Lituus - Revision history

Michael at 08:35, 8 June 2011

2011-06-08T08:35:02Z

← Older revision		Revision as of 08:35, 8 June 2011
Line 4:		Line 4:

	<jsxgraph width="500" height="500" box="box1">		<jsxgraph width="500" height="500" box="box1">
	var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,boundingbox: [-10, 10, 10, -10]});
	var k = b1.create('slider', [[1,8],[5,8],[0,1,4]]);		var k = b1.create('slider', [[1,8],[5,8],[0,1,4]]);
	var c = b1.create('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],		var c = b1.create('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
Line 12:		Line 12:
	===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="box1">~~		var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,boundingbox: [-10, 10, 10, -10]});
	var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		var k = b1.create('slider', [[1,8],[5,8],[0,1,4]]);
	var k = b1.create('slider', [[1,8],[5,8],[0,1,4]]);		var c = b1.create('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
	var c = b1.create('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:1});		{curveType:'polar', strokewidth:1});
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 07:46, 22 July 2010

2010-07-22T07:46:57Z

← Older revision		Revision as of 07:46, 22 July 2010
Line 5:		Line 5:
	<jsxgraph width="500" height="500" box="box1">		<jsxgraph width="500" height="500" box="box1">
	var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k = b1.~~createElement~~('slider', [[1,8],[5,8],[0,1,4]]);		var k = b1.create('slider', [[1,8],[5,8],[0,1,4]]);
	var c = b1.~~createElement~~('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],		var c = b1.create('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:1});
	</jsxgraph>		</jsxgraph>

Line 15:		Line 15:
	<jsxgraph width="500" height="500" box="box1">		<jsxgraph width="500" height="500" box="box1">
	var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b1 = JXG.JSXGraph.initBoard('box1', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k = b1.~~createElement~~('slider', [[1,8],[5,8],[0,1,4]]);		var k = b1.create('slider', [[1,8],[5,8],[0,1,4]]);
	var c = b1.~~createElement~~('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],		var c = b1.create('curve', [function(phi){return Math.sqrt(k.Value()/phi); }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:1});
	</jsxgraph>		</jsxgraph>
	</source>		</source>

A WASSERMANN at 15:22, 18 March 2009

2009-03-18T15:22:21Z

@@ Line 20: / Line 20: @@
 </jsxgraph>
 </source>
 ===External links===

A WASSERMANN at 15:20, 18 March 2009

2009-03-18T15:20:24Z

← Older revision		Revision as of 15:20, 18 March 2009
Line 26:		Line 26:

	If k is an integer, the curve will be rose shaped with		If k is an integer, the curve will be rose shaped with
	* 2k petals if k is even, and		* 2k petals if k is even, and
	* k petals if k is odd.		* 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.)		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.)

A WASSERMANN at 15:20, 18 March 2009

2009-03-18T15:20:11Z

← Older revision		Revision as of 15:20, 18 March 2009
Line 26:		Line 26:

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

	* 2k petals if k is even, and		* 2k petals if k is even, and
	* k petals if k is odd.		* 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.)		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.)

A WASSERMANN at 15:19, 18 March 2009

2009-03-18T15:19:18Z

@@ Line 21: / Line 21: @@
 </source>
 ===Other curves===
 The '''quadrifolium''' is a type of rose curve with n=2. It has polar equation:

A WASSERMANN at 15:17, 18 March 2009

2009-03-18T15:17:05Z

← Older revision		Revision as of 15:17, 18 March 2009
Line 34:		Line 34:
	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]]);
	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(Math.floor(k.Value())phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:2});		{curveType:'polar', strokewidth:2});
	</jsxgraph>		</jsxgraph>

A WASSERMANN at 15:15, 18 March 2009

2009-03-18T15:15:34Z

← Older revision		Revision as of 15:15, 18 March 2009
Line 21:		Line 21:
	</source>		</source>
	===Other curves===		===Other curves===
	The quadrifolium is a type of rose curve with n=2. It has polar equation:		The '''quadrifolium''' is a type of rose curve with n=2. It has polar equation:

	:<math> r = \cos(2\theta), \,</math>		:<math> r = \cos(2\theta), \,</math>
Line 31:		Line 31:
	<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 k = 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 c = b2.createElement('curve', [function(phi){return k.Value()Math.cos(2.0phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],		var k = b2.createElement('slider', [[1,6],[5,6],[0,2,10]]);
			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>

A WASSERMANN at 15:10, 18 March 2009

2009-03-18T15:10:47Z

← Older revision		Revision as of 15:10, 18 March 2009
Line 20:		Line 20:
	</jsxgraph>		</jsxgraph>
	</source>		</source>
			===Other curves===
			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">		<jsxgraph width="500" height="500" box="box2">

A WASSERMANN at 15:09, 18 March 2009

2009-03-18T15:09:39Z

← Older revision		Revision as of 15:09, 18 March 2009
Line 23:		Line 23:
	<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 k = b2.createElement('slider', [[1,8],[5,8],[0,1,4]]);		var k = 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 c = b2.createElement('curve', [function(phi){return k.Value()Math.cos(2.0phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],		var c = b2.createElement('curve', [function(phi){return k.Value()Math.cos(2.0phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:2});
	</jsxgraph>		</jsxgraph>