TeX stretches the space to the required length but it gives you a warning like ‘Underfull \hbox (badness 10000) detected at line 22’. (We won’t discuss badness.)
You can put both stretch and shrink in the same length, as in
1ex plus 0.05ex minus 0.02ex.
If TeX is setting two or more rubber lengths then it allocates the stretch or shrink in proportion.
ABC\showhbox{300pt}{%
\blackbar{100pt}% left
\hspace{0pt plus 50pt}\blackbar{80pt}\hspace{0pt plus 10pt}% middle
\blackbar{100pt}}YYY % right
The left and right bars take up 100 points, so the middle needs
another 100. The middle bar is 80 points so the two
\hspace’s must stretch 20 points. Because the two are
plus 50pt and plus 10pt, TeX gets 5/6 of the stretch
from the first space and 1/6 from the second.
The plus or minus component of a rubber length can contain
a fill component, as in 1in plus2fill. This gives the
length infinite stretchability or shrinkability so that TeX could set
it to any distance. Here the two figures will be equally spaced across
the page.
\begin{minipage}{\linewidth}
\hspace{0pt plus 1fill}\includegraphics{godel.png}%
\hspace{0pt plus 1fill}\includegraphics{einstein.png}%
\hspace{0pt plus 1fill}
\end{minipage}
TeX has three levels of infinity for glue components: fil,
fill, and filll. The later ones are more infinite than
the earlier ones. Ordinarily document authors only use the middle one
(see \hfill and see \vfill).
Multiplying a rubber length by a number turns it into a rigid length, so
that after \setlength{\ylength}{1in plus 0.2in} and
\setlength{\zlength}{3\ylength} then the value of
\zlength is 3in.