Pi (matematik)

Pi se yon lèt grèk ki deziyen yon nomb.
Senbòl li se :



Ou ap twouve valè li nan divizyon longè yon sèk pa dyamèt li.


Nou konnen kèk chif sou li : 3.14159265358

Matematisyen endyen sa Srinivasa Ramanujan te fè anpil travay sou li, li bay fòmil pou kalkile valè li yo ak yon òdinatè :

 \frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum^\infty_{k=0} \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}} 

Ak fomil sa, li pèmèt jenere dot fomil pli jeneral :
 \frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}} 

(David Chudovsky epi Gregory Chudnovsky)

## Kèk pwopryete sou li

* Pi se yon nonmb irasyonèl : li pa kapab ekri sou fòm sa a \frac{a}{b}, lè a epi b se nonm natirèl tankou 1 (yonn), 2 (de), 3 (twa) ...
* Pi se yon nonmb transandan : pa genyen polinòm ki genyen l tankou rasin li P(pi)0

## Kèk fòmil sou ki ap apwoche oubyen ki ap bay Pi

* \pi = \lim_{n \to \infty} \left( n \cdot \sin \left( { \pi \over n } \right) \right) = \lim_{n \to \infty} \left( n \cdot \tan \left( { \pi \over n } \right) \right)

## Pwoblèm ki sou nomb sa

* Matematisyen yo pa konnen kounye a si \pi se yon nomb ki kapab genyen nan desimal li yo nenpòt kalite lis nonmb (yo rele nonm sa yo nomb nòmal : pa egzanp, w ap bay yon lis nonb tankou 345678910111213141516171819... si li se yon nonb nòmal, nou ta dwe kapab twouve nan desimal li yo, kèlkeswa kote nou ale nan desimal li yo, lis chif sa a.

## Kèk pwogram ki kapab kalkile desimal
Langaj C, C++


```c
#include <stdio.h>
//pwogram sa a kapab kalkile 2400 desimal
void main(void)
{
int a = 10000, b, c = 8400, d, e, f[8401], g;

for ( ; b-c ; ) f[b++] = a/5;

for ( ; d = 0, g = c*2 ; c -= 14, printf("%.4d",e+d/a), e = d%a)
  {
  for (b = c ; d += f[b]*a, f[b] = d%--g, d /= g--, --b ; d *= b);
  }
}
```


## Chif sou li

: \pi = 3,
:: 141 592 653 589 793 238 462 643 383 279
:: 502 884 197 169 399 375 105 820 974 944
:: 592 307 816 406 286 208 998 628 034 825
:: 342 117 067 982 148 086 513 282 306 647
:: 093 844 609 550 582 231 725 359 408 128
:: 481 117 450 284 102 701 938 521 105 559
:: 644 622 948 954 930 381 964 428 810 975
:: 665 933 446 128 475 648 233 786 783 165
:: 271 201 909 145 648 566 923 460 348 610
:: 454 326 648 213 393 607 260 249 141 273
:: 724 587 006 606 315 588 174 881 520 920
:: 962 829 254 091 715 364 367 892 590 360
:: 011 330 530 548 820 466 521 384 146 951
:: 941 511 609 433 057 270 365 759 591 953
:: 092 186 117 381 932 611 793 105 118 548
:: 074 462 379 962 749 567 351 885 752 724
:: 891 227 938 183 011 949 129 833 673 362
:: 440 656 643 086 021 394 946 395 224 737
:: 190 702 179 860 943 702 770 539 217 176
:: 293 176 752 384 674 818 467 669 405 132
:: 000 568 127 145 263 560 827 785 771 342
:: 757 789 609 173 637 178 721 468 440 901
:: 224 953 430 146 549 585 371 050 792 279
:: 689 258 923 542 019 956 112 129 0...


## Referans

## Lyen deyò
* The Joy of Pi by David Blatner
* Decimal expansions of Pi and related links at the On-Line Encyclopedia of Integer Sequences
* J J O'Connor and E F Robertson: ''A history of pi''. Mac Tutor project
* Lots of formulas for ''π'' at MathWorld
* PlanetMath: Pi
* Finding the value of ''π''
* Determination of ''π'' at cut-the-knot
* BBC Radio Program about ''π''
* Statistical Distribution Information on PI based on 1.2 trillion digits of PI
* First 4 Million Digits of ''π'' - *Warning* - Roughly 2 megabytes will be transferred.
* One million digits of pi at piday.org
* Project Gutenberg E-Text containing a million digits of ''π''
* Search the first 200 million digits of ''π'' for arbitrary strings of numbers
* Source code for calculating the digits of ''π''
* π is Wrong! An opinion column on why 2π is more useful in mathematics.
* 70 Billion digits of Pi(π) downloads.