Estimating Pi using the Monte Carlo Method

Developer
Ed Ball
Size
3,025 Kb
Views
32,384
  1. Estimating Pi using the Monte Carlo Method Previews
  2. Estimating Pi using the Monte Carlo Method HTML Codes
  3. Estimating Pi using the Monte Carlo Method CSS Codes
  4. Estimating Pi using the Monte Carlo Method JS Codes

How do I make an estimating pi using the monte carlo method?

To celebrate Pi Day, here is a demo of how to estimate the value of Pi using the Monte Carlo method - generate a large number of random points and see how many fall in the circle enclosed by the unit square.This demo is originally from https://academo.org.. What is a estimating pi using the monte carlo method? How do you make a estimating pi using the monte carlo method? This script and codes were developed by Ed Ball on 12 November 2022, Saturday.

Estimating Pi using the Monte Carlo Method Previews
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Estimating Pi using the Monte Carlo Method - Script Codes HTML Codes

<!DOCTYPE html>
<html >
<head> <meta charset="UTF-8"> <title>Estimating Pi using the Monte Carlo Method</title> <link rel='stylesheet prefetch' href='https://academo.org/scss/main.css?v=1457985409494'> <link rel="stylesheet" href="css/style.css">
</head>
<body> <div id="demo">
</div>
<div id="ui-container">
</div>
<a id="academo-banner" href="https://academo.org/demos/estimating-pi-monte-carlo/" target="_blank">Find out more at Academo.org</a> <script src='http://cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js'></script>
<script src='https://academo.org/js/demoConcat.js?v=1457985409494'></script>
<script src='http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>
<script src='https://academo.org/js/lib/d3.v3.min.js'></script> <script src="js/index.js"></script>
</body>
</html>

Estimating Pi using the Monte Carlo Method - Script Codes CSS Codes

canvas { position:absolute; left:50%; margin-left:-250px; top:50%; margin-top:-250px; display:block;
}

Estimating Pi using the Monte Carlo Method - Script Codes JS Codes

/* This code comes from Academo.org */
var demo = new Demo({	ui: {	addOne: {	title: "Add points one-by-one",	type: "button"	},	animate: {	title: "Animate",	value: false,	},	speed: {	title: "Speed",	value: 1,	range: [5, 100],	resolution: 1,	input: "hidden",	},	reset: {	title: "Reset",	type: "button"	},	},	animateID: null,	totalPoints: 0,	innerPoints: 0,	radius: 250,	init: function(){	$('<canvas>').attr({	id: "my-canvas", height: "500px", width: "500px",	}).css({	width: "500px",	"height": "500px",	"display": "block",	"border": "solid 1px #CCC"	}).appendTo('#demo');	this.scale = d3.scale.linear() .domain([-1, 1]) .range([0, 500]); this.canvas = document.getElementById("my-canvas");	this.context = this.canvas.getContext("2d");	this.initCanvas();	$("#ui-container").prepend("<div class='interface' id='js-points-data'></div>");	$("#js-points-data").append("Total Number of points: <span class='js-total-points'>0</span><br />");	$("#js-points-data").append("Points within circle: <span class='js-inner-points'>0</span><br />");	$("#js-points-data").append("Pi estimation: <span class='js-pi-estimation'></span><br />");	},	initCanvas: function(){	this.context.clearRect(0,0,500,500);	this.context.strokeStyle = "#999";	this.context.beginPath();	this.context.arc(this.scale(0), this.scale(0), this.radius, 0, 2 * Math.PI);	this.context.stroke();	},	animate: function(){	this.animateID = window.requestAnimationFrame(this.animate.bind(this));	this.update();	},	reset: function(){	this.totalPoints = 0;	this.innerPoints = 0;	this.updateDisplay();	},	updateDisplay: function(){	$(".js-inner-points").html(this.innerPoints);	$(".js-total-points").html(this.totalPoints);	var piEstimate = (4 * this.innerPoints / this.totalPoints).toFixed(5);	if (this.totalPoints == 0){	piEstimate = "";	}	$(".js-pi-estimation").html(piEstimate);	},	update: function(e){	if (e == "speed"){	} else if (e == "animate" && this.ui.animate.value == true) {	this.animate();	} else if (e == "animate" && this.ui.animate.value == false) {	window.cancelAnimationFrame(this.animateID);	} else if (e == "reset") {	this.initCanvas();	this.reset();	} else {	if (e == "addOne"){	var numberToAdd = 1;	} else {	var numberToAdd = this.ui.speed.value;	}	for (var i = 0 ; i < numberToAdd ; i++){	var randomX = Math.random() * 2 - 1;	var randomY = Math.random() * 2 - 1;	this.context.beginPath();	if (Math.pow(this.scale(randomX) - this.scale(0), 2) + Math.pow(this.scale(randomY) - this.scale(0), 2) > Math.pow(this.radius, 2)){	this.context.fillStyle = "blue";	} else {	this.context.fillStyle = "red";	this.innerPoints++;	}	this.context.fillRect(this.scale(randomX),this.scale(randomY),1,1);	this.totalPoints++;	this.updateDisplay();	}	}	}
});
Estimating Pi using the Monte Carlo Method - Script Codes
Estimating Pi using the Monte Carlo Method - Script Codes
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Developer Ed Ball
Username edball
Uploaded November 12, 2022
Rating 3
Size 3,025 Kb
Views 32,384
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