Asekkud n Pythagore

Asekkud n Pythagore d yiwen seg yisekkuden igejdanen deg tussna n tusnakt. Yettwassen s waṭas ɣer yinelmaden n uswir alemmas, acku yeskan assaɣ yellan gar yidisan n ukerdis amaɣud.

udem 1

Asegzi n usekkud

Asekkud n Pythagore yeqqar-d:

Deg ukerdis amaɣud, tajumma n umkuẓ yebnan ɣef walubdis tegda d tajumma n yimkuẓen yebnan ɣef sin n yidisan-nniḍen.

S uslugen n tusnakt, nezmer ad t-naru akka:

$a^{2}+b^{2}=c^{2}$

Anda:

• a d b d idisan n tiɣemmar timaɣudin (90°)
• c d alubdis (idis ameqqran yemsadawen d tiɣmert tamaɣudt)

Anza

Llant aṭas n wanzayen i yesbegnen asekkud-a. Yiwet seg-sent tagi :

udem 2 :akerdis s yidisen a,b akked alubdis c

udem 3, udem 4

ad yili akerdis s yidisen a akked b , akked alubdis c , ad nessexdem kuẓ seg sen akken ad negg yiwen amkuẓ s yidisen $a+b$ am akka twalan deg udem 3

wagi ad yesnuleɣ amkuẓ deg tlemmast yesɛan idis teɣzi-s c yarnu tajumma-s $c^{2}$.

Ama, ma ad nbeddel idgan n kuẓ ikerdisen igi am akka twalam deg udem 4, nezmer ad nwali kuẓ imkuẓen daxel n yiwen amkuẓ ameqqran, yiwen yesɛa a2 deg tjumma-s d wayeḍ yesɛa b2 deg tjumma-s :

Am akken amkuẓ ameqqran yesɛa yiwet tjumma deg sin idgan-igi, i.e $(a+b)^{2}$arnu am akken ikerdisen d yiwen-sen deg sin idgan, ilaq ad nzemmem (conclure) belli d imkuẓen si sin yid-sen $a^{2}$ akked $b^{2}$ ugdan ar amkuẓ ameqqran $c^{2}$

dɣa : $a^{2}+b^{2}=c^{2}$

Amezruy

Tafelwit n Plimpton 322, i yesɛan azal n 1800 av. j.av.,

Asekkud-a yettwassen s yisem n Pythagore, amusnak agrigi i yedderen gar 570 d 495 send talalit n Ɛisa. Maca, aṭas n yimusnawen ɛerḍen ad d-sbanen belli asekkud-a yella yettwassen uqbel Pythagore, ladɣa sɣur Ibabuliyen d Yimaṣriyen iqburen. Akken yebɣu yili, d Pythagore i t-yessuffɣen-d s wudem ummid, yerna yefka-yas anzaten yesdukklen.

Seg tallit-nni ar ass-a, asekkud n Pythagore yuɣal d allal agejdan deg tusnakt, ladɣa deg tanzeggit (géométrie) d tussniwin n usihel (sciences de l'ingénieur).