Aggur:Tusnakt — Wikipedia

Aggur:Tusnakt — Wikipedia
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Zɣ Wikipedia
Aggur
Amsawal n waggur
Taggayt
Aggur n
Tusnakt
Uṭṭun n imnnitn g waggur ad :
46
Gr iwalln nnk f taggayin n waggur ad
Asnubg
Amzruy
Tusnakt
Tarakalt
Tutlayt
Tunnunt
Timassanin
Taẓuṛi
Tadlsa
Asgd
Ttiknulujya
Tasnijjit
Taɣrma
Tasnslkimt
Imaziɣn
Taflsuft
Tiwisi
Tasasfrt
Agemmay
Tamtti
50
Tiɣbula
Asɣiws
Amawal
Anmuggar
Amgrad n ɣassa
Alugaritm anipiri
Alugaritm agaman
nɣ
Alugaritm anipiri
(s
tanglizt
: Natural logarithm) tga yat tasɣnt nɣ twwuri tettuysan bahra ɣ
tusnakt
, ar tsnfal afaris s timrnit zund akkʷ
tisɣnin ilugaritm
. Ar tt ntara s ɣmk-ad :
ln
{\displaystyle \ln()}
. Ar nttini mas-d alugaritm agaman nɣ anipiri iga s uzadur n
{\displaystyle e}
acku
{\displaystyle ln(e)=1}
, iga alugaritm agaman ula tamnzut n tasɣnt :
{\displaystyle x\longmapsto 1/x}
ɣ uzilal
{\displaystyle ]0;+\infty [}
Alugaritm ad dars yan yism yaḍni abla "agaman", iga-tt "anipiri". Ism ad yuckad zɣ John Napir nna igan yan umusnak askatlandi, nttat ad akkʷ izwarn ay-skr taflwit talugaritm ( ur trwas xtad lli nssn ɣila nkkni ).
Tettyawskar tazmilt n ulugaritm nna f nsawal nkkni ɣila s ifassn n Grégoire de Saint-Vincent d Alphonse Antonio de Sarasa ɣ usggʷas n 1649
Ad tg
{\displaystyle a\in ]0;+\infty [}
, nzḍar ad nini mas-d asnml n tasɣnt talugaritm tga-tt unrar lli illan ɣ izddar n tasɣnt
{\displaystyle x\mapsto 1/x}
gr
{\displaystyle a}
d 1.
Ɣikad ast nttara :
ln
{\displaystyle \ln a=\int _{1}^{a}{\frac {1}{x}}\,dx.}
... (
Ɣr uggar
...
Ssnfl
Tawlaft n ɣassa
Asktiɣmr
tga yan ugmiw ɣ
tusnakt
nna itxdamn s izdayn gr izarutn d tiɣmriwin ɣ ammas n imkṛaḍn d tisɣan tisktuɣmirin zund ukan
sinus
kusinus
tanjunt
Ssnfl
Tamyagart n ɣassa
tusnakt
, Targadda nɣ tamyagart n
Cauchy–Schwarz
, tettawsan ula s yism n targadda n
Cauchy–Bunyakovsky–Schwarz
, tga yat targadda bahra istawhman ɣ
tusnakt
kullut, ar sis nswurri ɣ
aljibr imzirg
taslṭ
tiẓri n tsqqart
d kigan n tɣawsiwin yaḍni. Targadda ad issufɣt-id yan umusnak
afransis
iga s yism
Augustin-Louis Cauchy
ɣ usggwas n 1821, sliɣ yufa
Viktor Bunyakovsky
yat targadda trwast akk ɣ mad izdin d aɣrd ɣ usggwas n 1859, mn bɛd yufatt daɣ yan umusnak
almani
Hermann Amandus Schwarz
ɣ usggwas n 1888.
Mad aɣ tettini
Ar ttini targadda n Cauchy–Schwarz mas i akk sin imawayn
{\textstyle u}
{\textstyle v}
n yat
tallunt gis afaris agnsan
hann rad darnɣ tili
{\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle }
maɣ
{\displaystyle \langle \cdot ,\cdot \rangle }
iga yan
ufaris agnsan
. S umdya afaris agnsan gis afaris afsnan n ilawn d ismlaln. S ɣmkad, iɣ nusi aẓur uzmir-sin ɣ tsgiwin s snat, d iɣ asn nga alugn. Ar nttafa targadda ad :
{\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |\leq \|\mathbf {u} \|\|\mathbf {v} \|.}
D yat tɣawsa yaḍn, tasgiwin s snat gaddan iɣ
{\textstyle \mathbf {u} }
{\textstyle \mathbf {v} }
gan ilelliyn imzirgn (yaɛni gan imsadaɣn).
