Lituus: Difference between revisions

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<jsxgraph width="500" height="500" box="box2">
<jsxgraph width="500" height="500" box="box2">
  var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
  var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
  var k = b2.createElement('slider', [[1,8],[5,8],[0,1,4]]);
  var k = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);
  var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);  
  var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);  
  var c = b2.createElement('curve', [function(phi){return k.Value()*Math.cos(2.0*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
  var c = b2.createElement('curve', [function(phi){return k.Value()*Math.cos(2.0*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
             {curveType:'polar', strokewidth:4});       
             {curveType:'polar', strokewidth:2});       
</jsxgraph>
</jsxgraph>



Revision as of 15:09, 18 March 2009

A lituus is a spiral in which the angle is inversely proportional to the square of the radius (as expressed in polar coordinates).

[math]\displaystyle{ r^2\theta = k \, }[/math]

The JavaScript code to produce this picture

<jsxgraph width="500" height="500" box="box1">
 var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
 var k = b1.createElement('slider', [[1,8],[5,8],[0,1,4]]);
 var c = b1.createElement('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});      
</jsxgraph>


External links