Circles on circles rotating in opposite directions - Revision history

A WASSERMANN: /* The source code of this construction */

2020-06-23T12:16:49Z

The source code of this construction

← Older revision		Revision as of 12:16, 23 June 2020
Line 57:		Line 57:

	===The source code of this construction===		===The source code of this construction===
	~~This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet.~~ The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.		The main difficulty is to read the values of the sliders.
			This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.
	<source lang="html4strict">		<source lang="html4strict">
	<div style="margin:5px">		<div style="margin:5px">

A WASSERMANN at 12:16, 23 June 2020

2020-06-23T12:16:10Z

@@ Line 1: / Line 1: @@
 This is an example of a parametric curve plot. It shows the orbit of a point on a circle. The circle rotates on a circle which again rotates on the unit circle. The resulting curve is described by the function
 :<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\sin(f_2t)\choose \cos(f_2t)}</math>
-The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.
 <html>
 <div style="margin:5px">
    <p>
@@ Line 30: / Line 29: @@
          oninput="f2 = this.value; board.update();"
      />
    </p>
 </div>
@@ Line 62: / Line 59: @@
 This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.
 <source lang="html4strict">
-<html>
+<div style="margin:5px">
    <p>
      <label for="c1">c1:</label>
-     <input type="text" id="c1" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="c1" style="border:0; color:#f6931f; font-weight:bold;"
      <label for="f1">f1:</label>
-     <input type="text" id="f1" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="f1" style="border:0; color:#f6931f; font-weight:bold;"
      <label for="c2">c2:</label>
-     <input type="text" id="c2" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="c2" style="border:0; color:#f6931f; font-weight:bold;"
      <label for="f2">f2:</label>
-     <input type="text" id="f2" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="f2" style="border:0; color:#f6931f; font-weight:bold;"
    </p>
 </div>
-</html>
 <jsxgraph width="500" height="500" box="jxgbox">
 board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
@@ Line 138: / Line 95: @@
                function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.sin(f2*t);},
                function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.cos(f2*t);},
-,2.02*Math.PI],{strokeWidth:2});
+,2.02*Math.PI], {strokeWidth:2});
 </script>
 </source>
 [[Category:Examples]]
 [[Category:Curves]]

A WASSERMANN at 12:14, 23 June 2020

2020-06-23T12:14:35Z

← Older revision		Revision as of 12:14, 23 June 2020
Line 3:		Line 3:
	The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.		The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.

			<html>
	<div class="sliders" style="margin:5px">		<div class="sliders" style="margin:5px">
	<p>		<p>

A WASSERMANN at 12:14, 23 June 2020

2020-06-23T12:14:18Z

@@ Line 3: / Line 3: @@
 The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.
 <div class="sliders" style="margin:5px">
    <p>
      <label for="c1">c1:</label>
-     <input type="text" id="c1" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="c1" style="border:0; color:#f6931f; font-weight:bold;"
      <label for="f1">f1:</label>
-     <input type="text" id="f1" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="f1" style="border:0; color:#f6931f; font-weight:bold;"
      <label for="c2">c2:</label>
-     <input type="text" id="c2" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="c2" style="border:0; color:#f6931f; font-weight:bold;"
      <label for="f2">f2:</label>
-     <input type="text" id="f2" style="border:0; color:#f6931f; font-weight:bold;" />
+     <input type="range" id="f2" style="border:0; color:#f6931f; font-weight:bold;"
    </p>
 </div>
 </html>
 <jsxgraph width="500" height="500" box="jxgbox">
 board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
 var c1 = 0.6;
 var c2 = 0.0;
 var f1 = 7;
 var f2 = 17;
 var c = board.create('curve', [
                function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.sin(f2*t);},
                function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.cos(f2*t);},
-,2.02*Math.PI],{strokeWidth:2});
+,2.02*Math.PI], {strokeWidth:2});
 </jsxgraph>

Michael at 12:47, 7 June 2011

2011-06-07T12:47:29Z

← Older revision		Revision as of 12:47, 7 June 2011
Line 93:		Line 93:
	This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.		This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.
	<source lang="html4strict">		<source lang="html4strict">
			<html>
	<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>		<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>

