Difference between revisions of "Rose"

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Line 19: Line 19:
 
  var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
 
  var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
 
  var f = b2.createElement('slider', [[1,8],[6,8],[0,4,8]]);
 
  var f = b2.createElement('slider', [[1,8],[6,8],[0,4,8]]);
  var len = b2.createElement('slider', [[1,7],[6,7],[0,2,8]],{name:'len'});  
+
  var len = b2.createElement('slider', [[1,7],[6,7],[0,2,8]],{snapWidth:1,name:'len'});  
  var k = b2.createElement('slider', [[1,6],[6,6],[0,2,10]],{snapWidth:0.2,name:'k'});
+
  var k = b2.createElement('slider', [[1,6],[6,6],[0,2,12]],{snapWidth:0.2,name:'k'});
 
  var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
 
  var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
 
             {curveType:'polar', strokewidth:2});       
 
             {curveType:'polar', strokewidth:2});       
Line 30: Line 30:
 
<jsxgraph width="500" height="500" box="box2">
 
<jsxgraph width="500" height="500" box="box2">
 
  var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
 
  var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
  var f = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);
+
  var f = b2.createElement('slider', [[1,8],[6,8],[0,4,8]]);
  var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]],{name:'len'});  
+
  var len = b2.createElement('slider', [[1,7],[6,7],[0,2,8]],{snapWidth:1,name:'len'});  
  var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{snapWidth:0.2,name:'k'});
+
  var k = b2.createElement('slider', [[1,6],[6,6],[0,2,12]],{snapWidth:0.2,name:'k'});
 
  var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
 
  var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
 
             {curveType:'polar', strokewidth:2});       
 
             {curveType:'polar', strokewidth:2});       

Revision as of 19:00, 27 June 2009

A rose or rhodonea curve is a sinusoid plotted in polar coordinates. Up to similarity, these curves can all be expressed by a polar equation of the form

[math] \!\,r=\cos(k\theta).[/math]

If k is an integer, the curve will be rose shaped with

  • 2k petals if k is even, and
  • k petals if k is odd.

When k is even, the entire graph of the rose will be traced out exactly once when the value of θ changes from 0 to 2π. When k is odd, this will happen on the interval between 0 and π. (More generally, this will happen on any interval of length [math]2\pi[/math] for [math]k[/math] even, and [math]\pi[/math] for [math]k[/math] odd.)

The quadrifolium is a type of rose curve with n=2. It has polar equation:

[math] r = \cos(2\theta), \,[/math]

with corresponding algebraic equation

[math] (x^2+y^2)^3 = (x^2-y^2)^2. \, [/math]

The JavaScript code to produce this picture

<jsxgraph width="500" height="500" box="box2">
 var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
 var f = b2.createElement('slider', [[1,8],[6,8],[0,4,8]]);
 var len = b2.createElement('slider', [[1,7],[6,7],[0,2,8]],{snapWidth:1,name:'len'}); 
 var k = b2.createElement('slider', [[1,6],[6,6],[0,2,12]],{snapWidth:0.2,name:'k'});
 var c = b2.createElement('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
             {curveType:'polar', strokewidth:2});      
</jsxgraph>

External links