Watt curve - Revision history

A WASSERMANN at 16:17, 20 February 2013

2013-02-20T16:17:13Z

← Older revision		Revision as of 16:17, 20 February 2013
Line 14:		Line 14:
	g1 = board.create('glider', [0, 0, c1], {size:3,name:"Drag me"});		g1 = board.create('glider', [0, 0, c1], {size:3,name:"Drag me"});
	c3 = board.create('circle', [g1, 8]);		c3 = board.create('circle', [g1, 8]);
	g2 = board.create('~~point~~', [~~board.intersectionFunc(~~c2,c3,0)], {size:3, name: ""});		g2 = board.create('intersection', [c2,c3,0], {size:3, name: ""});
	g3 = board.create('~~point~~', [~~board.intersectionFunc(~~c2,c3,1)], {size:3, name: ""});		g3 = board.create('intersection', [c2,c3,1], {size:3, name: ""});
	m1 = board.create('midpoint', [g1,g2], {face:'[]',size:3,withLabel:false,trace:true});		m1 = board.create('midpoint', [g1,g2], {face:'[]',size:3,withLabel:false,trace:true});
	m2 = board.create('midpoint', [g1,g3], {face:'[]',size:3,withLabel:false,trace:true,strokeColor:'green'});		m2 = board.create('midpoint', [g1,g3], {face:'[]',size:3,withLabel:false,trace:true,strokeColor:'green'});

Michael at 14:43, 8 June 2011

2011-06-08T14:43:59Z

← Older revision		Revision as of 14:43, 8 June 2011
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	<html>		<html>
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />~~
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~
	<input type="button" value="Clear trace" onClick="clearTrace()" />		<input type="button" value="Clear trace" onClick="clearTrace()" />
	<~~div id~~="jxgbox" ~~class~~="~~jxgbox~~" ~~style="width:600px;~~ height~~:450px;"></div>~~		</html>
	~~<script language~~="~~JavaScript~~">
	board = JXG.JSXGraph.initBoard('jxgbox', {~~originX~~: 50, ~~originY: 400~~, ~~unitX: 25~~, ~~unitY: 25~~, axis: ~~false~~, grid: false});		<jsxgraph box="jxgbox" width="600" height="450">
	~~xax = board.createElement('axis', [[0,0],[1,0]]);~~		board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-2, 16, 22, -2], axis: true, grid: false});
	~~yax = board.createElement('axis', [[0,0],[0,1]]~~);		p1 = board.create('point', [7, 8], {face:'x',size:4,name:"",fixed:true});
	p1 = board.~~createElement~~('point', [7, 8], {~~style~~:2,name:"",fixed:true});		p2 = board.create('point', [15, 8], {face:'x',size:4,name:"",fixed:true});
	p2 = board.~~createElement~~('point', [15, 8], {~~style~~:2,name:"",fixed:true});		c1 = board.create('circle', [p1, 4.5]);
	c1 = board.~~createElement~~('circle', [p1, 4.5]);		c2 = board.create('circle', [p2, 4.5]);
	c2 = board.~~createElement~~('circle', [p2, 4.5]);		g1 = board.create('glider', [0, 0, c1], {size:3,name:"Drag me"});
	g1 = board.~~createElement~~('glider', [0, 0, c1], {~~style~~:5,name:"Drag me"});		c3 = board.create('circle', [g1, 8]);
	c3 = board.~~createElement~~('circle', [g1, 8]);		g2 = board.create('point', [board.intersectionFunc(c2,c3,0)], {size:3, name: ""});
	g2 = board.~~createElement~~('point', [board.intersectionFunc(c2,c3,0)], {~~style~~:5, name: ""});		g3 = board.create('point', [board.intersectionFunc(c2,c3,1)], {size:3, name: ""});
	g3 = board.~~createElement~~('point', [board.intersectionFunc(c2,c3,1)], {~~style~~:5, name: ""});		m1 = board.create('midpoint', [g1,g2], {face:'[]',size:3,withLabel:false,trace:true});
	m1 = board.~~createElement~~('midpoint', [g1,g2], {~~style~~:8,~~name~~:"",trace:true});		m2 = board.create('midpoint', [g1,g3], {face:'[]',size:3,withLabel:false,trace:true,strokeColor:'green'});
	m2 = board.~~createElement~~('midpoint', [g1,g3], {~~style~~:8,~~name~~:"",trace:true,strokeColor:'green'});

	function clearTrace() {		function clearTrace() {
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	m2.clearTrace();		m2.clearTrace();
	}		}
	</~~script>~~		</jsxgraph>
	~~</html~~>

