Calculate Pi with Monte-Carlo-method - Revision history

A WASSERMANN at 13:57, 10 January 2023

2023-01-10T13:57:22Z

← Older revision		Revision as of 13:57, 10 January 2023
Line 7:		Line 7:
	Please, move the mouse pointer over this area:		Please, move the mouse pointer over this area:
	<jsxgraph box="jxgbox" width="400" height="400">		<jsxgraph box="jxgbox" width="400" height="400">
	~~board2~~ = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
	c = ~~board2~~.create('circle', [[0,0], 1]);		c = board.create('circle', [[0,0], 1]);
	var p2 = [];		var p2 = [];
	for (var i=0;i<50;i++) {		for (var i=0;i<50;i++) {
	p2[i] = ~~board2~~.create('point',		p2[i] = board.create('point',
	[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],		[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],
	{face:'o',size:3,name:' '});		{face:'o',size:3,name:' '});
Line 44:		Line 44:
	}		}

	~~board2~~.on('update', updText);		board.on('update', updText);
	JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, ~~board2~~);		JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board);

	</jsxgraph>		</jsxgraph>

A WASSERMANN at 13:56, 10 January 2023

2023-01-10T13:56:19Z

← Older revision		Revision as of 13:56, 10 January 2023
Line 44:		Line 44:
	}		}

	~~//var hookid = board2.addHook(updText);~~
	board2.on('update', updText);		board2.on('update', updText);
	JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board2);		JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board2);
Line 58:		Line 57:
	The JavaScript code:		The JavaScript code:
	<source lang="javascript">		<source lang="javascript">
	~~board2~~ = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
	c = ~~board2~~.create('circle', [[0,0], 1]);		c = board.create('circle', [[0,0], 1]);
	var p2 = [];		var p2 = [];
	for (var i=0;i<50;i++) {		for (var i=0;i<50;i++) {
	p2[i] = ~~board2~~.create('point',		p2[i] = board.create('point',
	[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],		[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],
	{size:3,face:'o',name:' '});		{size:3,face:'o',name:' '});
Line 95:		Line 94:
	}		}

	~~var hookid = board2~~.~~addHook~~(updText);		board.on('update', updText);
	JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, ~~board2~~);		JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board);
	</source>		</source>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Statistics]]		[[Category:Statistics]]

A WASSERMANN at 13:55, 10 January 2023

2023-01-10T13:55:09Z

← Older revision		Revision as of 13:55, 10 January 2023
Line 44:		Line 44:
	}		}

	var hookid = board2.addHook(updText);		//var hookid = board2.addHook(updText);
			board2.on('update', updText);
	JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board2);		JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board2);

A WASSERMANN at 13:25, 3 March 2021

2021-03-03T13:25:19Z

← Older revision		Revision as of 13:25, 3 March 2021
Line 50:		Line 50:

	===The JavaScript code===		===The JavaScript code===
	~~Addition~~ to the usual JSXGraph container division we need another div tag to hold the text output seen above:		In addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:
	<source lang="xml">		<source lang="xml">
	<div id="resulttext"></div>		<div id="resulttext"></div>

A WASSERMANN at 13:25, 3 March 2021

2021-03-03T13:25:01Z

← Older revision		Revision as of 13:25, 3 March 2021
Line 49:		Line 49:
	</jsxgraph>		</jsxgraph>

	==The JavaScript ~~Code~~==		===The JavaScript code===
	Addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:		Addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:
	<source lang="xml">		<source lang="xml">

A WASSERMANN at 13:24, 3 March 2021

2021-03-03T13:24:34Z

← Older revision		Revision as of 13:24, 3 March 2021
Line 8:		Line 8:
	<jsxgraph box="jxgbox" width="400" height="400">		<jsxgraph box="jxgbox" width="400" height="400">
	board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
	c = board2.~~createElement~~('circle', [[0,0], 1]);		c = board2.create('circle', [[0,0], 1]);
	var p2 = [];		var p2 = [];
	for (var i=0;i<50;i++) {		for (var i=0;i<50;i++) {
	p2[i] = board2.~~createElement~~('point',		p2[i] = board2.create('point',
	[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],		[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],
	{face:'o',size:3,name:' '});		{face:'o',size:3,name:' '});
Line 49:		Line 49:
	</jsxgraph>		</jsxgraph>

	==Code==		==The JavaScript Code==
	Addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:		Addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:
	<source lang="xml">		<source lang="xml">
Line 58:		Line 58:
	<source lang="javascript">		<source lang="javascript">
	board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
	c = board2.~~createElement~~('circle', [[0,0], 1]);		c = board2.create('circle', [[0,0], 1]);
	var p2 = [];		var p2 = [];
	for (var i=0;i<50;i++) {		for (var i=0;i<50;i++) {
	p2[i] = board2.~~createElement~~('point',		p2[i] = board2.create('point',
	[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],		[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],
	{size:3,face:'o',name:' '});		{size:3,face:'o',name:' '});

Michael at 12:18, 7 June 2011

2011-06-07T12:18:45Z

← Older revision		Revision as of 12:18, 7 June 2011
Line 49:		Line 49:
	</jsxgraph>		</jsxgraph>

			==Code==
			Addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:
			<source lang="xml">
			<div id="resulttext"></div>
			</source>

			The JavaScript code:
	<source lang="javascript">		<source lang="javascript">
	board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});

Michael at 12:17, 7 June 2011

2011-06-07T12:17:31Z

← Older revision		Revision as of 12:17, 7 June 2011
Line 4:		Line 4:
	This can be used to calculate <math>\pi</math> using statistics. After each update we count the number of points inside the circle (with midpoint [0,0] and radius 1) and outside the circle. The points are restricted to the square with midpoint [0,0] and edges of length 2.		This can be used to calculate <math>\pi</math> using statistics. After each update we count the number of points inside the circle (with midpoint [0,0] and radius 1) and outside the circle. The points are restricted to the square with midpoint [0,0] and edges of length 2.

