Logarithmic spiral: Difference between revisions

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with real numbers <math>a</math> and <math>b</math>.
with real numbers <math>a</math> and <math>b</math>.
<html>
<jsxgraph box="jsxgbox" width="500" height="500">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
  board = JXG.JSXGraph.initBoard('jsxgbox', {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,-1],[5,-1],[0,0.3,1]],{name:'a'});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
  var b = board.create('slider', [[1,-2],[5,-2],[-1,0.15,1]],{name:'b'});
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
  var c = board.create('curve', [function(phi){return a.Value()*Math.exp(b.Value()*phi); }, [0, 0], 0, 8*Math.PI],
<script language="JavaScript">
  board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
  var a = board.createElement('slider', [[1,-1],[5,-1],[0,0.3,1]],{name:'a'});
  var b = board.createElement('slider', [[1,-2],[5,-2],[0,0.15,1]],{name:'b'});
  var c = board.createElement('curve', [function(phi){return a.Value()*board.pow(Math.E,b.Value()*phi); }, [0, 0], 0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});         
             {curveType:'polar', strokewidth:4});         
  var g = board.createElement('glider', [c]);
  var g = board.create('glider', [c]);
  var t = board.createElement('tangent', [g], {dash:2,strokeColor:'#a612a9'});
  var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'});
 
</jsxgraph>


</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});
  board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox: [-10, 10, 10, -10]});
  var a = board.createElement('slider', [[1,-1],[5,-1],[0,0.3,1]],{name:'a'});
  var a = board.create('slider', [[1,-1],[5,-1],[0,0.3,1]],{name:'a'});
  var b = board.createElement('slider', [[1,-2],[5,-2],[0,0.15,1]],{name:'b'});
  var b = board.create('slider', [[1,-2],[5,-2],[-1,0.15,1]],{name:'b'});
  var c = board.createElement('curve', [function(phi){return a.Value()*board.pow(Math.E,b.Value()*phi); }, [0, 0],0, 8*Math.PI],
  var c = board.create('curve', [function(phi){return a.Value()*JXG.Math.pow(Math.E,b.Value()*phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});         
             {curveType:'polar', strokewidth:4});         
  var g = board.createElement('glider', [c]);
  var g = board.create('glider', [c]);
  var t = board.createElement('tangent', [g], {dash:2,strokeColor:'#a612a9'});
  var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'});
</source>
</source>


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

Latest revision as of 12:50, 28 June 2019

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

[math]\displaystyle{ r = ae^{b\theta}\, }[/math]

with real numbers [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math].

The JavaScript code to produce this picture

 board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox: [-10, 10, 10, -10]});
 var a = board.create('slider', [[1,-1],[5,-1],[0,0.3,1]],{name:'a'});
 var b = board.create('slider', [[1,-2],[5,-2],[-1,0.15,1]],{name:'b'});
 var c = board.create('curve', [function(phi){return a.Value()*JXG.Math.pow(Math.E,b.Value()*phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});        
 var g = board.create('glider', [c]);
 var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'});