Pi

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mk iga ukdu n tẓayṛt 1 hat qad igdu usuty nns π.

Pi iga yan umḍan nna nttara s uskkil agriki ittyiɣrin s ɣmkad nik : π. d assaɣ imzgi gr usuty n yat tẓayṛt d ukdu nns ɣ yan ugwni uklid. nɣiy ula ad tt nsnml s mas iga assaɣ gr tjumma n yat tẓayṛt d umkkuẓ n uznẓar nns.

Azal nns yaẓn s uwnul s wattayn n 0,5×10-15 iga t 3,141 592 653 589 793 s tirra timrawanin.

da ittusmras π g kigan n tnfalitin n tfizikt, tajnyuṛt, d awd tusnakt, ig yan sg imzgitn ilan tawuri iggutn g tusnakt.

amḍan π d arẓuṛan, zɛma ur nẓḍaṛ ad t nsnfali s wassaɣ gr sin imḍann ummidn ; aya da issuɣun mas ur midnt tirra nns wala gant timrawanin, wala tiwalanin. iga awd amḍan amyuṛan, mɛna ur tlli awd yat tgtfult taramyant (ur tgdi 0) mm imskarn ummidn mi iga π aẓuṛ.

iga asuttu n yan wazal yaẓn wala inɣdn n π, d urmas n ugama nns idsn imsarasn issn umzruy n tusnakt ; iḍiṣ iskr umḍan ad yujja t ad yadf ɣr tdlsa taɣrfant.

ur d yuman ussmrs n uskkil agriki π, askkil amzwaru n « περίμετρος » - azzikit s tgrikit -, ar tasut tiss XVIII. g ma ayd izrin, da ittusnfali s mnnaw n tnfalitin amm « imzgi n tẓayṛt » nɣ amnaway nns g tutlayin myallanin.

Isnmal[ssnfl | Snfl asagm]

  • π: iga-t g tusnakt yan umḍan amilaw (réel) nna igdan asutey (circonférence) n yat tewrerrayt (cercle) mi iga uẓenẓar (rayon) 0,5 (s wawal-yaḍen: mi tegda tubdist (diagonale) 1).
  • Amḍan π ur igi amḍan ameɣẓan (nombre rationnel), s wawal-yaḍen, ur nufi ad t-nara s wassaɣ (rapport) n sin imḍanen imassaɣen (relatifs) (a/b aked (a;b) € Z×Z*).
  • Da wala ittufka i umḍan π yan wazal yaẓen (valeur approchée) s uwnul (défaut), ad t-igan d 3,14 aha da as-ittufka yan wazal-yaḍen yaẓen illan s talɣa n umḍan ameɣẓan ad t-igan d 22/7 (π≈3,14, π≈22/7).
  • Seg zik lḥal, ferken imassanen n tusnakt s tilawt n umḍan π meqqar ur ssinen azal as-yaẓen s tneɣda imeqquren. Ibabiliyen s umedya, attayen n 4000 n isegg°asen aya, ssnen mas iga wassaɣ ger usutey n tewrerrayt d tubdist-nnes yan umḍan imezgi (ur da ittrnfal ayenna ira ig-t uẓenẓar n tewrerrayt). Fkan-as imassanen n tallit-nna azal yaẓen i wassaɣ-a, ad t-igan d 25/8 ayenna yakkan 3,125. G tallit-a nit, mmwaten imassanen ad fken yan wazal yaẓen i π, ssmersen iqibṭiyen s umedya azal 256/81 nna yakkan 3,16. Maca azalen-a-akk° ttusɣeẓnen s waram (expérience).
  • Amusnakt Arcimid, iddren g Syracuse, ayd izwaren is isseɣẓen, g 250 dat tlalit n Yizus, tinfaliyin n tewrerrayt d mas d timezgit igan yat ad aha ittumanen g usiḍen n usutey d tjumma n tewrerrayt. Iɣḍef altu mas da tettili tewrerrayt ger sin igetdisen (polygones), yan agensu d yan beṛṛa n tewrerrayt. Iddeɣ as-inzel (facile)ad issiḍen asutey n ugetdis, inzel-as ad isseɣẓen mas tella π ger 223/71 d 22/7, ayenna yakkan mas tella ger 3,1408 d 3,1429. Ikka lḥal 1600 n isegg°asen afad ad ttyifin 10 n inemrawen yaḍen (izwilen illan ḍart ticcert).
  • Ffɣen imassanen s wis ur issefki ad ittyiri π s talɣa n wassaɣ n sin imḍanen imassaɣen (a/b), maca yufa umassan ahindi Madhava n Sangamagrama mas da ittyiri π s talɣa n yan useddi n wurriẓen (4/1)-(4/3)+(4/5)-(4/7)+(4/9)... maca aseddi-a da ittiri kigan n tizi d tsiḍan afad ad tafed yan wazal unɣid, yuweḍ umassan-a ar 11 n inemrawen ḍart ticcert (virgule), ḍart yan mnnaw n isegg°asen yufa yan umassan afarsi 16. ɣi, llant kigan n tenfaliyin ittawsen g ussiḍen n wazal yaẓen n π, s tneɣda ixatren uggar, s yan useddi idrusen uggar n yirmawen...

Azal yaẓn[ssnfl | Snfl asagm]

yan sg wazaln yaẓn n umḍan π :

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094 3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912 9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132 0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235 4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859 5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303 15982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989

Isaɣuln[ssnfl | Snfl asagm]