# Example: Arithmetic of the clock

Published 2011-12-22 | Author: Juan Luis Varona

This example shows the products i times j for i and j from 0 to 11 by using arithmetic modulo 12, i.e., the so called arithmetic of the clock.

The results of the products are represented both by the color of the clock and by the hand.

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% Arithmetic of the clock
% Author: Juan Luis Varona
% http://www.unirioja.es/cu/jvarona/
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
% Colors:
\definecolor{clock0}{cmyk}{1,0,0,0} % cyan
\definecolor{clock1}{cmyk}{0.75,0.25,0,0}
\definecolor{clock2}{cmyk}{0.5,0.5,0,0}
\definecolor{clock3}{cmyk}{0.25,0.75,0,0}
\definecolor{clock4}{cmyk}{0,1,0,0} % magenta
\definecolor{clock5}{cmyk}{0,0.75,0.25,0}
\definecolor{clock6}{cmyk}{0,0.5,0.5,0}
\definecolor{clock7}{cmyk}{0,0.25,0.75,0}
\definecolor{clock8}{cmyk}{0,0,1,0} % yellow
\definecolor{clock9}{cmyk}{0.25,0,0.75,0}
\definecolor{clock10}{cmyk}{0.5,0,0.5,0}
\definecolor{clock11}{cmyk}{0.75,0,0.25,0}
\begin{document}
\newcommand{\clock}[4]{%
\begin{scope}[xshift=2.25*#1cm,yshift=2.25*#2cm]
% \filldraw [fill=#3, line width=1.6pt] (0,0) circle (1cm); % simple fill (unused)
% \draw[fill] (0,0) circle (1mm); % border (unused)
\shadedraw [inner color=#3!30!white, outer color=#3!90!black,
line width=1.6pt] (0,0) circle (1cm); % disk with shadow and border
\foreach \angle in {0, 30, ..., 330}
\draw[line width=1pt] (\angle:0.82cm) -- (\angle:1cm);
\foreach \angle in {0,90,180,270}
\draw[line width=1.3pt] (\angle:0.75cm) -- (\angle:1cm);
\draw[line width=1.6pt] (0,0) -- (90-30*#4:0.6cm); % the hand
\end{scope}
}
% Default on latex.ltx: \fboxsep = 3pt \fboxrule = .4pt
\fboxsep = 3pt \fboxrule = 1.5pt
\newcounter{itimesj}
\fbox{%
\begin{tikzpicture}[scale=0.5]
\begin{scope}[line cap=round]
\foreach \i in {0,...,11}
\foreach \j in {0,...,11} {
% We use round by caution, because we are getting real numbers
\pgfmathparse{round(mod(\i*\j,12))}
% \pgfmathresult = 3.0 gives itimesj = 3
\pgfmathsetcounter{itimesj}{\pgfmathresult}
\clock{\i}{-\j}{clock\theitimesj}{\i*\j};
}
\end{scope}
\end{tikzpicture}%
}%
\end{document}