Iɣ
{\textstyle u_{1},\ldots ,u_{n}\in \mathbb {C} }
{\textstyle v_{1},\ldots ,v_{n}\in \mathbb {C} }
d ufaris agnsan iga afaris agnsan asmlal anaway, hann targadda tzḍar ad ttyura zund ɣikad (maɣ tirra n taɛṛṛaḍt ar sis nmmal unaftay n ismlaln): i
{\displaystyle \mathbf {u} ,\mathbf {v} \in \mathbb {C} ^{n}}
, darnɣ
{\displaystyle \left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|^{2}=\left|\sum _{k=1}^{n}u_{k}{\bar {v}}_{k}\right|^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \langle \mathbf {v} ,\mathbf {v} \rangle }
{\displaystyle =\left(\sum _{k=1}^{n}u_{k}{\bar {u}}_{k}\right)\left(\sum _{k=1}^{n}v_{k}{\bar {v}}_{k}\right)}
{\displaystyle =\sum _{j=1}^{n}|u_{j}|^{2}\sum _{k=1}^{n}|v_{k}|^{2}}
Ad t igan,
{\displaystyle |u_{1}{\bar {v}}_{1}+\cdots +u_{n}{\bar {v}}_{n}|^{2}\leq (|u_{1}|^{2}+\cdots +|u_{n}|^{2})(|v_{1}|^{2}+\cdots +|v_{n}|^{2})}
Ɣr uggar
...
Ssnfl
Imgrad mqqurnin
Tusnakt
Sinus (tusnakt)
e (amḍan n tusnakt)
Aljibr
Amḍan
Pi
Asktiɣmr
Euclide
Targadda n Cauchy Schwarz
Alugaritm agaman
Bnu Rucd
Gerolano Cardano
Wiki:Amawal
Lyunardu da Vintci
Uguṣtin-Luwis Kucy
Amḍan amnzu
Azwil
Asnful n Nyuṭun
Ssnfl
Amḍan amnzu
Amḍan amnzu
iga yan
umḍan
ummid agaman ilan ɣar sin inbḍayn imyallan igan ummidn gn imufrarn (ad tn igan 1 d nttan nit). S ɣmka, 1 ur igi amnzu acku ur dars abla yan unbḍay ummid amufrar; ula 0 ur t igi acku issn ad ittubḍa f imḍanen ummidn imufrarn s timmad nnsn.
Ɣ unmgal, amḍan ummid arilm igan afaris n sin imḍanen ummidn igamanen nttini as uddis. S umdya 6 d 12 d uddisn acku 6 = 2 × 3 d 12 = 3 × 4 nɣ 2 × 6, mac 11 iga amnzu acku 1 d 11 ka igan inbḍayn nns.
Imḍanen 0 d 1 ur gin imnza wala gan uddisn. kra n imusnaktn ssiḍinen zikk-lli (ar tasut tiss 19) 1 d amḍan amnzu, mac ɣ tizwuri n tasut tiss 20, issinf yan umsasa 1 zɣ imḍanen imnza
25 n imḍanen imnza imẓẓiyn f 100 :
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 d 91. (
Ɣr uggar
...
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Lqist n ɣassa
Fig. 1
taskriɣmrt
Asaḍuf n id kusinus
(ittawsan ula s yism n
tanfalit n kusinus
nɣ
askkud n Al Kaci
) tga yan usaḍuf nna ismunn tiɣziwin n tasgiwin n kra n umkṛaḍ d kusinus n yan zɣ tiɣmriwin. S uswuri n tirra zund tin Fig. 1, asaḍuf n iwankn n id kusinus
cos
{\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \gamma ,}
maɣ
{\displaystyle \gamma }
tga tiɣmrt lli illan gr tiɣziwin
{\displaystyle a}
{\displaystyle b}
d tasga tamuzzlt n
{\displaystyle c}
. I tawlaft ann nit rad darnɣ ilin ula:
cos
{\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos \alpha ,}
cos
{\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos \beta .}
Asaḍuf n id kusinus ar tskar asmata i
askkud n Pythagor
, nna ur illan dar imkṛaḍn unziɣn: iɣ tga
{\displaystyle \gamma }
tiɣmrt taɣadant (nna dar illa 90 daraja, nɣ
{\textstyle {\pi \over 2}}
s raḍyan), hann
{\textstyle cos(\gamma )=0}
, s ɣmk ad as iskar usaḍuf n id kusinus asmata i
askkud n Pythagor
{\displaystyle c^{2}=a^{2}+b^{2}.}
Ar nswurri s usaḍuf n id kusinus n id kusinus iɣ nra ad nḥasb tiɣmrt tiss kraḍt n kra n umkṛaḍ iɣ yad tawssan darnɣ snat tasgiwin d tiɣmrt nnsn iqqnn, d ula ɣ lḥsab n tiɣmriwin n kra n umkṛaḍ iɣ yad ttawssan darnɣ tasgiwin nns s kraḍ-itsnt. (
Ɣr uggar
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Tiwisi
Taɣarast
Ssnfl
Tusnakt
Tarakalt
Taflsuft
Amzruy
Asgd
Taẓuṛi
Tunnunt
Tatiknulujit
Tiwisi
Timassanin
Imaziɣn
Tamtti
Tasasfrt
Tasnslkimt
Tadlsa
Taɣrma
Tasnijjit
Tutlayt
Yurrid zɣ "
Ismiln
Aggur
Tusnakt
Tamassant
Pages qui utilisent un format obsolète des balises mathématiques
Aggur
Tusnakt
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