	==References==		==References==
Line 36:		Line 32:

	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('jxgbox', {~~originX~~: 50, ~~originY: 400~~, ~~unitX: 25~~, ~~unitY: 25~~, axis: ~~false~~, grid: false});		board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-2, 16, 22, -2], axis: true, grid: false});
	~~xax = board.createElement('axis', [[0,0],[1,0]]);~~		p1 = board.create('point', [7, 8], {face:'x',size:4,name:"",fixed:true});
	~~yax = board.createElement('axis', [[0,0],[0,1]]~~);		p2 = board.create('point', [15, 8], {face:'x',size:4,name:"",fixed:true});
	p1 = board.~~createElement~~('point', [7, 8], {~~style~~:2,name:"",fixed:true});		c1 = board.create('circle', [p1, 4.5]);
	p2 = board.~~createElement~~('point', [15, 8], {~~style~~:2,name:"",fixed:true});		c2 = board.create('circle', [p2, 4.5]);
	c1 = board.~~createElement~~('circle', [p1, 4.5]);		g1 = board.create('glider', [0, 0, c1], {size:3,name:"Drag me"});
	c2 = board.~~createElement~~('circle', [p2, 4.5]);		c3 = board.create('circle', [g1, 8]);
	g1 = board.~~createElement~~('glider', [0, 0, c1], {~~style~~:5,name:"Drag me"});		g2 = board.create('point', [board.intersectionFunc(c2,c3,0)], {size:3, name: ""});
	c3 = board.~~createElement~~('circle', [g1, 8]);		g3 = board.create('point', [board.intersectionFunc(c2,c3,1)], {size:3, name: ""});
	g2 = board.~~createElement~~('point', [board.intersectionFunc(c2,c3,0)], {~~style~~:5, name: ""});		m1 = board.create('midpoint', [g1,g2], {face:'[]',size:3,withLabel:false,trace:true});
	g3 = board.~~createElement~~('point', [board.intersectionFunc(c2,c3,1)], {~~style~~:5, name: ""});		m2 = board.create('midpoint', [g1,g3], {face:'[]',size:3,withLabel:false,trace:true,strokeColor:'green'});
	m1 = board.~~createElement~~('midpoint', [g1,g2], {~~style~~:8,~~name~~:"",trace:true});
	m2 = board.~~createElement~~('midpoint', [g1,g3], {~~style~~:8,~~name~~:"",trace:true,strokeColor:'green'});

	function clearTrace() {		function clearTrace() {
Line 54:		Line 48:
	m2.clearTrace();		m2.clearTrace();
	}		}

	</source>		</source>

A WASSERMANN at 17:34, 29 October 2009

2009-10-29T17:34:33Z

← Older revision		Revision as of 17:34, 29 October 2009
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/jsxgraph.css" />
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>~~
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<input type="button" value="Clear trace" onClick="clearTrace()" />		<input type="button" value="Clear trace" onClick="clearTrace()" />

Michael at 10:32, 27 April 2009

2009-04-27T10:32:52Z

← Older revision		Revision as of 10:32, 27 April 2009
Line 65:		Line 65:
	Where in this case <math>e=8</math>. Setting the polynomial to zero and plotting that equation with Maple results the following picture.		Where in this case <math>e=8</math>. Setting the polynomial to zero and plotting that equation with Maple results the following picture.

	[[Image:~~Plott_watt_curve~~.jpeg]]		[[Image:Plot_watt_curve.jpeg]]

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

Michael at 10:13, 27 April 2009

2009-04-27T10:13:18Z

← Older revision		Revision as of 10:13, 27 April 2009
Line 65:		Line 65:
	Where in this case <math>e=8</math>. Setting the polynomial to zero and plotting that equation with Maple results the following picture.		Where in this case <math>e=8</math>. Setting the polynomial to zero and plotting that equation with Maple results the following picture.