			<html><div id="resulttext"></div></html>
	Please, move the mouse pointer over this area:		Please, move the mouse pointer over this area:
	<~~html>~~		<jsxgraph box="jxgbox" width="400" height="400">
	~~<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="resulttext"></div>~~
	~~<div id~~="jxgbox" ~~class~~="~~jxgbox" style=~~"~~width:400px;~~ height~~:400px;" onmousemove="board2.update()"></div>~~
	~~<script language~~="~~JavaScript~~">
	board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
	c = board2.createElement('circle', [[0,0], 1]);		c = board2.createElement('circle', [[0,0], 1]);
	~~board2.suspendUpdate();~~
	var p2 = [];		var p2 = [];
	for (var i=0;i<50;i++) {		for (var i=0;i<50;i++) {
	p2[i] = board2.createElement('point',		p2[i] = board2.createElement('point',
	[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],		[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],
	{~~style~~:5,name:' '});		{face:'o',size:3,name:' '});
	}		}
	~~board2.unsuspendUpdate();~~

	var tin = 0;		var tin = 0;
Line 51:		Line 45:

	var hookid = board2.addHook(updText);		var hookid = board2.addHook(updText);
			JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board2);

	</~~script>~~		</jsxgraph>
	~~</html>~~

	~~<source lang="html4strict">~~
	~~<div id="jxgbox" class="jxgbox" style="width:400px; height:400px;" onmousemove="board2.update()"></div>~~
	~~</source~~>

	<source lang="javascript">		<source lang="javascript">
	board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});		board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
	c = board2.createElement('circle', [[0,0], 1]);		c = board2.createElement('circle', [[0,0], 1]);
	~~board2.suspendUpdate();~~		var p2 = [];
	var p2 = [];		for (var i=0;i<50;i++) {
	for (var i=0;i<50;i++) {		p2[i] = board2.createElement('point',
	p2[i] = board2.createElement('point',		[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],
	[function(){return 2Math.random()-1;},function(){ return 2Math.random()-1;}],		{size:3,face:'o',name:' '});
	{~~style~~:5,name:' '});		}
	}
	~~board2.unsuspendUpdate();~~

	var tin = 0;		var tin = 0;
	var tout = 0;		var tout = 0;
	var count = 0;		var count = 0;

	~~function updText() {~~
	~~count++;~~
	~~var text = ''~~;

	~~var inp = 0~~;		function updText() {
	var ~~outp~~ = 0;		count++;
			var text = '';

	~~for(~~var i=0; ~~i<p2.length;i++) {~~		var inp = 0;
	var x = ~~p2[i].X();~~		var outp = 0;
	~~var y = p2[i].Y()~~;

	if(xx+yy <= 1)		for(var i=0; i<p2.length;i++) {
	~~inp++~~;		var x = p2[i].X();
	~~else~~		var y = p2[i].Y();
	~~outp++~~;
	}

	tin += inp;		if(xx+yy <= 1) {
	tout += outp;		inp++;
			} else {
			outp++;
			}
			}
			tin += inp;
			tout += outp;

	text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio4: ' + (4inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio4: ' + (4tin/(tin+tout));		text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio4: ' + (4inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio4: ' + (4tin/(tin+tout));
	document.getElementById('resulttext').innerHTML = text;		document.getElementById('resulttext').innerHTML = text;
	}		}

	var hookid = board2.addHook(updText);		var hookid = board2.addHook(updText);
			JXG.addEvent(document.getElementById('jxgbox'), 'mousemove', function () { this.update(); }, board2);
	</source>		</source>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Statistics]]		[[Category:Statistics]]

A WASSERMANN at 15:21, 29 October 2009

2009-10-29T15:21:18Z

← Older revision		Revision as of 15:21, 29 October 2009
Line 7:		Line 7:
	<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="resulttext"></div>		<div id="resulttext"></div>
Line 48:		Line 47:

	text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio4: ' + (4inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio4: ' + (4tin/(tin+tout));		text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio4: ' + (4inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio4: ' + (4tin/(tin+tout));
	$('resulttext').innerHTML = text;		document.getElementById('resulttext').innerHTML = text;
	}		}

Line 97:		Line 96:

	text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio4: ' + (4inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio4: ' + (4tin/(tin+tout));		text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio4: ' + (4inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio4: ' + (4tin/(tin+tout));
	$('resulttext').innerHTML = text;		document.getElementById('resulttext').innerHTML = text;
	}		}

Michael at 10:02, 7 July 2009

2009-07-07T10:02:18Z

@@ Line 61: / Line 61: @@
 <source lang="javascript">
-  board2 = JXG.JSXGraph.initBoard('jxgbox', {originX: 10, originY:390 , unitX:380 , unitY: 380});
+  board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
   board2.suspendUpdate();
   for (var i=0;i<50;i++) {
-    var p2 = board2.createElement('point',
+    p2[i] = board2.createElement('point',
-            [function(){return Math.random();},function(){ return Math.random()}],
+            [function(){return 2*Math.random()-1;},function(){ return 2*Math.random()-1;}],
             {style:5,name:' '});
+  }
   board2.unsuspendUpdate();
 </source>
 [[Category:Examples]]
 [[Category:Statistics]]