Pythagoras ndi Filosofi ya Manambala
Pythagoras anali katswiri wodziwika bwino wafilosofi komanso masamu wachigiriki, nthawi zambiri amaonedwa kuti ndiye bambo wa nzeru za manambala. Anabadwa cha m'ma 570 BC pachilumba cha Ionian cha Samos, Greece, ndipo anamwalira cha m'ma 495 BC. Pythagoras amadziwika ndi mbali zambiri za malingaliro ake ndi ntchito yake, koma chimodzi mwazodziwika kwambiri ndi zomwe adapereka pa masamu, makamaka, chiphunzitso cha manambala. Nkhaniyi ifotokoza mozama za Pythagoras ndi nzeru za manambala, chifukwa chake komanso momwe manambala adathandizira kwambiri pamalingaliro a Pythagoras, komanso cholowa chake cha nzeru ndi masamu, chomwe chidakali chofunikira mpaka pano.
Moyo ndi Maziko a Pythagoras
Pythagoras anabadwira ku Samos, koma anayenda kwambiri m'madera monga Igupto ndi Babulo. Paulendo wake, anaphunzira maphunziro osiyanasiyana, kuphatikizapo masamu, zakuthambo, ndi nzeru za anthu. Pamapeto pake, Pythagoras anakhazikika ku Croton (tsopano kum'mwera kwa Italy), komwe anakhazikitsa gulu lachipembedzo komanso la nzeru za anthu lotchedwa Pythagoras Sect.
Gulu ili si sukulu yokha, komanso ndi gulu la abale lomwe lili ndi dongosolo ndi malamulo enaake. Mamembala amatsatira malangizo okhwima azakudya ndi moyo wawo ndipo amakhulupirira kwambiri kuti mzimu sufa komanso kubadwanso kwatsopano. Amadziperekanso kufufuza ubale wachinsinsi ndi masamu mkati mwa chilengedwe chonse.
Filosofi ya Pythagoras ndi Lingaliro la Manambala
Chimodzi mwa zinthu zazikulu zomwe Pythagoras adapereka chinali lingaliro lakuti chiwerengero ndiye maziko a zinthu zonse ndipo chilengedwe chonse chimayendetsedwa ndi mfundo zamasamu. Pythagoras ndi otsatira ake ankakhulupirira kuti chilichonse chingathe kufotokozedwa kudzera mu manambala ndi ubale wa manambala. Lingaliro limeneli ndilo maziko a "filosofi ya manambala" yotchedwa Pythagoras.
Mfundo Zazikulu za Filosofi ya Manambala
1. Manambala ngati Mtima wa Chilichonse:
A Pythagoreans ankaphunzitsa kuti manambala ndiye maziko a chilengedwe chonse. Mwachitsanzo, adapeza kuti ubale wa nyimbo ukhoza kufotokozedwa kudzera mu ma ratios a manambala athunthu. Mu kafukufuku wake wa zingwe zogwedezeka, Pythagoras adapeza kuti ma harmonic intervals amapezeka mu ma ratios osavuta—monga 1:2 (octave), 2:3 (quint), ndi 3:4 (quart). Izi zasonyeza kuti manambala si zida zamasamu zokha, komanso maziko a mgwirizano ndi kukongola m'chilengedwe.
2. Kudalira Kusatha ndi Manambala:
Pythagoras anafufuzanso lingaliro la kusatha poyerekeza ndi manambala. Manambala oganiza bwino (omwe angatchulidwe ngati magawo a manambala awiri athunthu) amaphatikizapo manambala ambiri omwe, mu lingaliro la Pythagoras, ali ndi mgwirizano. Komabe, adapezanso kuti pali manambala omwe sangatchulidwe ndi ma ratios, omwe amadziwika kuti manambala osamveka bwino. Kupeza kumeneku kunachepetsa chikhulupiriro chawo mu dongosolo la manambala ndi dongosolo la chilengedwe chonse, ndikuwulula zovuta zakuya za chilengedwe chonse.
Chiphunzitso cha Pythagorean
Chiphunzitso cha Pythagorean, chimodzi mwa zinthu zodziwika bwino za masamu zomwe Pythagoras adapereka, chimati mu kansalu kolondola, sikweya ya kutalika kwa hypotenuse ndi yofanana ndi kuchuluka kwa masikweya a kutalika kwa miyendo ina iwiri. Izi zitha kupangidwa motere:
a² + b² = c²,
kumene 'c' ndi kutalika kwa hypotenuse ndipo 'a' ndi 'b' ndi kutalika kwa miyendo iwiri yomwe imapanga ngodya yakumanja.
Chiphunzitsochi sichili chabe zotsatira zofunika zamasamu komanso chikuwonetsa chikhulupiriro cha Pythagorean chakuti manambala ndi ubale wa manambala ndiye maziko a chilengedwe chonse. Mu chitsanzo cha Pythagorean, chiphunzitsochi chimagwirizanitsa geometry ndi masamu, kusonyeza momwe manambala amakonzera kapangidwe ka malo enieni.
