Logarithmic spiral: Difference between revisions
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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"> | ||
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()*Math.exp(b.Value()*phi); }, [0, 0], 0, 8*Math.PI], | |||
board = JXG.JSXGraph.initBoard('jsxgbox', { | |||
var a = board. | |||
var b = board. | |||
var c = board. | |||
{curveType:'polar', strokewidth:4}); | {curveType:'polar', strokewidth:4}); | ||
</ | var g = board.create('glider', [c]); | ||
var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'}); | |||
</jsxgraph> | |||
===The JavaScript code to produce this picture=== | ===The JavaScript code to produce this picture=== | ||
<source lang="javascript"> | <source lang="javascript"> | ||
board = JXG.JSXGraph.initBoard('jsxgbox', { | board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox: [-10, 10, 10, -10]}); | ||
var a = board. | var a = board.create('slider', [[1,-1],[5,-1],[0,0.3,1]],{name:'a'}); | ||
var b = board. | var b = board.create('slider', [[1,-2],[5,-2],[-1,0.15,1]],{name:'b'}); | ||
var c = board. | 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}); | {curveType:'polar', strokewidth:4}); | ||
var g = board.create('glider', [c]); | |||
var t = board.create('tangent', [g], {dash:2,strokeColor:'#a612a9'}); | |||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Curves]] | [[Category:Curves]] | ||
Latest revision as of 12:50, 28 June 2019
It can be described in polar coordinates [math]\displaystyle{ (r, \theta) }[/math] by the equation
- [math]\displaystyle{ r = ae^{b\theta}\, }[/math]
with real numbers [math]\displaystyle{ a }[/math] and [math]\displaystyle{ 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'});
