Introduction: How to Find the Value of Pi to a Great Level of Accuracy.
I have found a series that can calculate PI to a great deal of accuracy with less terms.
I'll do that using JavaScript.
I'll do that using JavaScript.
Step 1: See the Formula We Use
The day was boring and I so to cut of the boredom, I searched for some formula to calculate PI. Then I found this formula and used it in the JavaScript. Just take a look at the formula:
Step 2: Translating the Formula to JavaScript
Then I used a while loop ( for-loop would have been better, but I forgot that) to use the formula up to accuracy you want. I have the formula:
3 + 4 / ( 2 * 3 * 4) + 4 / (4 * 5 * 6) + .....
The numbers at the denominator increases by 2 and we have used x+1 is 3 and x+2 is 4. SO we get 3 + 4/(2*(2+1)*(2+2))+.....
We use x instead of 2 because we need to add 2 to all of them every time. And now look.
Just use it if you want.
<!DOCTYPE html>
<html>
<head>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="latextit.js"></script>
<script type="text/javascript">
$(document).ready(function(){
$('#button').click(function(){
var value = $('input[name=accuracyPercent]').val();
if(parseInt(value) < 2 ){
alert("It should be more than " + parseInt(value) + " ");
}else if(parseInt(value) > 80 ){
alert("It should be less than " + parseInt(value) + " ");
}else{
//first lower
var x = 2;
// the variable to collect the estimation of pi
var n = 3;
//initial term
var i = 2;
var accuracy = parseInt(value) * 2000;//while loop
while(i <= accuracy){
//if the i is even, then do this
if(i % 2 === 0){
// the formula
n += (4 / ( x * ( x + 1) * ( x + 2)));
}else{ // else you do this
// the formula
n -= (4 / ( x * ( x + 1) * ( x + 2)));
}
// add 2 to x
x += 2;
// i
i++;
}
$('#item').replaceWith('<div id = "item">' + n + '</div>');
}
});
$('#button').mouseover(function(){
$(this).css('color', '#fff');
});
$('#button').mouseleave(function(){
$(this).css('color', '#000')
});
});
</script>
<style type="text/css">
body{
background: -webkit-linear-gradient(-45deg, #0ff, blue); /* For Safari */
background: -o-linear-gradient(-45deg, #0ff, blue); /* For Opera 11.1 to 12.0 */
background: -moz-linear-gradient(-45deg, #0ff, blue); /* For Firefox 3.6 to 15 */
background: linear-gradient(-45deg, #0ff, blue); /* Standard syntax */
}
form{
display: inline-block;
background-color: blue;
}
#button{
display: inline-block;
height:20px;
width:70px;
background-color:#cc0000;
font-family:arial;
font-weight:bold;
color:#000;
border-radius: 5px;
text-align:center;
margin-top:2px;
}
#item{
text-align: center;
font-size: 40px;
color: #000;
}
.list{
font-size: 20px;
}
</style>
</head>
<body>
<form name="accuracyPercent">
<input type="text" name="accuracyPercent"/>
</form>
<div id="button">Get!</div>
<p class = "list">
Let us find the value of <span lang="latex">$\pi$</span> to your accuracy point. (Remember, your value should be greater than 2, less than 1000 and an integer):
</p>
<div id = "item">
3.14159 26535 89793 23846
</div>
</body>
</html>
3 + 4 / ( 2 * 3 * 4) + 4 / (4 * 5 * 6) + .....
The numbers at the denominator increases by 2 and we have used x+1 is 3 and x+2 is 4. SO we get 3 + 4/(2*(2+1)*(2+2))+.....
We use x instead of 2 because we need to add 2 to all of them every time. And now look.
Just use it if you want.
<!DOCTYPE html>
<html>
<head>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="latextit.js"></script>
<script type="text/javascript">
$(document).ready(function(){
$('#button').click(function(){
var value = $('input[name=accuracyPercent]').val();
if(parseInt(value) < 2 ){
alert("It should be more than " + parseInt(value) + " ");
}else if(parseInt(value) > 80 ){
alert("It should be less than " + parseInt(value) + " ");
}else{
//first lower
var x = 2;
// the variable to collect the estimation of pi
var n = 3;
//initial term
var i = 2;
var accuracy = parseInt(value) * 2000;//while loop
while(i <= accuracy){
//if the i is even, then do this
if(i % 2 === 0){
// the formula
n += (4 / ( x * ( x + 1) * ( x + 2)));
}else{ // else you do this
// the formula
n -= (4 / ( x * ( x + 1) * ( x + 2)));
}
// add 2 to x
x += 2;
// i
i++;
}
$('#item').replaceWith('<div id = "item">' + n + '</div>');
}
});
$('#button').mouseover(function(){
$(this).css('color', '#fff');
});
$('#button').mouseleave(function(){
$(this).css('color', '#000')
});
});
</script>
<style type="text/css">
body{
background: -webkit-linear-gradient(-45deg, #0ff, blue); /* For Safari */
background: -o-linear-gradient(-45deg, #0ff, blue); /* For Opera 11.1 to 12.0 */
background: -moz-linear-gradient(-45deg, #0ff, blue); /* For Firefox 3.6 to 15 */
background: linear-gradient(-45deg, #0ff, blue); /* Standard syntax */
}
form{
display: inline-block;
background-color: blue;
}
#button{
display: inline-block;
height:20px;
width:70px;
background-color:#cc0000;
font-family:arial;
font-weight:bold;
color:#000;
border-radius: 5px;
text-align:center;
margin-top:2px;
}
#item{
text-align: center;
font-size: 40px;
color: #000;
}
.list{
font-size: 20px;
}
</style>
</head>
<body>
<form name="accuracyPercent">
<input type="text" name="accuracyPercent"/>
</form>
<div id="button">Get!</div>
<p class = "list">
Let us find the value of <span lang="latex">$\pi$</span> to your accuracy point. (Remember, your value should be greater than 2, less than 1000 and an integer):
</p>
<div id = "item">
3.14159 26535 89793 23846
</div>
</body>
</html>
