Lituus: Difference between revisions
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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 k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]); | var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]); | ||
var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}], | var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(Math.floor(k.Value())*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}], | ||
{curveType:'polar', strokewidth:2}); | {curveType:'polar', strokewidth:2}); | ||
</jsxgraph> | </jsxgraph> | ||
Revision as of 15:17, 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>
Other curves
The quadrifolium is a type of rose curve with n=2. It has polar equation:
- [math]\displaystyle{ r = \cos(2\theta), \, }[/math]
with corresponding algebraic equation
- [math]\displaystyle{ (x^2+y^2)^3 = (x^2-y^2)^2. \, }[/math]
