Difference between revisions of "Calculate Pi with Monte-Carlo-method"

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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.create('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',
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   p2[i] = board2.create('point',
 
           [function(){return 2*Math.random()-1;},function(){ return 2*Math.random()-1;}],
 
           [function(){return 2*Math.random()-1;},function(){ return 2*Math.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">
+
===The JavaScript code===
<div id="jxgbox" class="jxgbox" style="width:400px; height:400px;" onmousemove="board2.update()"></div>
+
In 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>
 
</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});
c = board2.createElement('circle', [[0,0], 1]);
+
c = board2.create('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.create('point',
  p2[i] = board2.createElement('point',
+
        [function(){return 2*Math.random()-1;},function(){ return 2*Math.random()-1;}],
          [function(){return 2*Math.random()-1;},function(){ return 2*Math.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() {
+
function updText() {
  count++;
+
    count++;
  var text = '';
+
    var text = '';
  
  var inp = 0;
+
    var inp = 0;
  var outp = 0;
+
    var outp = 0;
  
  for(var i=0; i<p2.length;i++) {
+
    for(var i=0; i<p2.length;i++) {
    var x = p2[i].X();
+
        var x = p2[i].X();
    var y = p2[i].Y();
+
        var y = p2[i].Y();
 
 
    if(x*x+y*y <= 1)
 
      inp++;
 
    else
 
      outp++;
 
  }
 
  
  tin += inp;
+
        if(x*x+y*y <= 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)) + ', ratio*4: ' + (4*inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio*4: ' + (4*tin/(tin+tout));
+
    text += '<b><u>Current</u></b><br/>In: ' + inp + ', out: ' + outp + ', total: ' + (inp+outp) + '; ratio: ' + (inp/(inp+outp)) + ', ratio*4: ' + (4*inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio*4: ' + (4*tin/(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]]

Latest revision as of 15:25, 3 March 2021

Here, at construction time each point receives a function pair as coordinates. In each update these functions which return Math.random() are called. Thus in each update each point receives new random coordinates. The 50 points are updated on the onmousemove event.

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.

Please, move the mouse pointer over this area:

The JavaScript code

In addition to the usual JSXGraph container division we need another div tag to hold the text output seen above:

<div id="resulttext"></div>

The JavaScript code:

board2 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 1, 1, -1], axis:true});
c = board2.create('circle', [[0,0], 1]);
var p2 = [];
for (var i=0;i<50;i++) {
    p2[i] = board2.create('point',
        [function(){return 2*Math.random()-1;},function(){ return 2*Math.random()-1;}],
        {size:3,face:'o',name:' '});
}

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

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

    var inp = 0;
    var outp = 0;

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

        if(x*x+y*y <= 1) {
            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)) + ', ratio*4: ' + (4*inp/(inp+outp)) + '.<br /><b><u>Total</u></b> (' + count + ' updates in total)<br/>In: ' + tin + ', out: ' + tout + ', total: ' + (tin+tout) + '; ratio: ' + (tin/(tin+tout)) + ', ratio*4: ' + (4*tin/(tin+tout));
    document.getElementById('resulttext').innerHTML = text;
}

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