Rose - Revision history

Michael at 12:39, 8 June 2011

2011-06-08T12:39:56Z

← Older revision		Revision as of 12:39, 8 June 2011
Line 17:		Line 17:

	<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,boundingbox: [-10, 10, 10, -10]});
	var f = b2.~~createElement~~('slider', [[1,8],[6,8],[0,4,8]]);		var f = b2.create('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 len = b2.create('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 k = b2.create('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.create('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});
	</jsxgraph>		</jsxgraph>
Line 27:		Line 27:
	===The JavaScript code to produce this picture===		===The JavaScript code to produce this picture===

	<source lang="~~xml">~~		<source lang="javascript">
	~~<jsxgraph width="500" height="500" box="box2~~">		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,boundingbox: [-10, 10, 10, -10]});
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		var f = b2.create('slider', [[1,8],[6,8],[0,4,8]]);
	var f = b2.~~createElement~~('slider', [[1,8],[6,8],[0,4,8]]);		var len = b2.create('slider', [[1,7],[6,7],[0,2,8]],{snapWidth:1,name:'len'});
	var len = b2.~~createElement~~('slider', [[1,7],[6,7],[0,2,8]],{snapWidth:1,name:'len'});		var k = b2.create('slider', [[1,6],[6,6],[0,2,12]],{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.create('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});
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 18:00, 27 June 2009

2009-06-27T18:00:28Z

A WASSERMANN at 17:58, 27 June 2009

2009-06-27T17:58:30Z

← Older revision		Revision as of 17:58, 27 June 2009
Line 18:		Line 18:
	<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]],{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],[0,2,10]],{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});

A WASSERMANN at 17:57, 27 June 2009

2009-06-27T17:57:06Z

A WASSERMANN at 17:11, 22 June 2009

2009-06-22T17:11:30Z

A WASSERMANN at 15:24, 18 March 2009

2009-03-18T15:24:22Z

← Older revision		Revision as of 15:24, 18 March 2009
Line 1:		Line 1:
	~~===Other curves===~~
	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		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

A WASSERMANN at 15:23, 18 March 2009

2009-03-18T15:23:51Z

← Older revision		Revision as of 15:23, 18 March 2009
Line 40:		Line 40:

	===External links===		===External links===
	* [http://en.wikipedia.org/wiki/Rose_(mathematics)]		* [http://en.wikipedia.org/wiki/Rose_(mathematics) http://en.wikipedia.org/wiki/Rose_(mathematics)]
	* [http://en.wikipedia.org/wiki/Quadrifolium]		* [http://en.wikipedia.org/wiki/Quadrifolium http://en.wikipedia.org/wiki/Quadrifolium]

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Curves]]		[[Category:Curves]]

A WASSERMANN: New page: ===Other curves=== 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 :
2009-03-18T15:23:22Z

New page: ===Other curves=== 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 :<m...

New page
===Other curves===
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>

<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],[5,8],[0,4,8]]);
var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);
var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]);
var c = b2.createElement('curve', [function(phi){return f.Value()Math.cos(Math.floor(k.Value())phi); }, [0, 0],0, function(){return len.Value()Math.PI;}],
{curveType:'polar', strokewidth:2});
</jsxgraph>

===The JavaScript code to produce this picture===

<source lang="xml">
<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],[5,8],[0,4,8]]);
var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);
var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]);
var c = b2.createElement('curve', [function(phi){return f.Value()Math.cos(Math.floor(k.Value())phi); }, [0, 0],0, function(){return len.Value()Math.PI;}],
{curveType:'polar', strokewidth:2});
</jsxgraph>
</source>

===External links===
* [http://en.wikipedia.org/wiki/Rose_(mathematics)]
* [http://en.wikipedia.org/wiki/Quadrifolium]

[[Category:Examples]]
[[Category:Curves]]

← Older revision		Revision as of 18:00, 27 June 2009
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});

← Older revision		Revision as of 17:57, 27 June 2009
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],[5,8],[0,4,8]]);		var f = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);
	var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);		var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]],{name:'len'});
	var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{snapWidth:1});		var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{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 31:		Line 31:
	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],[5,8],[0,4,8]]);
	var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);		var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]],{name:'len'});
	var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{snapWidth:1});		var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{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});

← Older revision		Revision as of 17:11, 22 June 2009
Line 20:		Line 20:
	var f = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);		var f = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);
	var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);		var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);
	var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]);		var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{snapWidth:1});
	var c = b2.createElement('curve', [function(phi){return f.Value()Math.cos~~(Math.floor~~(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});
	</jsxgraph>		</jsxgraph>
Line 32:		Line 32:
	var f = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);		var f = b2.createElement('slider', [[1,8],[5,8],[0,4,8]]);
	var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);		var len = b2.createElement('slider', [[1,7],[5,7],[0,2,2]]);
	var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]);		var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]],{snapWidth:1});
	var c = b2.createElement('curve', [function(phi){return f.Value()Math.cos~~(Math.floor~~(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});
	</jsxgraph>		</jsxgraph>