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171 lines
6.2 KiB
HTML
171 lines
6.2 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/geometry/tetrahedron.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:18 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Spinning Tetrahedron</title>
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<style type="text/css">
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.boxa {
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text-align: left;
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vertical-align:middle;
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display: inline-block;
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vertical-align:middle;
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margin: 0;
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padding: 2px;
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width:240px;
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background-color: hsla(240,100%,60%,0.1);
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}
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.boxb {
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display: inline-block;
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vertical-align: top;
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margin: 0 10px 10px 10px;
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width: 450px;
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}
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</style>
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<!-- #EndEditable -->
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<meta name="HandheldFriendly" content="true">
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<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
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<link rel="preload" href="../style4.css" as="style">
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<link rel="preload" href="../main4.js" as="script">
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</script>
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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">Tetrahedron</h1>
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<p class="center"><i>Go to <a href="#Area">Surface Area</a> or <a href="#Volume">Volume</a></i></p>
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<div class="boxa">
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<div class="head">Tetrahedron Facts</div>
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<p><b>Notice these interesting things:</b></p>
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<ul>
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<li>It has 4 Faces</li>
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<li>Each face is an <a href="../triangle.html">Equilateral Triangle</a></li>
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<li>It has 6 Edges</li>
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<li>It has 4 Vertices (corner points)</li>
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<li>and at each vertex 3 edges meet</li>
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<li>It is one of the <a href="../platonic_solids.html">Platonic Solids</a></li>
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</ul>
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</div>
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<div class="boxb">
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<div class="script" style="height: 450px;">
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images/polyhedra.js?mode=tetrahedron
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</div>
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</div>
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<div style="clear:both"></div>
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<div class="words">When we have more than one tetrahedron they are called <b>tetrahedra</b></div>
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<p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/tetrahedron.svg" alt="tetrahedron" height="198" width="186"></p>
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<p>The tetrahedron also has a beautiful and <i>unique</i> property ...<br>
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all four vertices are the same distance from each other!
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(thanks Ganesh)</p>
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<p>And it is the only Platonic Solid with no parallel faces.</p>
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<div style="clear:both"></div>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/tetrahedron-irregular.svg" alt="tetrahedron irregular" height="205" width="170"></p>
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<p>When we say "tetrahedron" we often mean "regular tetrahedron" (in other words all faces are the same size and shape)</p>
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<p align="right">But it could be an <b>irregular</b> tetrahedron, like this one:</p>
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<div style="clear:both"></div>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/dice-tetrahedron.jpg" alt="dice tetrahedron" height="152" width="182"></p>
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<p><b>4-Sided Dice?</b> Yes! A tetrahedron that has 4 equal faces has an equal chance of landing on any face.</p>
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<p>In fact, you can make <a href="fair-dice.html">fair dice</a> out of all of the Platonic Solids.</p>
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<div style="clear:both"></div>
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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><a href="tetrahedron-model.html">Make your own Tetrahedron</a> ,<br>
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cut out the shape and glue it together.</td>
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<td><a href="tetrahedron-model.html"><img src="images/tetrahedron-model-thumb.svg" alt="Tetrahedron Model Template" height="146" width="168"></a> </td>
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</tr>
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</tbody></table>
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<a id="Area"></a>
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<h2>Surface Area and Volume</h2>
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<p>For a regular tetrahedron:</p>
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<p class="center"><img src="images/tetrahedron-edge.svg" alt="tetrahedron edge length" height="204" width="188"></p>
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<p class="center"><b>Surface Area</b> = √3 × (Edge Length)<sup>2</sup></p>
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<a id="Volume"></a>
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<p class="center"><b>Volume</b> = <span class="intbl"><em>√2</em><strong>12
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</strong></span> × (Edge Length)<sup>3</sup></p>
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<h2>Inside a Cube</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/tetrahedron-cube.svg" alt="tetrahedron" height="270" width="260"></p>
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<p>Here we see a regular tetrahedron's corners matching neatly with half of the cube's corners.</p>
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<p>Can you work out the volume of the cube compared to that tetrahedron?</p>
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<div style="clear:both"></div>
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<div class="questions">1868, 1869, 1870, 1871</div>
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<div class="related">
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<a href="polyhedron-models.html">Animated Polyhedron Models</a>
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<a href="../platonic_solids.html">Platonic Solids</a>
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</div>
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<!-- #EndEditable -->
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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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