Fermat's spiral

It can be described in polar coordinates [math]\displaystyle{ (r, \theta) }[/math] by the equation

[math]\displaystyle{ r = \pm a\theta^{1/2}\, }[/math]

with a real number [math]\displaystyle{ a }[/math].

The JavaScript code to produce this picture

 var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
 var a = board.create('slider', [[1,9],[5,9],[0,1,4]],{name:'a'});
 var c1 = board.create('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});        
 var c2 = board.create('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});