Difference between revisions of "Archimedean spiral"

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Line 1: Line 1:
<jsxgraph width="500" height="500" box="box1">
 
</jsxgraph>
 
 
 
It can be described in polar coordinates <math>(r, \theta)</math> by the equation
 
It can be described in polar coordinates <math>(r, \theta)</math> by the equation
  
Line 7: Line 4:
  
 
with real numbers <math>a</math> and <math>b</math>.
 
with real numbers <math>a</math> and <math>b</math>.
<html>
+
<jsxgraph height="500" width="500" box="jxgbox">
<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', [[1,8],[5,8],[0,1,4]],{name:'a'});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
+
var b = board.create('slider', [[1,9],[5,9],[0,0.25,4]],{name:'b'});
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
+
 
<script language="JavaScript">
+
var c = board.create('curve', [function(phi){return a.Value()+b.Value()*phi; }, [0, 0],0, 8*Math.PI],
board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
 
var a = board.createElement('slider', [[1,8],[5,8],[0,1,4]]);
 
var b = board.createElement('slider', [[1,9],[5,9],[0,0.25,4]]);
 
var c = board.createElement('curve', [function(phi){return a.Value()+b.Value()*phi; }, [0, 0],0, 8*Math.PI],
 
 
             {curveType:'polar', strokewidth:4});       
 
             {curveType:'polar', strokewidth:4});       
var g = board.createElement('glider', [c]);
+
 
var t = board.createElement('tangent', [g], {dash:2,strokeColor:'#a612a9'});
+
var g = board.create('glider', [c]);
var n = board.createElement('normal', [g], {dash:2,strokeColor:'#a612a9'});
+
var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'});
</script>  
+
var n = board.create('normal', [g], {dash:2,strokeColor:'#a612a9'});
</html>
+
</jsxgraph>
 +
 
 
===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', [[1,8],[5,8],[0,1,4]]);
+
var a = board.create('slider', [[1,8],[5,8],[0,1,4]],{name:'a'});
var b = board.createElement('slider', [[1,9],[5,9],[0,0.25,4]]);
+
var b = board.create('slider', [[1,9],[5,9],[0,0.25,4]],{name:'b'});
var c = board.createElement('curve', [function(phi){return a.Value()+b.Value()*phi; }, [0, 0],0, 8*Math.PI],
+
 
             {curveType:'polar', strokewidth:4});      
+
var c = board.create('curve', [function(phi){return a.Value()+b.Value()*phi; }, [0, 0],0, 8*Math.PI],
var g = board.createElement('glider', [c]);
+
             {curveType:'polar', strokewidth:4});    
var t = board.createElement('tangent', [g], {dash:2,strokeColor:'#a612a9'});
+
 
var n = board.createElement('normal', [g], {dash:2,strokeColor:'#a612a9'});
+
var g = board.create('glider', [c]);
 +
var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'});
 +
var n = board.create('normal', [g], {dash:2,strokeColor:'#a612a9'});
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Curves]]
 
[[Category:Curves]]

Latest revision as of 13:35, 7 June 2011

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

[math]\, r=a+b\theta[/math]

with real numbers [math]a[/math] and [math]b[/math].

The JavaScript code to produce this picture

var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
var a = board.create('slider', [[1,8],[5,8],[0,1,4]],{name:'a'});
var b = board.create('slider', [[1,9],[5,9],[0,0.25,4]],{name:'b'});

var c = board.create('curve', [function(phi){return a.Value()+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'});
var n = board.create('normal', [g], {dash:2,strokeColor:'#a612a9'});