Making a thicker \cdot for dot product (that is thinner than \bullet)

Question

I'm trying to replicate the dot that my professor uses in his notes for the dot product between vectors but I am having a hard time doing so. This is what it looks like:

I have tried a couple of things. \cdot is too thin

and \bullet is too thick

and using \Large with \cdot gives an error. Moreover, after digging through the list of symbols I cannot find a nice medium between \cdot and \bullet.

How can I get a dot closest to the first picture?

Answer 1

May be you find a better name like \dotp or something like that.

\documentclass{scrartcl}
\usepackage{graphicx}

\makeatletter
\newcommand*\bigcdot{\mathpalette\bigcdot@{.5}}
\newcommand*\bigcdot@[2]{\mathbin{\vcenter{\hbox{\scalebox{#2}{$\m@th#1\bullet$}}}}}
\makeatother

\begin{document}
$a \bigcdot b$
\end{document}

Answer 2

Here is a simple trick which needs the amsmath package.

\[
a  \boldsymbol{\cdot} b  =  0
\]

and the result is

Answer 3

The following example extends Manuel's answer in two ways:

• The vertical position is fixed to center the symbol vertically around the math axis as \cdot and \bullet do.
• The width of the symbol is not the scaled down width of the \bullet (with scaled down side bearings), but a little larger width of \cdot.

The scale and width factor can be configured by macros \bigcdot@scalefactor and \bigcdot@widthfactor.

\documentclass{scrartcl}
\usepackage{color}
\usepackage{graphicx}

\makeatletter
\newcommand*{\bigcdot}{}% Check if undefined
\DeclareRobustCommand*{\bigcdot}{%
  \mathbin{\mathpalette\bigcdot@{}}%
}
\newcommand*{\bigcdot@scalefactor}{.5}
\newcommand*{\bigcdot@widthfactor}{1.15}
\newcommand*{\bigcdot@}[2]{%
  % #1: math style
  % #2: unused
  \sbox0{$#1\vcenter{}$}% math axis
  \sbox2{$#1\cdot\m@th$}%
  \hbox to \bigcdot@widthfactor\wd2{%
    \hfil
    \raise\ht0\hbox{%
      \scalebox{\bigcdot@scalefactor}{%
        \lower\ht0\hbox{$#1\bullet\m@th$}%
      }%
    }%
    \hfil
  }%
}
\makeatother

\begin{document}
\[ a \bigcdot b \]
%
% Comparison with \cdot and \bullet
\[ a \cdot b \bigcdot c \bullet d \]
%
% Different math styles
\[ a \bigcdot b \quad
   \scriptstyle a \bigcdot b \quad
   \scriptscriptstyle a \bigcdot b
\]
%
% Visualization of the math axis
\[
  \sbox0{${-}{\cdot}{\bigcdot}{\bullet}{-}$}
  \rlap{\copy0}%
  \vcenter{%
    \hbox{%
      \textcolor{red}{%
        \vrule width\wd0 height .05pt depth .05pt\relax
      }%
    }%
  }
\]
\end{document}

Answer 4

I provide not an answer, I demonstrate a caveat of the accepted solution, in hope for a more robust solution.

I used Heiko Oberdiek's solution, which is based on Manuel's solution. It has always worked well with the pdflatex compiler, thanks for that. But a while back I had to use the regular latex compiler, and the dot product then appears as a usual \bullet in the dvi file:

2020-06-08 update. For those interested, several solutions that work with dvi:

\documentclass{article}

\usepackage{lmodern}
\usepackage[T1]{fontenc}

\usepackage{scalefnt}
\usepackage{relsize}

\usepackage{mathtools}

\newcommand{\dotp}{
    \mathop{
        \mathchoice{\vcenter{\hbox{\LARGE$\cdot$}}}
                   {\vcenter{\hbox{\LARGE$\cdot$}}}
                   {\vcenter{\hbox{\normalsize$\cdot$}}}
                   {\vcenter{\hbox{\small$\cdot$}}}
    }
}

\begin{document}
\noindent
d\raisebox{-0.5ex}{\LARGE $\cdot$}b ~  d\parbox[c][0pt][c]{0.5em}{\LARGE$\cdot$}b ~ d$\vcenter{\hbox{\LARGE$\cdot$}}$b ~ d$\vcenter{\hbox{\scalefont{1.75}$\cdot$}}$b ~ d$\vcenter{\hbox{\relsize{+2.5}$\cdot$}}$b ~ d$\vcenter{\hbox{$\mathlarger{\mathlarger{\mathlarger{\mathlarger{\cdot}}}}$}}$b
\begin{align*}
    d\raisebox{-0.5ex}{\LARGE $\cdot$}b\\
    d\parbox[c][0pt][c]{0.5em}{\LARGE$\cdot$}b\\
    d\vcenter{\hbox{\LARGE$\cdot$}}b\\
    d\vcenter{\hbox{\scalefont{1.75}$\cdot$}}b\\
    d\vcenter{\hbox{\relsize{+2.5}$\cdot$}}b\\
    d\vcenter{\hbox{$\mathlarger{\mathlarger{\mathlarger{\mathlarger{\cdot}}}}$}}b
\end{align*}
d $\dotp$ b
\begin{align*}
    d \dotp b\\
    a_{d \dotp b}
\end{align*}
\end{document}

Only the \dotp solution is robust. The others require manual intervention for super- and subscripts for example. You probably do want to insert some negative kerning left and right of the \dotp.

For the record, Hosein's answer to use \boldsymbol{\cdot} is also what the physics package uses. It also works in dvi. Still, I find that dot too small.