calculating pi [Re: php and big data and predictive modelling...]

Luuk

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Dec 28, 2019, 3:52:33 AM12/28/19

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On 26-12-2019 23:18, Azathoth Hastur wrote:
> On Sunday, December 22, 2019 at 5:43:09 AM UTC-5, robamm...@gmail.com wrote:
>> pühapäev, 29. september 2019 18:41.47 UTC+3 kirjutas azathot...@gmail.com:
>>> Anyone doing php psotgresql for this?
>>>
>>> The java framework craziness I see at work must have better alternatives!
>>
>> I have used postgresql and php. And doing some statistical calculations in php. For example I have tried to calculate Pi. I used the so called "bombing"(method with random numbers). But the result came out so that the first 4 numbers of the number were only correct. 3.141 . I ran the code about 50 times, and there were no differences in the about 3-4 first numbers. Maybe the "bombing" method is not very good for this. I got the idea of it from schools programming lesson. I'm sure other mathematical methods would be better, but it was intresting for me to program and test it.
>>
>> Basically I think, if you can program, then there is no difference in which language you program.
>>
>> With the best wishes,
>> Kristjan Robam
>
> Why not use the postgresql to calculate and sort, and php to just get in put and output?
>

Ok, its not postgresql, i tried to do 'calculate pi' in MSSQL 2017:

WITH pi (x, f, a, kwartpi) as
(SELECT 1,1.0,1,
CONVERT(float(53), 0.0)
UNION ALL
SELECT x+2,-f,x,
CONVERT(float(53),kwartpi+(f/x)) from pi where x<20000 and x>=a
)

SELECT top 10
x, 4*kwartpi
FROM pi
order by x desc
OPTION(MAXRECURSION 10000)

Output:
x
----------- ----------------------
20001 3,14149265341197
19999 3,14169266341197
19997 3,14149263340797
19995 3,14169268341997
19993 3,14149261339597
19991 3,14169270343597
19989 3,14149259337597
19987 3,14169272345997
19985 3,14149257334797
19983 3,14169274349197

(10 rows affected)

Completion time: 2019-12-28T09:49:58.2239611+01:00

*Will postgresql be better in doing this job?*

Follow-up set to comp.databases.postgresql
--
Luuk

robamm...@gmail.com

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Dec 28, 2019, 5:22:10 AM12/28/19

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What is the idea of this ?
I used a circle inside a square and Pi=(Circle area)*4/(Square area)
And by the way the First numbers of pi area 3.14159.
My algorithm: https://groups.google.com/forum/#!topic/eesti-programmeerijad/qieWYzn8RxI

Luuk

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Dec 28, 2019, 6:32:27 AM12/28/19

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On 28-12-2019 11:22, robamm...@gmail.com wrote:
> On Saturday, December 28, 2019 at 10:52:33 AM UTC+2, Luuk wrote:
>> On 26-12-2019 23:18, Azathoth Hastur wrote:
>>> On Sunday, December 22, 2019 at 5:43:09 AM UTC-5, robamm...@gmail.com wrote:

Ah, this method
it looks better than trying to calculate 4*arctan(1), which can be
written as the sum of 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ......

But https://en.wikipedia.org/wiki/Squaring_the_circle pages says:
"In 1882, the task was proven to be impossible,"

--
Luuk

robamm...@gmail.com

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Dec 28, 2019, 7:55:03 AM12/28/19

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Ok. Proof.
d = 2r
Pi = C / 2r
Here we need a picture. Please look at :
https://www.basic-mathematics.com/proof-of-the-area-of-a-circle.html
Area of a circle = (1/2)r*2Pi*r
Area of a Circle=r*r*Pi
Area of a Square=(2r)*(2r)=4r*r

r*r*Pi Points in Circle
------- =~ -----------------
4r*r Points in Square

So Pi =~ 4*(Points in Circle)/(Points in Square)
The bigger the Square, the more precise Pi we have.

Luuk

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Dec 28, 2019, 11:03:24 AM12/28/19

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If i do more steps, my result should get more precise (but it is not
because of precision of used tool )

Doing it your way you have to do a lot of steps to get, close to, a
correct value.

--
Luuk

robamm...@gmail.com

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Dec 28, 2019, 11:30:20 AM12/28/19

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I think it would take about same time to calculate into the same precision,
because the basic idea behind it all should be the Pythagoras theorem a*a+b*b=c*c. There is a Javascript Library BigNumber, with which it all could be resolved.

Here is a code, that uses it. It is only a test to use BigNumber, but it would need only few modifications, for it to calculate Pi in real, if somebody would like to use it.

-----------------------------------

Findingpi.html:

<html>
<head>
<meta charset="utf-8">
<title>Calculating pi</title>
<script src='bignumber/bignumber.js'></script>
<style>
#pivalue {
border: 1px solid green;
margin: 5px;
height: 40px;
width: 300px;
}
</style>
</head>
<body>

<form onsubmit="findnumber(); return false;">
<h1>
<p>Pi(The Circle circumference divided with it's diameter)</p>
<p>Pi can be calculated with a circle inside a square. The Pi estimated value is the following: (Circle area)*4/(Square area).
</p>
<p>Please enter square width <input style="width: 100px; height: 40px; font-size: 30px;" type="text" id="squarew"></input></p>
<p><button type="submit" style="width: 200px; height: 40px; font-size: 30px;">Calculate pi</button></p>
<p id="pivalue"></p>
<p>For estonians: Soovitan kasutada translate.google.com-i kui inglise keelt ei mõika.</p>

