Set the short display skip as in Coxeter, “Regular Complex Polytopes (1974)”

I was reading Coxeter's "Regular Complex Polytopes" from 1974 and was struck not just by the mathematical content but also by the beautiful typesetting. In particular, I liked the fact that the vertical skip of a display equation after a short previous line w.r.t. two lines above is set to be the same as the vertical skip of a standard display equation. As I'm afraid that my description would be incomprehensible, I put a couple of paragraphs from p.54 of the said book:

I can mimic this effect by manually choosing \abovedisplayshortskip by referring to \abovedisplayskip and \baselineskip, but is there a way to automatically do that?

Unless the “short line” has excessive height or depth, this should do: setting \abovedisplayshortskip to the same as \abovedisplayskip minus the \baselineskip. Also \belowdisplayshortskip should be set to equal \belowdisplayskip.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\setlength\abovedisplayshortskip{\glueexpr\abovedisplayskip-\baselineskip}%
\setlength\belowdisplayshortskip{\belowdisplayskip}%
}
\makeatother

\begin{document}

\section{With Coxeter's setting}

An arbitrary inversion yields a new diagram formed by $n+2$ points
on a circle, and arcs through pairs of them orthogonal to this circle.
If $X_sX_tX_uX_v$ is a convex quadrilateral, Ptolemy's theorem tells us
that
$X_sX_t.X_uX_v-X_sX_u.X_tX_v+X_sX_v.X_tX_u=0,$
suggesting the investigation of numbers $(s,t)$ (functions of integers
$s$~and~$t$) that satisfy
$(s,t)(u,v)+(s,u)(v,t)+(s,v)(t,u)=0$
(Coxeter~1963), p.~160). This functional equation provides the rule
for constructing our modified frieze patterns'.

\section{Standard}

\setlength{\abovedisplayshortskip}{0pt plus 3pt}
\setlength{\belowdisplayshortskip}{6pt plus 3pt minus 3pt}

An arbitrary inversion yields a new diagram formed by $n+2$ points
on a circle, and arcs through pairs of them orthogonal to this circle.
If $X_sX_tX_uX_v$ is a convex quadrilateral, Ptolemy's theorem tells us
that
$X_sX_t.X_uX_v-X_sX_u.X_tX_v+X_sX_v.X_tX_u=0,$
suggesting the investigation of numbers $(s,t)$ (functions of integers
$s$~and~$t$) that satisfy
$(s,t)(u,v)+(s,u)(v,t)+(s,v)(t,u)=0$
(Coxeter~1963), p.~160). This functional equation provides the rule
for constructing our modified frieze patterns'.

\end{document}


If you plan to use displays also in \footnotesize (or other similar situations), you have to update also the setting for those.