Lituus: Difference between revisions

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<jsxgraph width="500" height="500" box="box2">
b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]]);
var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]]);
var c = b2.createElement('curve',
            [function(t){ return k1.Value()*b2.I([0,t],function(u){return Math.sin(u*u*0.5);}); },
              function(t){ return k1.Value()*b2.I([0,t],function(u){return Math.cos(u*u*0.5);}); },
              function(){return -len.Value()*Math.PI;}, function(){return len.Value()*Math.PI;}],
            {strokewidth:1});     
</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).



Revision as of 08:37, 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>

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