Archimedean spiral: Difference between revisions

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<html>
It can be described in polar coordinates <math>(r, \theta)</math> by the equation
<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>
:<math>\, r=a+b\theta</math>
<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>
with real numbers <math>a</math> and <math>b</math>.
<script language="JavaScript">
<jsxgraph height="500" width="500" box="jxgbox">
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,-1],[5,-1],[-2,1,2]]);
var a = board.create('slider', [[1,8],[5,8],[0,1,4]],{name:'a'});
var b = board.createElement('slider', [[1,-2],[5,-2],[-2,1,2]]);
var b = board.create('slider', [[1,9],[5,9],[0,0.25,4]],{name:'b'});
var c = board.createElement('curve', [function(phi) a.Value()+b.Value()*phi; }, [0, 0],'phi',0, 4*Math.PI],
 
             {curveType:'polar', strokewidth:2});      
var c = board.create('curve', [function(phi){return a.Value()+b.Value()*phi; }, [0, 0],0, 8*Math.PI],
</script>  
             {curveType:'polar', strokewidth:4});     
</html>
 
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'});
</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,-1],[5,-1],[-2,1,2]]);
var a = board.create('slider', [[1,8],[5,8],[0,1,4]],{name:'a'});
var b = board.createElement('slider', [[1,-2],[5,-2],[-2,1,2]]);
var b = board.create('slider', [[1,9],[5,9],[0,0.25,4]],{name:'b'});
var c = board.createElement('curve', [function(phi) a.Value()+b.Value()*phi; }, [0, 0],'phi',0, 4*Math.PI],
 
             {curveType:'polar', strokewidth:2});      
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'});
</source>
</source>


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

Latest revision as of 11:35, 7 June 2011

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

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

with real numbers [math]\displaystyle{ a }[/math] and [math]\displaystyle{ 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'});