Situational assessment about vertical space commands

Question

I would like some assessment on the situational utilities of various vertical space commands, namely: \smallskip, \medskip, \bigskip, \vspace*{value}, \\[value].

\smallskip, \medskip, \bigskip, and \vfill are formed using \vspace.

But the above do not produce a vertical space in the following code

    \documentclass{book}
\usepackage{geometry}
\geometry{ paperheight=21cm, paperwidth=21cm, left=8mm, right=8mm,
  top=21mm, bottom=21mm}

\usepackage{fix-cm}
\makeatletter
\renewcommand\normalsize{%
   \@setfontsize\normalsize{13pt}{15pt}
   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
   \abovedisplayshortskip \z@ \@plus3\p@
   \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
   \belowdisplayskip \abovedisplayskip
   \let\@listi\@listI}
\makeatother

\usepackage{bm}                % makes bold arguments
\usepackage[x11names]{xcolor}  % loads 317 named rgb colours

\usepackage{amsmath}
\usepackage{amsthm}

\boldmath
\renewcommand{\seriesdefault}{\bfdefault}

\newcommand\blskip{\\[0.3\baselineskip]}

\begin{document}

\normalsize

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}

\section{Fourier Transform}

\begin{theorem}
  [\color{blue} \textbf{Convolution Property of Fourier Transform}]
  \label{convolution}

  \textcolor{blue}{\bigskip This is not insterted on a new line}
  \textcolor{blue}{\vspace{8pt} This does not work either}

  \textcolor{blue}{\blskip This worked as intended}

  The Fourier transform of the product of two functions, \( u_1(t) \)
  and \( u_2(t) \), is equal to the product of the Fourier transforms
  \( F(u_1) \) and \( F(u_2) \).

\end{theorem}


\end{document}
What is happening?  How does the utilisation of \\{skip}, but the others based upon \vspace do not?

Answer 1

By design the initial text of the theorem is inline, theamsthm documatioon shows a break style that always starts a new line.

\documentclass{article}
\usepackage{amsthm,color}
\newtheoremstyle{break}%
{}{}%           % Note that final punctuation is omitted.
{\itshape}{}%
{\bfseries}{}%
{\newline}{}
\theoremstyle{break}
\newtheorem{theorem}{thm}
\begin{document}
\newcommand\blskip{\\[0.3\baselineskip]}

\begin{theorem}
  [\color{blue} \textbf{Convolution Property of Fourier Transform}]
  \label{convolution}

  \textcolor{blue}{\bigskip This is not insterted on a new line}
  \textcolor{blue}{\vspace{8pt} This does not work either}

  \textcolor{blue}{\blskip This worked as intended}

  The Fourier transform of the product of two functions, \( u_1(t) \)
  and \( u_2(t) \), is equal to the product of the Fourier transforms
  \( F(u_1) \) and \( F(u_2) \).

\end{theorem}


\end{document}

\textcolor (ulike \color) starts a paragraph and horizontal mode, so your \bigskip (which is \vspace{\bigskipamount}) does work but adds vertical sppace after the paragraph has been broken in to lines and adds it immediately after the line that has the vadjust node containing the skip, so the vertical space appears after the first line of the paragraph, not before the paragraph.

Conversely the last line, igoring the color is

\mbox{}\\[0.3\baselineskip]

so you get parskip space then a "white" line of a paragraph, with just the paragraph indentation box, then you get a forced line break with .3\baselineskip. So it may look a bit like a vertical space of 1.3\baselineskip but it will behave very strangely at a page break. If a page breaks before the paragraph, the blank line will not be dropped at the start of a page, as vertical space would be. If a page break happens after the blank line, you will have a blank line at the bottom of on page then the .3\baselineskip space will be dropped at the start of the next.