how accurate are your π calculations?

[bikeman564™]

While riding today we stopped at a bakery called Sister Pie. They have pi on their chalk board😁

[Ralphie ★]

Did you check it for accuracy?

[Ralphie ★]

I can vouch for the first 11 digits. 

[bikeman564™]

3 minutes ago, Ralphie said:

Did you check it for accuracy?

I did not

[shootingstar]

Sometimes when I read stuff like this, I just wonder how much the parent is encouraging this or how much is child naturally getting a happy buzz doing it themselves on their own without anyway telling them:  B.C. boy, 9, loves hockey, his rabbit and pi, which he has memorized to 2,030 digits - The Globe and Mail

 

[maddmaxx ★]

I know that pi r'nt square.

[Longjohn ★]

Wife and I had dinner tonight at eat and park. They had lots of good looking pie in the glass case. We resisted.

[Further]

I guesstimate the diameter of the spool, count the wraps and multiply by 3

Mostly close enough 

[Ralphie ★]

6 hours ago, Further said:

I guesstimate the diameter of the spool, count the wraps and multiply by 3

Mostly close enough 

Gives you a nice little safety factor.

 

[Mr. Silly]

In high school, 1980'ish, a guy in my programming class calculated pi to the most digits I have ever seen in real life.  I have no idea the number of digits but it was a wall of numbers that completely filled a sheet of green bar paper used with our teletype console.

[Kzoo]

Dr Mickn would scold you. Accurate vs. precise?

[Ralphie ★]

4 hours ago, Mr. Silly said:

In high school, 1980'ish, a guy in my programming class calculated pi to the most digits I have ever seen in real life.  I have no idea the number of digits but it was a wall of numbers that completely filled a sheet of green bar paper used with our teletype console.

I was just wondering how you calculate pi. 
Hmm, looks like the reader’s digest version is Archimedes got very close by comparing 96 sided polygons that fit inside and ootside a circle so that gave upper and lower limits on it. Then infinite series came later, and I did not happen upon a similarly understandable explanation of how they work. 

[Razors Edge ★]

18 hours ago, Ralphie said:

Did you check it for accuracy?

Would it matter? Past 3.14 (and I know to 3.1415!) is about useless in all but a tiny amount of uses.

[Kzoo]

35 minutes ago, Razors Edge said:

Would it matter? Past 3.14 (and I know to 3.1415!) is about useless in all but a tiny amount of uses.

Back in my mechanical design days it was 3.1416.  Have to round the 5 up.

[Mr. Silly]

1 hour ago, Ralphie said:

I was just wondering how you calculate pi. 
Hmm, looks like the reader’s digest version is Archimedes got very close by comparing 96 sided polygons that fit inside and ootside a circle so that gave upper and lower limits on it. Then infinite series came later, and I did not happen upon a similarly understandable explanation of how they work. 

It is something like:

4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 (...)

[bikeman564™]

47 minutes ago, Mr. Silly said:

It is something like:

4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 (...)

and so on, and so, and so on

[bikeman564™]

1 hour ago, Razors Edge said:

Would it matter? Past 3.14 (and I know to 3.1415!) is about useless in all but a tiny amount of uses.

not for things I do, my calculator IIRC is 10 digits. In Excel, I use =Pi()

[bikeman564™]

1 hour ago, Kzoo said:

Back in my mechanical design days it was 3.1416.  Have to round the 5 up.

In school, we were told to use 3.1415 (or 6) can't remember. But this way everyone would get the same answer if correct. Despite calculators having a Pi function. When I'm at the store buying tape for my wheels, I use 3 so I can do it in my head   

[Razors Edge ★]

1 hour ago, Kzoo said:

Back in my mechanical design days it was 3.1416.  Have to round the 5 up.

3.14. Forget the rest! Jeebus man. 

[MickinMD ★]

My nephew, now the flight attendant, won tickets to an AA Minor League Bowie Baysox game for reciting pi to something like 17 decimal places when he was in elementary school.  The modern minor league stadiums have playgrounds for kids, picnic tables for adults McDonald's-size prices for concessions and cheap tickets.

Taking a few kids to see the nearby, major league Orioles or Nationals is a financial adventure.

[Kzoo]

19 hours ago, Razors Edge said:

3.14. Forget the rest! Jeebus man. 

When you're working on a tool that is machined to ten thousands of an inch you need 4 significant digits.  Jeebus man, everyone knows that.

 

[Razors Edge ★]

1 minute ago, Kzoo said:

When you're working on a tool that is machined to ten thousands of an inch you need 4 significant digits.  Jeebus man, everyone knows that.

Darn it! You're a tiny tool? I thought you were a huge tool, but I'm known to be wrong quite often.

[Bikeguy]

On 3/17/2024 at 11:55 AM, Mr. Silly said:

It is something like:

4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 (...)

Yes but that will take 500,000 iterations to be accurate to 5 decimal places.   https://www.wikihow.com/Calculate-Pi

On 3/17/2024 at 12:44 PM, bikeman564™ said:

not for things I do, my calculator IIRC is 10 digits. In Excel, I use =Pi()

Yeah... I just use the π key on my calculator.  and the Excel PI().   

[Bikeguy]

On 3/17/2024 at 11:55 AM, Mr. Silly said:

It is something like:

4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 (...)

I was curious (and bored watching a movie with WoBG) so I used the Gregory-Leibniz series and wrote an Excel macro to calculate π.  

The macro uses 500,000 iterations and the answer is indeed close.   

I've exceeded my useless drivel quota for the day. 

 

[Mr. Silly]

I plagiarized a good chunk of this from Stack Overflow if you want to calculate PI to an arbitrary number of digits using C#.:

 

 

using System ;

namespace SillyMath {

   class Program {

      public static string CalculatePi(int digits) {  

         digits++;

 

         uint[] x = new uint[digits*10/3+2];

         uint[] r = new uint[digits*10/3+2];

         uint[] pi = new uint[digits];

 

         for (int j = 0; j < x.Length; j++)

            x[j] = 20;

         

         for (int i = 0; i < digits; i++) {

            uint carry = 0;

            for (int j = 0; j < x.Length; j++) {

               uint num = (uint)(x.Length - j - 1);

               uint dem = num * 2 + 1;

 

               x[j] += carry;

 

               uint q = x[j] / dem;

               r[j] = x[j] % dem;

 

               carry = q * num;

            }

 

            pi[i] = (x[x.Length-1] / 10);

            r[x.Length - 1] = x[x.Length - 1] % 10; ;

         

            for (int j = 0; j < x.Length; j++)

               x[j] = r[j] * 10;

         }

     

         var result = "";

         uint c = 0;

     

         for(int i = pi.Length - 1; i >=0; i--) {

            pi[i] += c;

            c = pi[i] / 10;

         

            result = (pi[i] % 10).ToString() + result;

         }

      return result;

   }

      static void Main(String[] args) {

         int numDigits = 132 ;

         

         string result = CalculatePi(numDigits) ;

         result = result.Insert(1, ".") ;

         Console.WriteLine(result) ;

      }

   }

}

PS C:\Users\MrSilly\Documents\Dev\CPP\CalcPI\CalcPI> dotnet run
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550

 

[bikeman564™]

8 hours ago, Bikeguy said:

I was curious (and bored watching a movie with WoBG) so I used the Gregory-Leibniz series and wrote an Excel macro to calculate π.  

The macro uses 500,000 iterations and the answer is indeed close.   

I've exceeded my useless drivel quota for the day. 

I started to do this on Excel also but w/o the macro. I figured it was going to be a lot