Difference between revisions of "Lituus"

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===Other curves===
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The quadrifolium is a type of rose curve with n=2. It has polar equation:
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:<math>    r = \cos(2\theta), \,</math>
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with corresponding algebraic equation
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:<math>    (x^2+y^2)^3 = (x^2-y^2)^2. \, </math>
  
 
<jsxgraph width="500" height="500" box="box2">
 
<jsxgraph width="500" height="500" box="box2">

Revision as of 17:10, 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>

Other curves

The quadrifolium is a type of rose curve with n=2. It has polar equation:

[math] r = \cos(2\theta), \,[/math]

with corresponding algebraic equation

[math] (x^2+y^2)^3 = (x^2-y^2)^2. \, [/math]


External links