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

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(2 intermediate revisions by the same user not shown)
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 2*Math.random()-1;},function(){ return 2*Math.random()-1;}],
 
           [function(){return 2*Math.random()-1;},function(){ return 2*Math.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:
+
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>
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 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:' '});
 
         {size:3,face:'o',name:' '});

Latest revision as of 14:25, 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);