A equation skip problem (amsmath package and \above/belowdisplayskip)

Question

I puzzled by a problem about math equation skip for days. I set the \lineskiplimit, \lineskip, \abovedisplayskip and others length macros before and after equations all to zero, but there has still some skip (see pic). I wanted to know how to get rid of these skip.

There is the code

\documentclass{article}
\usepackage{amsmath}
\usepackage[margin=2in]{geometry}
\begin{document}
\setlength{\lineskiplimit}{0pt}
\setlength{\lineskip}{0pt}
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}
\setlength{\abovedisplayshortskip}{0pt}
\setlength{\belowdisplayshortskip}{0pt}\noindent
Some text some text some text some text some text 
some text
\begin{equation*}
a+b=c
\end{equation*}
Some text some text some text some text some text some text
\begin{equation*}
1^2+2^2+\dotsb+n^2=\frac{n(n+1)(2n+1)}{6}
\end{equation*}
Some text some text some text some text some text some text
\end{document}

Answer 1

Very strange request but you need (perhaps) \baselineskip=0pt but it's not easy to use it at only some places.

\documentclass{article}
\usepackage{amsmath}
\usepackage[margin=2in]{geometry}
\begin{document}
 \setlength{\lineskiplimit}{0pt}
 \setlength{\lineskip}{0pt}
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}
\setlength{\abovedisplayshortskip}{0pt}
\setlength{\belowdisplayshortskip}{0pt}    
\noindent
{\baselineskip=0pt
AAAA BBBBB  AAAA BBBBB AAAA BBBBB AAAA BBBBB 
\begin{equation*}
a+b=c
\end{equation*}
AAAA BBBBB  AAAA BBBBB AAAA BBBBB AAAA BBBBB 
\begin{equation*}
1^2+2^2+\dotsb+n^2=\frac{n(n+1)(2n+1)}{6}
\end{equation*}
AAAA BBBBB  AAAA BBBBB AAAA BBBBB AAAA BBBBB }
\baselineskip=10pt plus 2pt minus 3pt
AAAA BBBBB  AAAA BBBBB AAAA BBBBB AAAA BBBBB 
\begin{equation*}
a+b=c
\end{equation*}
AAAA BBBBB  AAAA BBBBB AAAA BBBBB AAAA BBBBB
\begin{equation*}
1^2+2^2+\dotsb+n^2=\frac{n(n+1)(2n+1)}{6}
\end{equation*}
AAAA BBBBB  AAAA BBBBB AAAA BBBBB AAAA BBBBB
\end{document} 

Answer 2

Under usual circumstances you shouldn't want to get rid of that skip. Altermundus told you how you can do it, namely by setting \baselineskip=0pt, but you see that the result is rather ugly. The reason for the skip is that the standard \baselineskip is 12pt, and you can check that the distance between the baselines is exactly 12pt in lines 1--3.

So why is there no skip around the second formula line? The point is: \baselineskip=12pt means that the distance of the baselines has to be at least 12pt, and you get that distance from the large fraction already, so TeX doesn't have put an additional skip.

Answer 3

Some text some text some text some text some text some
Some text some text some text some text some text some
Some text some text some text some text some text some
Some text some text some text some text\par\nointerlineskip
\vbox{\baselineskip=0pt\centering
\[a+b=c\]}\nointerlineskip
\noindent Some text some text some text some text some text some text

Other solutions, such as setting \baselineskip=0pt, have the defect that all the paragraph will be typeset with that parameter, with no separation between lines. Setting only \lineskip is also not a solution, as it will give uneven spacing between lines.