<?xml version="1.0"?>
<?xml-stylesheet type="text/xsl" href="pmathml.xsl"?>
<!--

Use and distribution of this code are permitted under the terms of the <a
href="http://www.w3.org/Consortium/Legal/copyright-software-19980720"
>W3C Software Notice and License</a>.
-->
<!--
  pref:renderer="techexplorer-plugin"
  pref:renderer="techexplorer"
  pref:renderer="css"
  pref:renderer="mathplayer"
  pref:renderer="mathplayer-dl"
-->
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
  <meta http-equiv="Content-Type" content="text/html" />
  <title>Inscribed and Circumscribed Spheres</title>

 <style type="text/css">

  img {

   border-left: 4px solid green;
   border-bottom: 4px solid brown;
   margin-right: 2em;

  }

  img:hover {

  	background-color: yellow

  }

 </style>

<script type="text/javascript" src="ASCIIMathML.js"></script>
<script type="text/javascript" src="ASCIIsvg.js"></script>

</head>



<body  onload="drawPictures();translate()"  >
 <script type="text/javascript" src="http://ie7-js.googlecode.com/svn/test/ie7-demo.js"></script>
 <h2>&lt;img src="http://ie7-js.googlecode.com/svn/test/*.png"&gt;</h2>

<h2>Can your browser display MathML?</h2> <!--  ;MathPlayer 2.10b;  -->

<!--    navigator.userAgent.substring(navigator.userAgent.indexOf(";MathPlayer",0),17)  -->

<p>
<script language="javascript">
 document.write(location.host+" "+location.port+" "+location.hash+" "+" "+location.search+" "+location.post);
  //  document.write(navigator.userAgent);
  if(navigator.userAgent.indexOf("MathPlayer",0) > 0)
         document.write(navigator.userAgent.substring(navigator.userAgent.indexOf(";MathPlayer",0),17));
  </script>
</p>


<p>Below is an equation with a radical relating to pentagonal symmetry:</p>

` R =   \sqrt(3) * \sqrt(5-2 \sqrt(5))) * r `  and conversely
` r =   ( \sqrt(5-2 \sqrt(5))) / \sqrt(15))* R `


<p>
 circumscribed sphere/inscribed sphere =   

<math xmlns="http://www.w3.org/1998/Math/MathML">
    <msqrt>
      <mrow>
        <mi>3</mi>
      </mrow>
    </msqrt>


    <msqrt>
        <mi>5</mi>
        <mo>-</mo>

      <mi>2</mi>

    <msqrt>
      <mrow>
        <mi>5</mi>
      </mrow>
    </msqrt>
    </msqrt>

</math>


inscribed sphere/circumscribed sphere=    

<math xmlns="http://www.w3.org/1998/Math/MathML">



   <apply><divide/>


    <msqrt>
        <mi>5</mi>
        <mo>+</mo>

      <mi>2</mi>

    <msqrt>
      <mrow>
        <mi>5</mi>
      </mrow>
    </msqrt>
    </msqrt>

    <mrow>


    <msqrt>
      <mrow>
        <mi>15</mi>
      </mrow>
    </msqrt>

    </mrow>
   </apply>





</math>


</p>



     <!--        obscures MathML
           style="position:relative; top:-200; left:0;"          -->
<div    style="position:absolute; top:-160; left:70;"   >
<p>
sphere
<img src="sphere-trans.png" alt="sphere.svg" longdesc="inscribed and circumscribed"
   type="image/svg+xml" width="564" height="564" />
</p>
</div>

<!--  style="position:absolute; top:-100; left:0;"  -->


<p></p>

<p>
<!--
<embed src="sphere.svg" alt="sphere.png" longdesc="circumscribed and inscribed"
   type="image/svg+xml" width="282" height="282" />
    -->
</p>



<p>If your browser displays those equations correctly, it is enabled to
display Design Science, Presentation, MathPlayer, ... MathML.</p> 

<a href="http://www.w3.org/Math/XSL/pmathml2.xml"> the original </a>

<p>METHODS TO WRITE PORTABLE and PRESENTABLE EQUATIONS WITHOUT BITMAPS or PROPRIETARY TOOLS
</p>------------------- -----------------------------------------------------------
   --------------------- ---------<p></p>
<a href="links.html"> references </a> and tests
<a href="http://math.chapman.edu/~jipsen/mathml/asciimathandmathmlsvg.xhtml"> MathML,ASCIIMathML,SVG together </a>
<a href="http://www.echoofeden.com/htmlTests/xhtml/xhtml_svg_mathml.xhtml"> MathML,SVG together </a>
<a href="http://www.pieperu.de/mathmlgraph/"> further combinations </a>
<a href="http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd"> in xhtml </a>



<img src="http://www.w3.org/Math/mathmlSmall.png" alt="MathML inside!"/>

</body>
</html>


<!--   from    to ? edwards.add

< ! DOC TYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
 <title>IE7 {CSS2: auto}</title>
-->
 <!-- http://ie7-js.googlecode.com/svn/test/png.html -->
 <!-- compliance patch for microsoft browsers -->
 <!--[if lt IE 8]><script src="http://ie7-js.googlecode.com/svn/trunk/lib/IE8.js" type="text/javascript"></script><![endif]-->


<!--

</head>
<body  bgcolor="teal" >

<embed  src="arbor.svg" type="image/svg+xml"  alt="arbor.svg"  width="282" height="282"/>

 <p>&lt;&nbsp;<a href="index.html">back</a></p>


<p><div height="700" width="564"  >
<img src="star.png"   alt="star.png"
  style="position:absolute; top:200; left:0; "
  type="image/svg+xml"   width="282" height="282"/>
<img src="scales_4-trans.png"   alt="_3-trans.png"
  style="position:absolute; top:250; left:100; "
   type="image/svg+xml"  width="400" height="400"  />
</div>
</p>

&nbsp;




<img src="arbor.svg" type="image/svg+xml"  alt="arbor.svg"  width="225" height="225"/>
 <p>&lt;&nbsp;<a href="index.html">back</a></p>
</body>
</html>       -->


<!--  skeleton.xml from phase.xml  -->