	[[Image:~~Plot_watt_curve~~.jpeg]]		[[Image:Plott_watt_curve.jpeg]]

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

Michael at 09:55, 27 April 2009

2009-04-27T09:55:18Z

← Older revision		Revision as of 09:55, 27 April 2009
Line 1:		Line 1:
			=Trace=
	With JSXGraph elements can be traced to visualize construced loci.		With JSXGraph elements can be traced to visualize construced loci.

Line 56:		Line 57:

	</source>		</source>

			=Compute Locus Equation=
			One way to compute the locus equation of the traced points in the above construction is the Groebner-Basis-Method. Applying this method to the above construction we get this polynomial:

			<math>16e^4s^2 - 96e^3s^3 + 208e^2s^4 - 192es^5 + 64s^6 + 16e^4t^2 - 96e^3st^2 + 288e^2s^2t^2 - 384es^3t^2 + 192s^4t^2 + 80e^2t^4 - 192est^4 + 192s^2t^4 + 64t^6 + 136e^3s - 680e^2s^2 + 1088es^3 - 544s^4 - 1432e^2t^2 + 1088est^2 - 1088s^2t^2 - 544t^4 + 289e^2 - 1156es + 1156s^2 + 1156t^2</math>

			Where in this case <math>e=8</math>. Setting the polynomial to zero and plotting that equation with Maple results the following picture.

			[[Image:Plot_watt_curve.jpeg]]

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

Michael at 07:39, 16 March 2009

2009-03-16T07:39:46Z

← Older revision		Revision as of 07:39, 16 March 2009
Line 31:		Line 31:
	==References==		==References==

	* [http://en.wikipedia.org/wiki/Watt_curve]		* [http://en.wikipedia.org/wiki/Watt_curve http://en.wikipedia.org/wiki/Watt_curve]

	==The underlying JavaScript code==		==The underlying JavaScript code==

Michael at 07:39, 16 March 2009

2009-03-16T07:39:13Z

Michael: New page: With JSXGraph elements can be traced to visualize construced loci.

← Older revision		Revision as of 07:39, 16 March 2009
Line 11:		Line 11:
	xax = board.createElement('axis', [[0,0],[1,0]]);		xax = board.createElement('axis', [[0,0],[1,0]]);
	yax = board.createElement('axis', [[0,0],[0,1]]);		yax = board.createElement('axis', [[0,0],[0,1]]);
	p1 = board.createElement('point', [7, 8], {style:2,name:"",fixed:true}); ~~// Angabe fester Koordinaten~~		p1 = board.createElement('point', [7, 8], {style:2,name:"",fixed:true});
	p2 = board.createElement('point', [15, 8], {style:2,name:"",fixed:true}); ~~// Angabe fester Koordinaten~~		p2 = board.createElement('point', [15, 8], {style:2,name:"",fixed:true});
	c1 = board.createElement('circle', [p1, 4.5]);		c1 = board.createElement('circle', [p1, 4.5]);
	c2 = board.createElement('circle', [p2, 4.5]);		c2 = board.createElement('circle', [p2, 4.5]);
Line 39:		Line 39:
	xax = board.createElement('axis', [[0,0],[1,0]]);		xax = board.createElement('axis', [[0,0],[1,0]]);
	yax = board.createElement('axis', [[0,0],[0,1]]);		yax = board.createElement('axis', [[0,0],[0,1]]);
	p1 = board.createElement('point', [7, 8], {style:2,name:"",fixed:true}); ~~// Angabe fester Koordinaten~~		p1 = board.createElement('point', [7, 8], {style:2,name:"",fixed:true});
	p2 = board.createElement('point', [15, 8], {style:2,name:"",fixed:true}); ~~// Angabe fester Koordinaten~~		p2 = board.createElement('point', [15, 8], {style:2,name:"",fixed:true});
	c1 = board.createElement('circle', [p1, 4.5]);		c1 = board.createElement('circle', [p1, 4.5]);
	c2 = board.createElement('circle', [p2, 4.5]);		c2 = board.createElement('circle', [p2, 4.5]);