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Nth-digit of an irrational number

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Is there a way to directly find the Nth digit of the fractional part of an irrational number. For example how to 1000th digit of ${pi}$?

real-analysis sequences-and-series numerical-methods irrational-numbers

share|cite|improve this question

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417

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• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You might be interested in this.
  $endgroup$
  – Infiaria
  Mar 24 at 19:47
  

  
  
  
  


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  As far as I know, such a method was only discovered for $pi$ and only in base $2$. Usually, you will have to calculate the number precisely enough.
  $endgroup$
  – Peter
  Mar 24 at 19:53
  

  
  
  
  


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  @Infiaria I Knew Plouffe formula. But it only works for pi.
  $endgroup$
  – HAMIDINE SOUMARE
  Mar 24 at 19:57
  

  
  
  
  


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  You can't have a formula for each irrational. The set of formulas is countable, the set of irrationals is not. There are irrationals which can't be computed, like Chaitin's constant.
  $endgroup$
  – rtybase
  Mar 24 at 20:04
  
  
  

  
  
  
  


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  1
  

  
  
  
  
  
  

  
  $begingroup$
  And Plouffe's formula is not actually direct, it requires some of the first digits of the number. It is more efficient than brute force, but does not give the result "immediately".
  $endgroup$
  – Peter
  Mar 24 at 20:09
  

  
  
  
  

 | 
show 3 more comments

2

2

$begingroup$

Is there a way to directly find the Nth digit of the fractional part of an irrational number. For example how to 1000th digit of ${pi}$?

real-analysis sequences-and-series numerical-methods irrational-numbers

share|cite|improve this question

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You might be interested in this.
  $endgroup$
  – Infiaria
  Mar 24 at 19:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  As far as I know, such a method was only discovered for $pi$ and only in base $2$. Usually, you will have to calculate the number precisely enough.
  $endgroup$
  – Peter
  Mar 24 at 19:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Infiaria I Knew Plouffe formula. But it only works for pi.
  $endgroup$
  – HAMIDINE SOUMARE
  Mar 24 at 19:57
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  You can't have a formula for each irrational. The set of formulas is countable, the set of irrationals is not. There are irrationals which can't be computed, like Chaitin's constant.
  $endgroup$
  – rtybase
  Mar 24 at 20:04
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  And Plouffe's formula is not actually direct, it requires some of the first digits of the number. It is more efficient than brute force, but does not give the result "immediately".
  $endgroup$
  – Peter
  Mar 24 at 20:09
  

  
  
  
  

 | 
show 3 more comments

$begingroup$

Is there a way to directly find the Nth digit of the fractional part of an irrational number. For example how to 1000th digit of ${pi}$?

real-analysis sequences-and-series numerical-methods irrational-numbers

share|cite|improve this question

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417

$endgroup$

share|cite|improve this question

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417

share|cite|improve this question

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417

asked Mar 24 at 19:45

HAMIDINE SOUMAREHAMIDINE SOUMARE

2,570417