Twelve angles defined <a href="https://en.wikipedia.org/wiki/Modular_arithmetic" class="extiw" title="w:Modular arithmetic">modulo</a> 360 degrees correspond to times, defined modulo 12 hours.  For example, a clock hand has one only position numbered zero or twenty-four, because  <span style="white-space:nowrap">0 = 24  modulo 12. </span> This position corresponds to  90  or  –270 degrees  modulo 360 degrees.  Thus we identify direction and sense of <a href="https://en.wikipedia.org/wiki/Line_(geometry)#Ray" class="extiw" title="w:Line (geometry)">a ray</a> or <a href="https://en.wikipedia.org/wiki/Euclidean_vector" class="extiw" title="w:Euclidean vector">a vector</a> in <a href="https://en.wikipedia.org/wiki/Polar_coordinate_system" class="extiw" title="w:Polar coordinate system">polar</a> coordinates, or the angle of a <a href="https://en.wikipedia.org/wiki/Rotation_(mathematics)" class="extiw" title="w:Rotation (mathematics)">given rotation</a>, or the <a href="https://en.wikipedia.org/wiki/Argument_(complex_analysis)" class="extiw" title="w:Argument (complex analysis)">argument</a> of a given <a href="https://en.wikipedia.org/wiki/Complex_number" class="extiw" title="w:Complex number">complex number</a>.
<p>The drawing on the clock face evokes <a href="https://en.wikipedia.org/wiki/Arithmetic_progression" class="extiw" title="w:Arithmetic progression">arithmetic progressions</a> with <a href="https://en.wikipedia.org/wiki/Wiktionary:common_difference" class="extiw" title="en:Wiktionary:common difference">common differences</a>  5  or  7  modulo 12.  For example, by turning clockwise from 1, we pass through the terms:  <span style="white-space:nowrap">1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8. </span> This sequence corresponds to a progression with common difference  210 degrees  modulo 360 degrees.
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If the twelve positions of a clock hand are numbered in set <i>P</i>  of twelve elements, from 1 to 12 modulo 12, and if set <i>A</i>  consists of the angles written within the image, a <a href="https://en.wikipedia.org/wiki/bijection" class="extiw" title="w:bijection">bijection</a> <i>B</i>  from <i>P</i>  onto <i>A</i>  can be defined by  <span style="white-space:nowrap">B( <i>t</i> ) = 90 – 30 <i>t.</i> </span> For example,  <span style="white-space:nowrap">B( 12 ) = 90 – 30 × 12 = 90 degrees </span> modulo 360 degrees.<br> 
<a href="//commons.wikimedia.org/wiki/User:Baelde" title="User:Baelde">Baelde</a>
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