Logarithmic spiral

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

[math]r = ae^{b\theta}\,[/math]

with real numbers [math]a[/math] and [math]b[/math].

The JavaScript code to produce this picture

 board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox: [-10, 10, 10, -10]});
 var a = board.create('slider', [[1,-1],[5,-1],[0,0.3,1]],{name:'a'});
 var b = board.create('slider', [[1,-2],[5,-2],[-1,0.15,1]],{name:'b'});
 var c = board.create('curve', [function(phi){return a.Value()*JXG.Math.pow(Math.E,b.Value()*phi); }, [0, 0],0, 8*Math.PI],
             {curveType:'polar', strokewidth:4});        
 var g = board.create('glider', [c]);
 var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'});