Archimedean spiral

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It can be described in polar coordinates (r,θ) by the equation

\, r=a+b\theta

with real numbers a and b.

The JavaScript code to produce this picture

var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
var a = board.create('slider', [[1,8],[5,8],[0,1,4]],{name:'a'});
var b = board.create('slider', [[1,9],[5,9],[0,0.25,4]],{name:'b'});
 
var c = board.create('curve', [function(phi){return a.Value()+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'});
var n = board.create('normal', [g], {dash:2,strokeColor:'#a612a9'});
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