Difference between revisions of "Lituus"

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Line 1: Line 1:
 
<jsxgraph width="500" height="500" box="box2">
 
<jsxgraph width="500" height="500" box="box2">
 
  b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
 
  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 k1 = b2.createElement('slider', [[1,8],[5,8],[0,1,4]]);
 
  var c = b2.createElement('curve',  
 
  var c = b2.createElement('curve',  
             [function(t){ return k.Value()*b2.I([0,t],function(u){return Math.sin(u)*Math.sin(u);}); },  
+
             [function(t){ return k1.Value()*b2.I([0,t],function(u){return Math.sin(u)*Math.sin(u);}); },  
               function(t){ return k.Value()*b2.I([0,t],function(u){return Math.cos(u)*Math.cos(u);}); },
+
               function(t){ return k1.Value()*b2.I([0,t],function(u){return Math.cos(u)*Math.cos(u);}); },
 
             0, 8*Math.PI],
 
             0, 8*Math.PI],
 
             {strokewidth:4});       
 
             {strokewidth:4});       

Revision as of 10:18, 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]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