Pi

Amḍan ${\displaystyle \pi }$ ( yettwanṭeq "pi") d timezgit n tusnakt , netta d wassaɣ n tiseɣleyt n twinest ar wakdu-ines, s temẓawt yegda-d 3.14159. Amḍan ${\displaystyle \pi }$ yetban-d deg mennaw n tenfaliyin deg tusnakt d tfizikt.

${\displaystyle \pi }$ d amḍan armeɣẓan, alnamek-is ur yezmir ara ad yettwaru s taẓunt n sin ummiden, ama nezmer ad d-t-naru s umata s temẓawt s tirẓi ${\displaystyle {\frac {22}{7}}}$.

dɣa, amḍan ${\displaystyle \pi }$ ur d-yetfuk ara akk.

Azamul-nni yusad seg usekkil agrigi ${\displaystyle \pi }$ s tuget n tutlayin n umaḍal yettwanṭeq pi.

S teqbaylit daɣen yettwanṭeq "pi".

${\displaystyle \pi }$ d wassaɣ n tiseɣleyt n twinest ar wakdu-ines$${\displaystyle \pi ={\frac {C}{d}}}$$

${\displaystyle \pi }$ d amḍan armeɣẓan, alnamek-is ur yezmir ara ad yettwaru s taẓunt n sin ummiden, ama nezmer ad d-t-naru s umata s temẓawt s tirẓi ${\displaystyle {\frac {22}{7}}}$ d ${\displaystyle {\frac {355}{113}}}$.

${\displaystyle \pi }$ d amḍan amyuṛan, lmaɛna-ines dakken ur yezmir ara ad yili tifrat n tegda tagetfulf ur nelli timezgit s imuskiren imeɣẓanen am : ${\displaystyle {\frac {x^{5}}{120}}-{\frac {x^{3}}{6}}+x=0}$

Am akken ${\displaystyle \pi }$ d amḍan armeɣẓan, alnamek-is ur yezmir ara ad yettwaru s taẓunt n sin ummiden. Ama ${\displaystyle \pi }$ am akk imḍanen nniḍen, nezmer ad-d-naru s umazrar imifeḍ n tiṛziwin yedduklen gar-asent, qaren-as tirẓi tamaɣlalt ${\displaystyle \pi =3+\textstyle {\cfrac {1}{7+\textstyle {\cfrac {1}{15+\textstyle {\cfrac {1}{1+\textstyle {\cfrac {1}{292+\textstyle {\cfrac {1}{1+\textstyle {\cfrac {1}{1+\textstyle {\cfrac {1}{1+\ddots }}}}}}}}}}}}}}}$

Kra n temẓawin n ${\displaystyle \pi }$ d wigi:

• Ummiden: 3
• Tirẓiyin: 22/73, 333/106, 355/113, 52163/16604, 103993/33102, 104348/33215 d 245850922/78256779.^[1]   (umuɣ seg OEIS:A063674 d OEIS: A063673.)
• izwilen: 50 izwilen imezwura n ${\displaystyle \pi }$ d 3.14159265358979323846264338327950288419716939937510(ẓer OEIS: A000796 )

1. ↑ (Eymard & Lafon 2004)