A WASSERMANN at 10:19, 25 March 2011

2011-03-25T10:19:38Z

← Older revision		Revision as of 10:19, 25 March 2011
Line 4:		Line 4:

	<html>		<html>
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />~~
	<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>		<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~

	<style type="text/css">		<style type="text/css">
	#slider-frame > div.sliders { padding: 10px !important; };		#slider-frame > div.sliders { padding: 10px !important; };
Line 71:		Line 68:
	<div id="sliderf2" style="width:300px;margin:10px;"></div>		<div id="sliderf2" style="width:300px;margin:10px;"></div>
	</div>		</div>
	<~~div id~~="~~jsxgbox~~" ~~class~~="~~jxgbox~~" ~~style~~="~~width:500px; height:500px;"></div>~~		</html>
	~~<script language="JavaScript~~">		<jsxgraph width="500" height="500" box="jxgbox">
	board = JXG.JSXGraph.initBoard('~~jsxgbox~~', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});		board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
	var c1 = 0.6;		var c1 = 0.6;
	var c2 = 0.0;		var c2 = 0.0;
	var f1 = 7;		var f1 = 7;
	var f2 = 17;		var f2 = 17;
	var c = board.~~createElement~~('curve', [		var c = board.create('curve', [
	function(t) { return Math.cos(t)+ c1Math.cos(f1t)+ c2Math.sin(f2t);},		function(t) { return Math.cos(t)+ c1Math.cos(f1t)+ c2Math.sin(f2t);},
	function(t) { return Math.sin(t)+ c1Math.sin(f1t)+ c2Math.cos(f2t);},		function(t) { return Math.sin(t)+ c1Math.sin(f1t)+ c2Math.cos(f2t);},
	0,2.02*Math.PI],{strokeWidth:2});		0,2.02*Math.PI],{strokeWidth:2});
	</~~script>~~		</jsxgraph>
	~~</html~~>

	'''Variation:'''		'''Variation:'''
Line 97:		Line 93:
	This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.		This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.
	<source lang="html4strict">		<source lang="html4strict">
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />~~
	<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>		<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~

	<style type="text/css">		<style type="text/css">
Line 164:		Line 158:
	<div id="sliderf2" style="width:300px;margin:10px;"></div>		<div id="sliderf2" style="width:300px;margin:10px;"></div>
	</div>		</div>
	<~~div id~~="~~jsxgbox~~" ~~class~~="~~jxgbox~~" ~~style~~="~~width:500px; height:500px;"></div>~~		</html>
	~~<script language="JavaScript~~">		<jsxgraph width="500" height="500" box="jxgbox">
	board = JXG.JSXGraph.initBoard('~~jsxgbox~~', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});		board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
	var c1 = 0.6;		var c1 = 0.6;
	var c2 = 0.0;		var c2 = 0.0;
	var f1 = 7;		var f1 = 7;
	var f2 = 17;		var f2 = 17;
	var c = board.~~createElement~~('curve', [		var c = board.create('curve', [
	function(t) { return Math.cos(t)+ c1Math.cos(f1t)+ c2Math.sin(f2t);},		function(t) { return Math.cos(t)+ c1Math.cos(f1t)+ c2Math.sin(f2t);},
	function(t) { return Math.sin(t)+ c1Math.sin(f1t)+ c2Math.cos(f2t);},		function(t) { return Math.sin(t)+ c1Math.sin(f1t)+ c2Math.cos(f2t);},

Michael: Undo revision 3147 by Annie (Talk), Reason: Spam

2009-10-09T20:35:25Z

Undo revision 3147 by Annie (Talk), Reason: Spam

New page

This is an example of a parametric curve plot. It shows the orbit of a point on a circle. The circle rotates on a circle which again rotates on the unit circle. The resulting curve is described by the function
:<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\sin(f_2t)\choose \cos(f_2t)}</math>
The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.

