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

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>

 board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
 var a = board.createElement('slider', [[1,9],[5,9],[0,1,4]]);
 var c1 = board.createElement('curve', [function(phi){return a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});        
 var c2 = board.createElement('curve', [function(phi){return -a.Value()*Math.sqrt(phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});