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Amgrad ad icqqa ad t tfhmt ! amgrad-ad gis kra n iwalwn nna ur iẓḍaṛ ad tn ifhm yan iɣ ur issinn ɣ umawal iẓlin n tutlayt taclḥiyt tatrart. Mad igan afssay ? Fad ad tfhmt mad gis illan tzḍart ad tawst i yixf nnk s umawal lli illan ɣ izddar akkʷ n tasna. Iɣ t ur tufit, tzḍart ad nn taggʷt ɣ imawaln d isgzawaln.
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Tannayt f mamnk asa itgga usɣlu n kra n usnful.
Tga tanfalit n usnful n Nyuṭun yat tanfalit tusnakt iskr tt umusnak imqqurn Isḥaq Nyuṭun[1] fad ad yaf usbuɣlu n kraygat taẓḍurt n kra n usnful. Tṭṭaf ismawn yaḍna zun d tanfalit n usnful nɣ tanfalit n Nyuṭun.
Iɣ gan
d
sin ifrdisn n kra n uzbg (s umdya sin imḍanen ilawn nɣ ismlaln, sin igtfuln, sin isiruwn imkkuẓn nna dar illa nafs tiddi, atg.) nna ɣ tlla tasunflt[2] (ad t-igan mas-d
— s umdya i isiruwn :
iga-tt isiruw n tulut) s ɣikk ad, i kraygat
amḍan ummid agaman, nṭṭaf :
,
Ma ɣ imḍann
(kra n twal ar tt nttara ula
) gan imuskirn isnfal, « ! » ɛnan sis uskir d
afrdis-tiggt n uzbg.
S usnfl ɣ tanfalit
s
, ar nttafa:
Imdyatn:

Ha asnful ad ittuyskar i id
mẓẓiynin:
Nẓḍar ad nsml tanfalit ad s tinawt n ullus.[3]
Tummla nɣ taflalit igan tamakazt uggar[4] ar tswurri s usfki n imuskirn isnfal
mas iga umḍan n tifulin n
ifrdisn ɣ yat tagrumma nna ɣ illa
ifrdisn. Kudnna nsbuɣla tanfalit

ar nttafa yat timrnit n iynfuln s talɣa n
ma ɣ
d
ar mmaln s trtib ad nit uṭṭun n twal nna ɣ nxtar
nɣ
lliɣ tn nkka art nsbuɣlu. Illa darnɣ s bzziz
, acku kraygat twal ur ar gis ntxtar
, ar ntxtar
. S tɣarast yaḍna, maḥd darɣ
n tɣarasin ur mrwasnin n lixtiyyar n
twal atig n
zɣ
tinfulin
isggt ddaw as, aynful
ixṣṣa ad ibayn ɣ usbuɣlu d umuskir
.
Ar nsiggil ad nml masd tanfalit ad n
tṣḥa s tinawt n ullus
d
s
(maɣ
iga uzbg mknna ira igt)
Iɣ
Tazwart n tanfalit tṣḥa
Rad nɣal mas tanfalit ad tṣḥa ar twala n
Ad nsrs
S tifadiwin lli nfka i
d
, tanfalit
tṣḥa i
.
Nẓḍar ad nals i usbuɣlu s ullus fad ad nml tanfalit n Laybniz i tazllumt tis-
n kra n ufaris.
Taɣarast tamsuddst n tawlawalt ad aɣ yujjan ad nskr asmata n tulut agtful
s
,
maɣ id
nɛna sisn igtfuln ujjuṛn ifrdasn.
Nẓḍar ula ad nskr asmata n tanfalit ad s timrniyin n
irman ismlaln lan yat tuẓḍurt tummidt

d s imksanen ur gin ummidn nɣ gan ummidn izdrn.
- ↑ S ṣṣaḥt, tanfalit ad tettussan yad zɣ tasut tis-X, slawann akk dar id bu-tusnakt ihindiyn, iɛrabn d ifarisiyn (Al-Karaji) d ɣ tasut tis-XIII, amusnak acinwi Yang Hui imlatt. Ɣ 1665, Nyuṭun iskr as asmata nns s tuẓḍurin ur gin ummidn.
- ↑ Tafada ad tga ḍaṛuṛiyya, d tga tagdazalt i tidt n tanfalit i n = 2.
- ↑ Tummla n Asnful n Nyuṭun : s tinawt n ullus - AVIDYU YUTUB
- ↑ Tummla n Asnful n Nyuṭun : s tinawt n uddun - AVIDYU YUTUB
==
(en) J. L. Coolidge, « The Story of the Binomial Theorem », Amer. Math. Monthly, vol. 56, no 3, 1949, p. 147-157 (JSTOR 2305028, Ɣr ɣ wanṭirnit)
(en) Graham, Ronald; Knuth, Donald; Patashnik, Oren (1994). "(5) Binomial Coefficients". Concrete Mathematics (2nd ed.). Addison Wesley. pp. 153–256. ISBN 978-0-201-55802-9. OCLC 17649857.
(en) Bag, Amulya Kumar (1966). "Binomial theorem in ancient India". Indian J. History Sci. 1 (1): 68–74.
(en) Solomentsev, E.D. (2001) [1994], " Newton binomial ", , Encyclopedia of Mathematics, EMS Press
- Tanfalit = formule
- Asnful = binome
- Amusnak = mathematicien
- Asbuɣlu = developpement
- Taẓḍurt = puissance
- Azbg = anneau
- Afrdis = element
- Amḍan = nombre
- Ilaw = reel
- Asmlal = complexe
- Agtful = polynome
- Isiruw = matrice
- Amkkuẓ = carre
- Tasunflt = commutativite
- Tulut = identite
- Ummid = entier
- Agaman = naturel
- Amuskir = coeficient
- Uskir = factorielle
- Afrdis-tiggt = element unite
- Tinawt = énoncé
- Ullus = recurence
- Asfki = definion
- Amakaz = intuitif
- Tafult = partie
- Tagrumma = ensemble
- Timrnit = somme
- Iynfuln = monômes
- Tazllumt = derive
- Tamsuddst = derive
- Awlawal = variant
- Agtful = polynimiale
- Ujjuṛ = symetrique
- Afrdas = elementaire
- Irm = terme
- Amksan = exposant
- Uzdir = negatif
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