Pythagoreanism: Chikhalidwe ndi Zinsinsi
Chiphunzitso cha Pythagorean sichinali kokha gulu la ziphunzitso za masamu ndi filosofi, komanso gulu lauzimu ndi gulu lachipembedzo. Anthu a m'gulu la Pythagorean ankatsatira malamulo enieni, kuphatikizapo kudya nyama ndi malamulo okhudza chiyero, komanso mfundo zawo za makhalidwe abwino.
Chiphunzitso cha Pythagorean
Pythagoras ankadziwikanso kuti ndi munthu wodziwa zinthu zachinsinsi. Otsatira ake ankakhulupirira kuti mzimu unali chinthu chosafa chomwe chimabadwanso mwatsopano kangapo ndipo moyo wokhazikika komanso wodzipereka ukhoza kuyeretsa mzimu ku choipa ndikuukweza kufika pamlingo wapamwamba wa moyo. Manambala ndi ubale wawo ankaganiziridwa kuti anali ndi gawo lofunika kwambiri pa dongosolo la chilengedwe ndi lauzimu.
Pythagoras anaphunzitsanso kuti chilichonse chili ndi "nomos," kapena lamulo lachilengedwe , lomwe lingamveke bwino kudzera mu kuphunzira manambala ndi ma ratios. Mwachitsanzo, mu zaluso ndi nyimbo, a Pythagoras ankagwiritsa ntchito mfundo za masamu kuti apeze mgwirizano ndi dongosolo.
Cholowa cha Pythagoras mu Masamu ndi Filosofi
Cholowa cha Pythagoras ndi chachikulu, chimaphatikizapo magawo ambiri kupatula masamu. Nzeru zake za chiwerengero monga maziko a zinthu zonse zinakhudza maganizo a filosofi ndi sayansi amtsogolo.
Mphamvu mu Masamu
Zotsatira zambiri ndi ziphunzitso zomwe Pythagoras ndi omutsatira ake adapeza kapena kuphunzira koyamba zakhala maziko a maphunziro opitilira a masamu. Chiphunzitso cha Pythagoras chikadali chimodzi mwa mfundo zofunika kwambiri mu masamu ndipo chikuphunzitsidwabe padziko lonse lapansi.
Mphamvu mu Filosofi
Pythagoras anakhudza akatswiri ambiri afilosofi, kuphatikizapo Plato ndi Aristotle. Plato, makamaka, anachita chidwi ndi malingaliro a Pythagoras okhudza chiwerengero ndi mgwirizano wa chilengedwe ndipo anawaphatikiza mu filosofi yake. Lingaliro la Plato la "dziko la malingaliro," momwe zenizeni zenizeni zingamvekere kokha kudzera mu chidziwitso choyera osati kuzindikira kwa malingaliro, linauziridwa ndi lingaliro la Pythagoras la chiwerengero ndi masamu ngati chinsinsi chomvetsetsa chilengedwe.
Nyimbo ndi Mgwirizano
Zimene Pythagoras anathandiza pa chiphunzitso cha nyimbo zinalinso zofunika kwambiri. Mfundo zambiri zofunika kwambiri za chiphunzitso cha nyimbo za kumadzulo zimachokera ku zomwe Pythagoras anapeza zokhudza ubale wa manambala ndi mgwirizano. Lingaliro lakuti nyimbo zitha kukonzedwa motsatira mfundo za masamu likupitirirabe mu chiphunzitso cha nyimbo mpaka lero.
Mapeto
Pythagoras ndi nzeru za chiwerengero sizingasiyanitsidwe ndi mbiri ya masamu ndi filosofi ya Kumadzulo. Ndi ziphunzitso zake zokhudza kufunika kwa chiwerengero ndi mgwirizano wa chilengedwe chonse, Pythagoras anasiya cholowa chomwe chimaposa maphunziro ndi nthawi. Kuyambira pa mfundo zazikulu za geometric mpaka malingaliro achinsinsi a chilengedwe chonse, mfundo za Pythagoras zimakhalabe zofunikira m'magawo ambiri ophunzirira ndi kuchita.
Tikamaphunzira masamu kapena kuganizira za kukongola kwa chilengedwe, nthawi zambiri timabwerera ku mfundo zazikulu zomwe Pythagoras ndi anthu ammudzi mwake adapanga poyamba. M'lingaliro limeneli, Pythagoras ndi nzeru za chiwerengero ndi mlatho wofunika pakati pa masamu ndi nzeru, zomwe zimatikumbutsa kuti dziko lapansi, ndi mgwirizano wake wonse ndi kukongola kwake, ndi chinsinsi chomwe chikuyembekezera kufotokozedwa ndi manambala ndi ma ratios obisika pansi pake.