<html>
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>

<style type="text/css">
#slider-frame > div.sliders { padding: 10px !important; };
</style>
<script type="text/javascript">
$(function() {
$("#sliderc1").slider({
orientation: "horizontal",range: "min",min: 0,max: 100,value: 60,
slide: function(event, ui) {
$("#c1").val(ui.value*0.01);
c1 = ui.value*0.01;
board.update();
}
});
$("#sliderf1").slider({
orientation: "horizontal",range: "min",min: 1,max: 100,value: 7,
slide: function(event, ui) {
$("#f1").val(ui.value);
f1 = ui.value;
board.update();
}
});
$("#c1").val($("#sliderc1").slider("value")*0.01);
$("#f1").val($("#sliderf1").slider("value"));

$("#sliderc2").slider({
orientation: "horizontal",range: "min",min: 0,max: 100,value: 0,
slide: function(event, ui) {
$("#c2").val(ui.value*0.01);
c2 = ui.value*0.01;
board.update();
}
});
$("#sliderf2").slider({
orientation: "horizontal",range: "min",min: 1,max: 100,value: 17,
slide: function(event, ui) {
$("#f2").val(ui.value);
f2 = ui.value;
board.update();
}
});
$("#c2").val($("#sliderc2").slider("value")*0.01);
$("#f2").val($("#sliderf2").slider("value"));
});
</script>

<div class="sliders" style="margin:5px">
<p>
<label for="c1">c1:</label>
<input type="text" id="c1" style="border:0; color:#f6931f; font-weight:bold;" />
<label for="f1">f1:</label>
<input type="text" id="f1" style="border:0; color:#f6931f; font-weight:bold;" />
<label for="c2">c2:</label>
<input type="text" id="c2" style="border:0; color:#f6931f; font-weight:bold;" />
<label for="f2">f2:</label>
<input type="text" id="f2" style="border:0; color:#f6931f; font-weight:bold;" />
</p>
<div id="sliderc1" style="width:300px;margin:10px;"></div>
<div id="sliderf1" style="width:300px;margin:10px;"></div>
<div id="sliderc2" style="width:300px;margin:10px;"></div>
<div id="sliderf2" style="width:300px;margin:10px;"></div>
</div>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
<script language="JavaScript">
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
var c1 = 0.6;
var c2 = 0.0;
var f1 = 7;
var f2 = 17;
var c = board.createElement('curve', [
function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.sin(f2*t);},
function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.cos(f2*t);},
0,2.02*Math.PI],{strokeWidth:2});
</script>
</html>

'''Variation:'''
* [[Circles on circles]]

===External references===
Epicycloidal curves have been used by the ancient greeks to describe the orbits of the planets, see
* [http://arxiv.org/abs/chao-dyn/9907004 Giovanni Gallavotti: Quasi periodic motions from Hipparchus to Kolmogorov]
* [http://www.swisseduc.ch/mathematik/schwingungen/docs/kapitel3.pdf http://www.swisseduc.ch/mathematik/schwingungen/docs/kapitel3.pdf] for a detailed explanation in German
* [http://www.uni-graz.at/~fripert/kreise/index.html Experiments by Harald Fripertinger]

===The source code of this construction===
This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables <math>c1, c2, f1, f2</math>.
<source lang="html4strict">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>

<style type="text/css">
#slider-frame > div.sliders { padding: 10px !important; };
</style>
<script type="text/javascript">
$(function() {
$("#sliderc1").slider({
orientation: "horizontal",range: "min",min: 0,max: 100,value: 60,
slide: function(event, ui) {
$("#c1").val(ui.value*0.01);
c1 = ui.value*0.01;
board.update();
}
});
$("#sliderf1").slider({
orientation: "horizontal",range: "min",min: 1,max: 100,value: 7,
slide: function(event, ui) {
$("#f1").val(ui.value);
f1 = ui.value;
board.update();
}
});
$("#c1").val($("#sliderc1").slider("value")*0.01);
$("#f1").val($("#sliderf1").slider("value"));

