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153 lines
6.0 KiB
HTML
153 lines
6.0 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/sets/set-of-points.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:33 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<title>Set of All Points</title>
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</head>
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Set of All Points That ...</h1>
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<p class="center">In Mathematics we often say <i>"the set of all points that ... ".</i><br>
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What does it mean?</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="../images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td>A <a href="sets-introduction.html">set</a> is just a collection of things with some common property.</td>
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</tr>
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<tr>
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<td><img src="../images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td>When we collect ALL points that share a property we can end up with a line, a surface or other interesting thing.</td>
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</tr>
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</tbody></table><br>
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<div class="beach">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="images/set-points-line.svg" alt="set of points make line" height="10" width="280"></td>
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<td><b>Points can make a line</b></td>
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</tr>
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</tbody></table>
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</div>
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<p> </p>
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<div class="example">
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<h3><i>Example:</i> A <a href="../geometry/circle.html">Circle</a> is:</h3>
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<p>"<b>the set of all points</b> on a <a href="../geometry/plane.html">plane</a> that are a fixed distance from a central point".</p>
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<p class="center"><img src="images/set-points-circle.svg" alt="set of points make circle" style="max-" height="105" width="479"></p>
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<p>So, just a few points start to <i>look like a circle</i>, but when we collect ALL the points we will actually <b>have</b> a circle.</p>
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</div>
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<p>Try drawing one yourself (move any point):</p>
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<div class="script" style="height: 360px;">
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images/geom-locus.js
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</div>
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<p class="center">(Note: the points are drawn as dots so you can see them,<br>
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but they really should have<b> no size at all</b>)</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../geometry/images/sphere-radius.svg" alt="sphere radius" height="180" width="180"></p>
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<h2>Surface</h2>
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<p>Imagine this happening in <b>3D space</b>: all the points that are a fixed distance from a center make a <a href="../geometry/sphere.html">sphere</a>!</p>
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<div style="clear:both"></div>
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<h2>Locus</h2>
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<p>The idea of "the set of all points that ..." is used so much it has a name: <b>Locus.</b></p>
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<div class="words">
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<p><b>A Locus is a set of points that share a property.</b></p>
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</div>
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<p>So, a circle is "the locus of points on a plane that are a fixed distance from the center".</p>
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<p>Note: "Locus" usually means that the points make a continuous curve or surface.</p>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../geometry/images/ellipse.svg" alt="ellipse" height="210" width="220"></p>
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<h3>Example: An <a href="../geometry/ellipse.html">ellipse</a> is the <b>locus</b> of points whose distance from two fixed points add up to a constant.</h3>
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<p>So, no matter where we are on the ellipse, we can add up the distance to point "F" and to point "G" and it will always be the same result.</p>
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<p>(The points "F" and "G" are called the <b>foci</b> of the ellipse)</p>
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</div>
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<p>The idea of "Locus" can be used to create some weird and wonderful shapes!</p>
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<p> </p>
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<div class="questions">7922, 7923, 7924, 7925, 7926, 7927, 7928, 7929, 7930, 7931</div>
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<div class="related">
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<a href="../geometry/circle.html">Circle</a>
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<a href="index.html">Sets Index</a>
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</div>
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</article>
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<div id="adend" class="centerfull noprint"></div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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