Hyperbolic spiral - Revision history

Michael at 07:29, 8 June 2011

2011-06-08T07:29:00Z

← Older revision		Revision as of 07:29, 8 June 2011
Line 5:		Line 5:
	with a real number <math>a</math>.		with a real number <math>a</math>.
	<jsxgraph width="500" height="500">		<jsxgraph width="500" height="500">
	var board = JXG.JSXGraph.initBoard('jxgbox', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
	var a = board.create('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});		var a = board.create('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	var c = board.create('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],		var c = board.create('curve', [function(phi){return a.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="javascript">		<source lang="javascript">
	var board = JXG.JSXGraph.initBoard('jxgbox', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 50~~, ~~unitY: 50~~});		var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10]});
	var a = board.create('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});		var a = board.create('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	var c = board.create('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],		var c = board.create('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],

A WASSERMANN at 20:52, 29 September 2010

2010-09-29T20:52:35Z

← Older revision		Revision as of 20:52, 29 September 2010
Line 4:		Line 4:

	with a real number <math>a</math>.		with a real number <math>a</math>.
	<~~html>~~		<jsxgraph width="500" height="500">
	~~<link rel="stylesheet" type="text/css" href="http://~~jsxgraph~~.uni-bayreuth.de/distrib/jsxgraph.css" />~~		var board = JXG.JSXGraph.initBoard('jxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~		var a = board.create('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	~~<div id="jsxgbox" class~~="~~jxgbox~~" ~~style="width:500px;~~ height~~:500px;"></div>~~		var c = board.create('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	~~<script language~~="~~JavaScript~~">
	board = JXG.JSXGraph.initBoard('~~jsxgbox~~', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.~~createElement~~('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	var c = board.~~createElement~~('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
	</~~script>~~		</jsxgraph>
	~~</html~~>
	===The JavaScript code to produce this picture===		===The JavaScript code to produce this picture===
	~~<source lang="html4strict">~~
	~~<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>~~
	~~<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>~~
	~~</source>~~
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('~~jsxgbox~~', {originX: 250, originY: 250, unitX: 50, unitY: 50});		var board = JXG.JSXGraph.initBoard('jxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
	var a = board.~~createElement~~('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});		var a = board.create('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	var c = board.~~createElement~~('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],		var c = board.create('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
	</source>		</source>

A WASSERMANN at 17:08, 29 October 2009

2009-10-29T17:08:32Z

← Older revision		Revision as of 17:08, 29 October 2009
Line 6:		Line 6:
	<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>
	<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
Line 19:		Line 18:
	<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/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>
	<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>

A WASSERMANN at 09:58, 2 July 2009

2009-07-02T09:58:38Z

← Older revision		Revision as of 09:58, 2 July 2009
Line 11:		Line 11:
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);		var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
Line 25:		Line 25:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
	var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);		var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]],{name:'a'});
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});

A WASSERMANN at 11:47, 10 March 2009

2009-03-10T11:47:24Z

← Older revision		Revision as of 11:47, 10 March 2009
Line 12:		Line 12:
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);		var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0]~~,'phi'~~,0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
	</script>		</script>
Line 26:		Line 26:
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
	var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);		var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0]~~,'phi'~~,0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
	</source>		</source>

A WASSERMANN at 10:51, 6 March 2009

2009-03-06T10:51:33Z

← Older revision		Revision as of 10:51, 6 March 2009
Line 11:		Line 11:
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.createElement('slider', [[1,-1],[9,-1],[0,4,30]]);		var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
Line 25:		Line 25:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
	var a = board.createElement('slider', [[1,-1],[9,-1],[0,4,30]]);		var a = board.createElement('slider', [[0,5],[8,5],[0,4,30]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});

A WASSERMANN at 10:50, 6 March 2009

2009-03-06T10:50:51Z

← Older revision		Revision as of 10:50, 6 March 2009
Line 11:		Line 11:
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.createElement('slider', [[1,-1],[7,-1],[0,4,15]]);		var a = board.createElement('slider', [[1,-1],[9,-1],[0,4,30]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
Line 25:		Line 25:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
	var a = board.createElement('slider', [[1,-1],[5,-1],[0,4,8]]);		var a = board.createElement('slider', [[1,-1],[9,-1],[0,4,30]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});

A WASSERMANN at 10:50, 6 March 2009

2009-03-06T10:50:12Z

← Older revision		Revision as of 10:50, 6 March 2009
Line 11:		Line 11:
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.createElement('slider', [[1,-1],[5,-1],[0,4,8]]);		var a = board.createElement('slider', [[1,-1],[7,-1],[0,4,15]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});

A WASSERMANN at 17:30, 10 February 2009

2009-02-10T17:30:28Z

← Older revision		Revision as of 17:30, 10 February 2009
Line 11:		Line 11:
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = board.createElement('slider', [[1,-1],[5,-1],[0,1,4]]);		var a = board.createElement('slider', [[1,-1],[5,-1],[0,4,8]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});
Line 25:		Line 25:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
	var a = board.createElement('slider', [[1,-1],[5,-1],[0,1,4]]);		var a = board.createElement('slider', [[1,-1],[5,-1],[0,4,8]]);
	var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],		var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8*Math.PI],
	{curveType:'polar', strokewidth:4});		{curveType:'polar', strokewidth:4});

A WASSERMANN: New page: It can be described in polar coordinates $(r, \theta)$ by the equation : $r = \frac{a}{\theta}\,$ with a real number $a$ .
2009-02-10T17:29:57Z

New page: It can be described in polar coordinates <math>(r, \theta)</math> by the equation :<math>r = \frac{a}{\theta}\,</math> with a real number <math>a</math>. <html> <link rel="stylesheet" ty...

New page
It can be described in polar coordinates <math>(r, \theta)</math> by the equation

:<math>r = \frac{a}{\theta}\,</math>

with a real number <math>a</math>.
<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/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
<script language="JavaScript">
board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
var a = board.createElement('slider', [[1,-1],[5,-1],[0,1,4]]);
var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8Math.PI],
{curveType:'polar', strokewidth:4});
</script>
</html>
===The JavaScript code to produce this picture===
<source lang="html4strict">
<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>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
</source>
<source lang="javascript">
board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 50, unitY: 50});
var a = board.createElement('slider', [[1,-1],[5,-1],[0,1,4]]);
var c = board.createElement('curve', [function(phi){return a.Value()/phi; }, [0, 0],'phi',0, 8Math.PI],
{curveType:'polar', strokewidth:4});
</source>

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