</h1>

</form>
<script>
var incircle=0;
var area=0;
function pointisincircle(xx0,yy0,xx,yy,radius) {
return (xx.minus(xx0).multipliedBy(xx.minus(xx0)).plus(yy.minus(yy0).multipliedBy(yy.minus(yy0))).isLessThanOrEqualTo(radius.multipliedBy(radius)));
}
function findnumber() {
incircle=0;
var squarew=parseInt(document.getElementById("squarew").value);
//document.getElementById("pivalue").innerHTML
//alert(howmanynumbers);
area=squarew*squarew;
var xmax=new BigNumber(squarew);
var ymax=new BigNumber(squarew);
var radius=new BigNumber(squarew/2);
var x0=new BigNumber(squarew).dividedBy(new BigNumber(2));
var y0=new BigNumber(squarew).dividedBy(new BigNumber(2));
var x=new BigNumber(0);
var y=new BigNumber(0);
var increment=new BigNumber(1);
var run2=true;
while(true) {
//alert(x.toString());
//console.log("x: "+x.valueOf());
if(x.isEqualTo(xmax)) break;
while(run2) {
if(y.isEqualTo(ymax)) run2=false;
if(run2) {
y=y.plus(1);
//console.log(x.valueOf());
//console.log(y.valueOf());

} else {
y=new BigNumber(0);
}
if(pointisincircle(x0,y0,x,y,radius)) incircle++;
}
run2=true;
x=x.plus(1);
}
var pivalue=incircle*4/area;
//alert("In circle: "+incircle+" Area: "+area+" Pi value: "+pivalue);
document.getElementById("pivalue").innerHTML=pivalue;
}
</script>
</body>
</html>

-----------------------------------

robamm...@gmail.com

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Dec 28, 2019, 12:40:38 PM12/28/19

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The BigNumber library is available at : https://github.com/MikeMcl/bignumber.js/ .
I modified this code a little bit.
For example with width 5000 square The Pi came out 3.1415....
It took about 1 minute.

findingpi.html:

<html>
<head>
<meta charset="utf-8">
<title>Calculating pi</title>
<script src='bignumber/bignumber.js'></script>
<style>
#pivalue {
border: 1px solid green;
margin: 5px;

height: 200px;
width: 500px;
overflow-x: auto;
overflow-wrap: break-word;

}
</style>
</head>
<body>

<form onsubmit="findnumber(); return false;">
<h1>
<p>Pi(The Circle circumference divided with it's diameter)</p>
<p>Pi can be calculated with a circle inside a square. The Pi estimated value is the following: (Circle area)*4/(Square area).
</p>

<p>Please enter square width <input style="width: 200px; height: 40px; font-size: 30px;" type="text" id="squarew"></input></p>

<p><button type="submit" style="width: 200px; height: 40px; font-size: 30px;">Calculate pi</button></p>
<p id="pivalue"></p>
<p>For estonians: Soovitan kasutada translate.google.com-i kui inglise keelt ei mõika.</p>

</h1>

</form>
<script>

var incircle=new BigNumber(0);
var area=new BigNumber(0);
function pointisincircle(xx0,yy0,xx,yy,radius) {
var aaa1=xx0.minus(xx);
var aaa2=(yy0).minus(yy);
var isin=(aaa1.multipliedBy(aaa1).plus(aaa2.multipliedBy(aaa2))).isLessThanOrEqualTo(radius.multipliedBy(radius));
return isin;
}
function findnumber() {
incircle=new BigNumber(0);
area=new BigNumber(0);

var squarew=new BigNumber(document.getElementById("squarew").value);
//document.getElementById("pivalue").innerHTML
//alert(squarew.valueOf());
area=squarew.multipliedBy(squarew);

var xmax=new BigNumber(squarew);
var ymax=new BigNumber(squarew);

//alert(xmax.valueOf());
var radius=new BigNumber(squarew.dividedBy(2));
var x0=new BigNumber(squarew).dividedBy(2);
var y0=new BigNumber(squarew).dividedBy(2);

var x=new BigNumber(0);
var y=new BigNumber(0);

var run2=true;
while(true) {

if(x.isEqualTo(xmax)) break;
while(run2) {
if(y.isEqualTo(ymax)) run2=false;
if(run2) {

y=y.plus(new BigNumber(1));

} else {
y=new BigNumber(0);
}
if(pointisincircle(x0,y0,x,y,radius)) {
incircle=incircle.plus(1);
}
}
run2=true;
x=x.plus(1);
}
var pivalue=incircle.multipliedBy(4).dividedBy(area);

Luuk

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Dec 29, 2019, 4:15:01 AM12/29/19

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On 28-12-2019 18:40, robamm...@gmail.com wrote:
> The BigNumber library is available at : https://github.com/MikeMcl/bignumber.js/ .
> I modified this code a little bit.
> For example with width 5000 square The Pi came out 3.1415....
> It took about 1 minute.
>

Ok, my script loads within 1 second, and does not need an input, and pi
came out with 15 decimals as: 3.141592653589793

<html>
<head>
<meta charset="utf-8">
<title>Calculating pi</title>

robamm...@gmail.com

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Dec 29, 2019, 7:15:07 AM12/29/19

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Yes, it's a little bit more difficult. You need super fast computer for it to calculate. But I think somewhere are these kind of computers already available. But we don't have access for them. Or you have to optimize code.
I tested it on 2600px width, it took 48 seconds. So to get precision 16 decimals it will take about a year on my computer.

I fixed a little bit of it's code.
index.html:

<html>
<head>
<meta charset="utf-8">
<title>Calculating pi</title>

---------------
Kristjan Robam
E-mail: robamman2019x @ aol.com
(Please remove x, when writing to me)