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137 lines
5.4 KiB
HTML
137 lines
5.4 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/eccentricity.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:43:59 GMT -->
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<article id="content" role="main">
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<h1 class="center">Eccentricity</h1>
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<p class="center"><i>Eccentricity: how much a <a href="conic-sections.html">conic section</a> (a circle, ellipse, parabola or hyperbola)<br>
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varies from being circular.</i></p>
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<div class="def">
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<p>A circle has an <b>eccentricity of zero</b>, so the eccentricity shows you how "un-circular" the curve is. Bigger eccentricities are less curved.</p>
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</div><p style="float:right; margin: 0 0 5px 10px;"><img src="images/eccentricity.svg" alt="Eccentricity" height="350" width="300"></p>
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<p>Different values of eccentricity make different curves:</p>
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<ul>
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<li>At <b>eccentricity</b> = 0 we get a <a href="circle.html">circle</a></li>
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<li>for 0 <<b> eccentricity</b> < 1 we get an <a href="ellipse.html">ellipse</a></li>
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<li>for <b>eccentricity</b> = 1 we get a <a href="parabola.html">parabola</a></li>
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<li>for <b>eccentricity</b> > 1 we get a <a href="hyperbola.html">hyperbola</a></li>
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<li>for infinite <b>eccentricity</b> we get a <a href="line.html"> line</a></li>
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</ul>
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<p>Eccentricity is often shown as the letter <span class="large">e</span> (don't confuse this with <a href="../numbers/e-eulers-number.html">Euler's number "e"</a>, they are totally different)</p>
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<h2>Animation</h2>
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<p>Try the slider to see what happens:</p>
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<div class="script" style="height: 400px;">
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images/eccentricity-graph.js
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</div>
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<h2>Calculating The Value</h2>
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<div class="simple">
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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 align="center" bgcolor="#FFFFFF"><img src="images/circle.svg" alt="circle" height="225" width="212"></td>
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<td>For a circle, eccentricity is <b>0</b></td>
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</tr>
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<tr>
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<td align="center" bgcolor="#FFFFFF"><img src="images/ellipse-cartesian.svg" alt="ellipse on xy graph" height="223" width="260"></td>
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<td>
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<p>For an ellipse, eccentricity is:</p>
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<div class="center large"><span class="intbl"><em><span style="font-size:120%;">√</span><span class="overline">a<sup>2</sup> − b<sup>2</sup></span></em><strong>a</strong></span></div>
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<!-- SQR(a^2-b^2)/a -->
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</tr>
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<tr>
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<td align="center" bgcolor="#FFFFFF"><img src="images/parabola-names.svg" alt="parabola" height="212" width="288"></td>
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<td>For a parabola, eccentricity is <b>1</b></td>
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</tr>
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<tr>
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<td align="center" bgcolor="#FFFFFF"><img src="images/hyperbola6.svg" alt="hyperbola on xy graph" height="220" width="260"></td>
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<td>
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<p>For a hyperbola, eccentricity is:</p>
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<div class="center large"><span class="intbl"><em><span style="font-size:120%;">√</span><span class="overline">a<sup>2</sup> + b<sup>2</sup></span></em><strong>a</strong></span></div>
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</tr>
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</tbody></table>
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</div><p> </p>
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<div class="related">
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<a href="conic-sections.html">Conic Sections</a>
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<a href="index.html">Geometry Index</a>
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