Difference between revisions of "Lituus"

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Line 1: Line 1:
 +
<jsxgraph width="500" height="500" box="box2">
 +
b2 = JXG.JSXGraph.initBoard('box2', {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(t){ return b2.I([0,t],function(u){return Math.sin(u)*Math.sin(u);}); },
 +
              function(t){ return b2.I([0,t],function(u){return Math.sin(u)*Math.sin(u);}); },
 +
            0, 8*Math.PI],
 +
            {strokewidth:4});     
 +
</jsxgraph>
 +
 +
 
A '''lituus''' is a spiral in which the angle is inversely proportional to the square of the radius (as expressed in polar coordinates).
 
A '''lituus''' is a spiral in which the angle is inversely proportional to the square of the radius (as expressed in polar coordinates).
  
Line 4: Line 15:
  
 
<jsxgraph width="500" height="500" box="box1">
 
<jsxgraph width="500" height="500" box="box1">
  b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
+
  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 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],
 
  var c = b1.createElement('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
Line 14: Line 25:
 
<source lang="xml">
 
<source lang="xml">
 
<jsxgraph width="500" height="500" box="box1">
 
<jsxgraph width="500" height="500" box="box1">
  b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
+
  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 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],
 
  var c = b1.createElement('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],

Revision as of 10:16, 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