$("#sliderc2").slider({
orientation: "horizontal",range: "min",min: 0,max: 100,value: 0,
slide: function(event, ui) {
$("#c2").val(ui.value*0.01);
c2 = ui.value*0.01;
board.update();
}
});
$("#sliderf2").slider({
orientation: "horizontal",range: "min",min: 1,max: 100,value: 17,
slide: function(event, ui) {
$("#f2").val(ui.value);
f2 = ui.value;
board.update();
}
});
$("#c2").val($("#sliderc2").slider("value")*0.01);
$("#f2").val($("#sliderf2").slider("value"));
});
</script>

<div class="sliders" style="margin:5px">
<p>
<label for="c1">c1:</label>
<input type="text" id="c1" style="border:0; color:#f6931f; font-weight:bold;" />
<label for="f1">f1:</label>
<input type="text" id="f1" style="border:0; color:#f6931f; font-weight:bold;" />
<label for="c2">c2:</label>
<input type="text" id="c2" style="border:0; color:#f6931f; font-weight:bold;" />
<label for="f2">f2:</label>
<input type="text" id="f2" style="border:0; color:#f6931f; font-weight:bold;" />
</p>
<div id="sliderc1" style="width:300px;margin:10px;"></div>
<div id="sliderf1" style="width:300px;margin:10px;"></div>
<div id="sliderc2" style="width:300px;margin:10px;"></div>
<div id="sliderf2" style="width:300px;margin:10px;"></div>
</div>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
<script language="JavaScript">
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
var c1 = 0.6;
var c2 = 0.0;
var f1 = 7;
var f2 = 17;
var c = board.createElement('curve', [
function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.sin(f2*t);},
function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.cos(f2*t);},
0,2.02*Math.PI],{strokeWidth:2});
</script>
</source>
[[Category:Examples]]
[[Category:Curves]]

A WASSERMANN at 11:50, 30 June 2009

2009-06-30T11:50:23Z

← Older revision		Revision as of 11:50, 30 June 2009
Line 91:		Line 91:
	Epicycloidal curves have been used by the ancient greeks to describe the orbits of the planets, see		Epicycloidal curves have been used by the ancient greeks to describe the orbits of the planets, see
	* [http://arxiv.org/abs/chao-dyn/9907004 Giovanni Gallavotti: Quasi periodic motions from Hipparchus to Kolmogorov]		* [http://arxiv.org/abs/chao-dyn/9907004 Giovanni Gallavotti: Quasi periodic motions from Hipparchus to Kolmogorov]
			* [http://www.swisseduc.ch/mathematik/schwingungen/docs/kapitel3.pdf http://www.swisseduc.ch/mathematik/schwingungen/docs/kapitel3.pdf] for a detailed explanation in German
	* [http://www.uni-graz.at/~fripert/kreise/index.html Experiments by Harald Fripertinger]		* [http://www.uni-graz.at/~fripert/kreise/index.html Experiments by Harald Fripertinger]

A WASSERMANN at 11:23, 30 June 2009

2009-06-30T11:23:45Z

← Older revision		Revision as of 11:23, 30 June 2009
Line 1:		Line 1:
	This is an example of a parametric curve plot. The curve is described by the function		This is an example of a parametric curve plot. It shows the orbit of a point on a circle. The circle rotates on a circle which again rotates on the unit circle. The resulting curve is described by the function
	:<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\sin(f_2t)\choose \cos(f_2t)}</math>		:<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\sin(f_2t)\choose \cos(f_2t)}</math>
	The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.		The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.

A WASSERMANN at 11:13, 30 June 2009

2009-06-30T11:13:38Z

← Older revision		Revision as of 11:13, 30 June 2009
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	Epicycloidal curves have been used by the ancient greeks to describe the orbits of the planets, see		Epicycloidal curves have been used by the ancient greeks to describe the orbits of the planets, see
	* [http://arxiv.org/abs/chao-dyn/9907004 Giovanni Gallavotti: Quasi periodic motions from Hipparchus to Kolmogorov]		* [http://arxiv.org/abs/chao-dyn/9907004 Giovanni Gallavotti: Quasi periodic motions from Hipparchus to Kolmogorov]
			* [http://www.uni-graz.at/~fripert/kreise/index.html Experiments by Harald Fripertinger]

	===The source code of this construction===		===The source code of this construction===