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Change the value of the built-in constant Pi ?

Posted 10 years ago

Is it possible to change the value of Pi in Mathematica ? I found a mathematician who claims the value of Pi is wrong.

He claims it is 3.14460551102969314427823434337183571809248823135089

http://www.jainmathemagics.com/page/10/default.asp

He offers a mathematical proof.

POSTED BY: Dale Robinson
11 Replies
Posted 10 years ago
POSTED BY: Dale Robinson
POSTED BY: Udo Krause
In[60]:= $MaxExtraPrecision = 100;
With[{n = 230},
 N[Nest[(2 # /. Sqrt[2] -> Sqrt[2 + Sqrt[2]]) &, 8 Sqrt[2 - Sqrt[2]], n], 2 n]
]
Out[61]= 6.2831853071795864769252867665590057683943387987502116419498891846156328\
         1257241799725606965068423413596429617302656461329418768921910116446339\
         6474981544670372844957415414786659532250483273698781854534057944059546\
         4212296618059297008796444429703575644151907239674056074649721389388916\
         1213270255123692078791957639371103935869813954758177340916591587988374\
         6503651680389738061149696087711647752438660059276698901240933525983438\
         366816684508234992463156512294881674612

In[62]:= %61 - N[2 \[Pi], 2 230]
Out[62]= -5.4243834712291862055610789989090382678868805972199128006229870913562404\
          9106372304510215955879291233601848394031005731664413132322487697144048\
          1465451196926136175952959761950159181765162349426015224934226755084498\
          9281529039632922999947944845331120541465222963942167213299797993200467\
          81755555025563023112305372480126725015*10^-140
POSTED BY: Udo Krause
POSTED BY: Szabolcs Horvát

enter image description here

POSTED BY: David Reiss
POSTED BY: Daniel Lichtblau

Maybe this explains why the Brooklyn Bridge is up for sale. It was constructed using the wrong value of Pi.

POSTED BY: Frank Kampas
Posted 10 years ago

Mathematica rules JainPi to 60 decimal places 3.14460551102969314427823434337183571809248823135089295065961

======================

JainPhi = N[(1 + Sqrt[5])/2, 60] JainPi = N[4/Sqrt[JainPhi], 60]

POSTED BY: Dale Robinson
Posted 10 years ago

Thank you. I kind of figured it would be something like that. Most CAD programs use the same value of Pi as Mathematica. I have several goals with this question;

  1. I mainly use Mathematica to calculate a very complex polynomial algorithm and it never donned on me that Pi could have an alternate value. This could explain why physical models of the complex CAD part fails.

  2. It would be nice to run Jain's mathematical proof through Mathematica and see if he is right or not.

  3. It would also be nice to calculate jainPi to the same resolution as he has published.

  4. A programmable way to 'modify' built in Pi and a way to 'revert' back to the original Pi would be nice.

===============

As to 'Changing Pi in Mathematica would mess up a lot of internal calculations.'

This is my point exactly. I ran a simple test on Pi * D = C vs the jainPi * D = C and the difference was significant.

'of course D = Diameter and C = Circumference '

I use C / 360 for a constant in my algorithm. And if the Pi constant is wrong then my constant is wrong.

FYI Jain claims NASA uses a different value of Pi. But I had another inside source that verified that NASA always had to make course corrections for their space vehicles and could not explain why. Victor Schumberg also had an explanation in that planetary orbits were egg shaped and not truly elliptic.

ps I hope somebody flames me for referring to Jain. Because he is basically challenging the world on the true value of Pi. He is also challenging Mathematica :)

POSTED BY: Dale Robinson

Rather than change the built-in symbol Pi, it would be better to create a new symbol, for example,

   jainPi = 3.14460551102969314427823434337183571807248823135089; 

Changing Pi in Mathematica would mess up a lot of internal calculations.

It is fine if other replies show how to modify built-in symbols.

Please do not flame at Mr. Robinson about the other web site.

POSTED BY: Moderation Team

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