Arcing the center dots between factors to show repeated multiplication

Question

Consider the center dots to show repeated multiplication:

\[
x \cdot x \cdot x \cdots x.
\]

I want to use five dots instead of the three from the \cdots command, and I also want to have them subtly arced like on the path of part of a downward-opening parabola or something.

Does such a command already exist? If not, is it possible to create such a command or achieve it on a one-off/as-needed basis?

pdfLaTeX user.

The purpose of this is visual. I think it might add a touch of visual stimulation to my written explanations or illustrative examples to students. — Ungar Linski, Nov 30 '21 at 23:32

Steven B. Segletes · Accepted Answer · 2021-11-30T21:05:51.483

7

If the horizontal spacing needs changing, that can be done with kerns. If it is needed in smaller (script) mathstyles, let me know in a comment and I will revise my answer to provide them.

\documentclass[10pt]{article}
\usepackage{amsmath}
\newcommand\repdots{\mathbin{{\cdot}\raisebox{.75pt}{$\cdot$}%
  \raisebox{1pt}{$\cdot$}\raisebox{.75pt}{$\cdot$}{\cdot}}}
\begin{document}
$x \cdot x \cdot x \cdots x.$
$x \cdot x \cdot x  \repdots x.$
\end{document}

SUPPLEMENT to add extra \cdot kern (also supports smaller mathstyles)

The value of \dotkern is used to space out the \cdots. The value 1\LMpt (Local Math pt) is 1 pt in text and display styles, but proportionately smaller in the smaller math styles.

\documentclass[10pt]{article}
\usepackage{amsmath,scalerel}
\newcommand\dotkern{\kern1\LMpt}
\newcommand\repdots{\mathbin{\ThisStyle{{\cdot}\dotkern%
  \raisebox{.75\LMpt}{$\SavedStyle\cdot$}\dotkern
  \raisebox{1\LMpt}{$\SavedStyle\cdot$}\dotkern%
  \raisebox{.75\LMpt}{$\SavedStyle\cdot$}\dotkern{\cdot}}}}
\begin{document}
$x \cdot x \cdot x \cdots x.$
$x \cdot x \cdot x  \repdots x.$
$\scriptstyle x \cdot x \cdot x  \repdots x.$
$\scriptscriptstyle x \cdot x \cdot x  \repdots x.$
\end{document}

edited Nov 30 '21 at 21:05

answered Nov 30 '21 at 20:30

Steven B. Segletes

237,551

2

To make it truly parabolic change .7pt to .75 pt: \newcommand\repdots{\mathbin{{\cdot}\raisebox{.75pt}{$\cdot$}\raisebox{1pt}{$\cdot$}\raisebox{.75pt}{$\cdot$}{\cdot}}} – Dan Nov 30 '21 at 20:40
@Dan LOL :-)...I like the parabolic dots :-)))) – Sebastiano Nov 30 '21 at 20:42
3

Thanks, @Dan. If I had given it more thought, I should have known that. Retired for 2 months and all my elementary skills evaporate!! – Steven B. Segletes Nov 30 '21 at 20:46
Perfect! How to adjust the horizontal spacing so that it is the same as in \cdots or ever so slightly closer? – Ungar Linski Nov 30 '21 at 20:58
2

@UngarLinski Please see my SUPPLEMENT – Steven B. Segletes Nov 30 '21 at 21:06

Dan · Answer 2 · 2021-11-30T22:13:39.653

4

Steven's answer is excellent, but just for fun we can make a macro for arbitrary dots and curvature.

Use as follows: \repdots{# dots}{max vertical displacement in pt}.

\documentclass{article}
\usepackage{pgffor}
\usepackage[nomessages]{fp}
\newcommand\repdots[2]{\mathbin{\foreach \n in {1,...,#1}{\FPeval\temp{(-((\n-1)/(#1-1))*((\n-1)/(#1-1)-1)*4*(#2))}\raisebox{\temp pt}{$\cdot$}}}}
\begin{document}
$x \repdots{5}{1} x \repdots{4}{-3} x \repdots{30}{6} x \repdots{7}{-2} x$\\
\end{document}

edited Nov 30 '21 at 22:13

answered Nov 30 '21 at 21:27

Dan

3,699

2

Excellent answer also this :-)...more parabolic..... – Sebastiano Nov 30 '21 at 21:46
Now can we spell out my name in cursive with the dots? :) – Ungar Linski Nov 30 '21 at 23:27
1

@UngarLinski Easier to do something like https://tex.stackexchange.com/questions/96766/writing-practice-sheets-dotted-letters to make letters. – Dan Dec 01 '21 at 00:19

Arcing the center dots between factors to show repeated multiplication

2 Answers2