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216 lines
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HTML
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<title>Rotational Symmetry</title>
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<meta name="description" content="A shape has Rotational Symmetry when it still looks the same after some rotation." />
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Rotational Symmetry</h1>
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<h2>Rotational Symmetry</h2>
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<p>A shape has Rotational Symmetry when it still looks the same after some rotation (of less than one full turn).<br>
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</p>
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<div style="background-color: #e2e2ff; border: 1px solid #aa44aa; border-radius: 10px; margin: auto; padding:5px; text-align:center;">
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<iframe src="isym-rot2.html" scrolling="no" style="width:222px; height:222px; overflow:hidden; margin:auto; border: none;"></iframe><br>
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<span class="large">Rotational Symmetry<br>
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Order 2</span> </div>
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<div style="display:inline-block;">
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<iframe src="isym-rot3.html" scrolling="no" style="width:222px; height:222px; overflow:hidden; margin:auto; border: none;"></iframe><br>
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<span class="large">Rotational Symmetry<br>
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Order 3</span> </div>
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<table border="0">
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<noscript><object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="173" height="156" id="images/symmetry-rotate2.swf" align="middle">
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</td>
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</tr>
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</table>
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</div>
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-->
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<p class="center"> How <b>many times it matches</b> as we go once around is called the <b class="large">Order</b>. </p>
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<p>Think of propeller blades (like below), it makes it easier.</p>
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<div style="clear:both"></div>
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<h2>Examples of Different Rotational Symmetry Order</h2>
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<div class="simple"> <table border="0" align="center">
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<tr>
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<th> Order</th>
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<th>Example Shape</th>
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<th>Artwork </th>
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</tr>
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<tr>
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<td>
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<div align="center"></div>
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</td>
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<td>
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<div align="center"></div>
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</td>
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<td class="tiny">
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<div align="center">(using <a href="symmetry-artist.html">Symmetry Artist</a>)</div>
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</td>
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</tr>
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<tr>
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<td><img src="images/symmetry-order-2.jpg" width="151" height="151" alt="symmetry order 2" /></td>
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<td><img src="images/symmetry-shape-r2.gif" width="151" height="151" alt="symmetry shape order 2" /></td>
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<td><img src="images/symmetry-art-r2.gif" width="151" height="151" alt="symmetry art order 2" /></td>
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</tr>
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<tr>
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<td><img src="images/symmetry-order-3.jpg" width="151" height="151" alt="symmetry order 3" /></td>
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<td><img src="images/symmetry-shape-r3.gif" width="151" height="151" alt="symmetry shape order 3" /></td>
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<td><img src="images/symmetry-art-r3.gif" width="151" height="151" alt="symmetry art order 3" /></td>
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</tr>
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<tr>
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<td><img src="images/symmetry-order-4.jpg" width="151" height="151" alt="symmetry order 4" /></td>
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<td><img src="images/symmetry-shape-r4.gif" width="151" height="151" alt="symmetry shape order 4" /></td>
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<td><img src="images/symmetry-art-r4.gif" width="151" height="151" alt="symmetry art order 4" /></td>
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</tr>
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<tr>
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<td colspan="3" align="center">... and there is also Order 5, 6, 7, and ...</td>
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</tr>
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<tr>
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<td><img src="images/symmetry-order-8.jpg" width="151" height="151" alt="symmetry order 8" /></td>
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<td><img src="images/symmetry-shape-r8.gif" width="151" height="151" alt="symmetry shape order 8" /></td>
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<td><img src="images/symmetry-art-r8.gif" width="151" height="151" alt="symmetry art order 8" /></td>
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</tr>
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<tr align="center">
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<td colspan="3"> ... and then there is Order 9, 10, and so on ...</td>
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</tr>
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</table></div><p> </p>
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<p class="center larger">Try rotational symmetry yourself with <a href="symmetry-artist.html">Symmetry Artist</a> ... !</p>
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<p> </p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/symmetry-order-1-no.jpg" width="151" height="153" alt="symmetry order 1 no" /></p>
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<h2>Is there Rotational Symmetry of Order 1 ?</h2>
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<p><b>Not really!</b> If a shape only matches itself <b>once</b> as we go around (ie it matches itself after one full rotation) there is really no symmetry at all ...</p>
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<p>... because the word "Symmetry" comes from <i> syn- <b>together</b></i> and<i> metron <b>measure</b>, </i>and there can't be "together" if there is just one thing.</p>
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<p> </p>
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<h2>Real World Examples</h2>
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<table border="0" align="center">
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<tr align="center">
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<td width="180"><img src="images/dart-board.jpg" width="180" height="181" alt="dart board" /></td>
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<td width="180" align="center"><img src="images/bronze-star.jpg" width="114" height="180" alt="bronze star" /></td>
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<td width="180"><img src="images/london-eye.jpg" width="180" height="180" alt="london eye" /></td>
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</tr>
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<tr align="center">
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<td width="180">A Dartboard has Rotational Symmetry of Order 10</td>
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<td width="180" align="center">The US Bronze Star Medal has Order 5</td>
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<td width="180">The London Eye has Order ... oops, I lost count!</td>
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</tr>
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</table>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(849, 850, 2137, 2138, 3360, 3361, 3362, 3363, 5033, 5034);</script>
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</div>
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<div class="activity"><a href="../activity/mandala.html">Activity: Make a Mandala </a></div>
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<div class="related">
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<a href="symmetry.html">Symmetry</a>
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<a href="symmetry-artist.html">Symmetry Artist</a>
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<a href="symmetry-reflection.html">Reflection Symmetry</a>
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<a href="symmetry-point.html">Point Symmetry</a>
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<a href="transformations.html">Transformations</a>
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<a href="rotation.html">Rotation</a>
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<a href="index.html">Geometry Index</a>
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