Fermat's spiral: Difference between revisions

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with a real number <math>a</math>.
with a real number <math>a</math>.
<html>
<jsxgraph width="500" height="500">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
  var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
  var a = board.create('slider', [[1,9],[5,9],[0,1,4]],{name:'a'});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
  var c1 = board.create('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
<script language="JavaScript">
  board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
  var a = board.createElement('slider', [[1,9],[5,9],[0,1,4]]);
  var c1 = board.createElement('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});         
             {curveType:'polar', strokewidth:4});         
  var c2 = board.createElement('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
  var c2 = board.create('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});     
             {curveType:'polar', strokewidth:4});     
var g = board.createElement('glider', [1,1,c2]);
</jsxgraph>  
var t = board.createElement('tangent', [g], {dash:2,strokeColor:'#a612a9'});
 
</script>
</html>
===The JavaScript code to produce this picture===
===The JavaScript code to produce this picture===
<source lang="html4strict">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
</source>
<source lang="javascript">
<source lang="javascript">
  board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
  var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
  var a = board.createElement('slider', [[1,9],[5,9],[0,1,4]]);
  var a = board.create('slider', [[1,9],[5,9],[0,1,4]],{name:'a'});
  var c1 = board.createElement('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
  var c1 = board.create('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});         
             {curveType:'polar', strokewidth:4});         
  var c2 = board.createElement('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
  var c2 = board.create('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});      
             {curveType:'polar', strokewidth:4});    
var g = board.createElement('glider', [c1]);
var t = board.createElement('tangent', [g], {dash:2,strokeColor:'#a612a9'});
</source>
</source>


[[Category:Examples]]
[[Category:Examples]]
[[Category:Curves]]
[[Category:Curves]]

Latest revision as of 14:11, 7 June 2011

It can be described in polar coordinates [math]\displaystyle{ (r, \theta) }[/math] by the equation

[math]\displaystyle{ r = \pm a\theta^{1/2}\, }[/math]

with a real number [math]\displaystyle{ a }[/math].

The JavaScript code to produce this picture

 var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
 var a = board.create('slider', [[1,9],[5,9],[0,1,4]],{name:'a'});
 var c1 = board.create('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});        
 var c2 = board.create('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});