# Difference between revisions of "Logarithmic spiral"

From JSXGraph Wiki

A WASSERMANN (talk | contribs) |
A WASSERMANN (talk | contribs) |
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with real numbers <math>a</math> and <math>b</math>. | with real numbers <math>a</math> and <math>b</math>. | ||

<jsxgraph box="jsxgbox" width="500" height="500"> | <jsxgraph box="jsxgbox" width="500" height="500"> | ||

− | board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox: [-10, 10, 10, -10] | + | 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 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 b = board.create('slider', [[1,-2],[5,-2],[-1,0.15,1]],{name:'b'}); | ||

− | var c = board.create('curve', [function(phi){return a.Value()*Math.exp(b.Value()*phi); }, [0, 0], 0, | + | var c = board.create('curve', [function(phi){return a.Value()*Math.exp(b.Value()*phi); }, [0, 0], 0, 8*Math.PI], |

{curveType:'polar', strokewidth:4}); | {curveType:'polar', strokewidth:4}); | ||

var g = board.create('glider', [c]); | var g = board.create('glider', [c]); |

## Latest revision as of 14:50, 28 June 2019

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'});
```