Kwa chaka chatsopano cha sukulu

Owerenga ambiri anali kwinakwake patchuthi - kaya m'dziko lathu lokongola, m'maiko oyandikana nawo, kapena ngakhale kutsidya lina. Tiyeni titengepo mwayi pa izi pomwe malire ali otsegukira kwa ife ... Uwu ndi muvi womwe umaloza potuluka mumsewu, kupitiliza njira yamapiri, khomo la nyumba yosungiramo zinthu zakale, polowera kunyanja, ndi zina zotero. Chosangalatsa ndi chiyani pa zonsezi? Masamu, osati kwambiri. Koma tiyeni tiganizire: chizindikiro ichi ndi chodziwikiratu kwa onse ... oimira chitukuko momwe mivi inawombera kamodzi. Zowona, sikutheka kutsimikizira izi. Ife sitikudziwa chitukuko china chirichonse. Komabe, pentagon yokhazikika komanso mawonekedwe ake owoneka ngati nyenyezi, pentagram, ndizosangalatsa masamu.

Sitifunika maphunziro aliwonse kuti tipeze ziwerengerozi kukhala zosangalatsa komanso zosangalatsa. Ngati, Owerenga, mwamwa mowa wa nyenyezi zisanu mu hotelo ya nyenyezi zisanu pa Place des Stars ku Paris, ndiye mwina… munabadwa pansi pa nyenyezi yamwayi. Wina akatifunsa kuti tijambule nyenyezi, tidzajambula nsonga zisanu popanda kukayika, ndipo pamene interlocutor akudabwa: "Ichi ndi chizindikiro cha USSR yakale!", Tikhoza kuyankha: Stables! ".

Pentagram, kapena nyenyezi ya nsonga zisanu, pentagon yokhazikika, yakhala yodziwika bwino ndi anthu onse. Pafupifupi gawo limodzi mwa magawo atatu a mayiko, kuphatikiza US ndi USSR wakale, adaziphatikiza muzizindikiro zawo. Monga ana, tinaphunzira kujambula nyenyezi ya nsonga zisanu popanda kukweza pensulo kuchokera patsamba. Akakula, amakhala nyenyezi yathu yotsogolera, yosasinthika, yakutali, chizindikiro cha chiyembekezo ndi tsogolo, oracle. Tiyeni tiyang'ane pa izo kuchokera kumbali.

Kodi nyenyezi zimatiuza chiyani?

Akatswiri a mbiri yakale amavomereza kuti mpaka zaka za m'ma XNUMX BC, cholowa chaluntha cha anthu a ku Ulaya chinakhalabe mumthunzi wa zikhalidwe za Babulo, Egypt ndi Foinike. Ndipo mwadzidzidzi zaka za zana lachisanu ndi chimodzi zimabweretsa kutsitsimuka ndi chitukuko chofulumira cha chikhalidwe ndi sayansi kuti atolankhani ena (mwachitsanzo, Daniken) amati - n'zovuta kunena ngati iwo eni amakhulupirira izi - kuti izi sizikanatheka popanda kulowererapo. a akaidi. kuchokera mlengalenga.

Zikafika ku Greece, mlanduwu uli ndi tanthauzo lomveka: chifukwa cha kusamuka kwa anthu, anthu okhala pachilumba cha Peloponnesian amaphunzira zambiri za chikhalidwe cha mayiko oyandikana nawo (mwachitsanzo, zilembo za Foinike zimalowa mu Greece ndikuwongolera zilembo zachi Greek. ), ndipo iwo eniwo akuyamba kulamulira nyanja ya Mediterranean. Izi nthawi zonse zimakhala zabwino kwambiri pakukula kwa sayansi: kudziyimira pawokha komanso kulumikizana ndi dziko lapansi. Popanda kudziyimira pawokha, timadzitengera tokha ku tsogolo la maiko a nthochi ku Central America; popanda kulumikizana, ku North Korea.

Numeri Ndi Yofunika

Zaka za m'ma XNUMX BC zinali zaka zapadera m'mbiri ya anthu. Popanda kudziwa kapena kusamva za wina ndi mzake, oganiza bwino atatu adaphunzitsa: Buddha, Confucius i Pythagoras. Zipembedzo ziwiri zoyambirira zinapanga zipembedzo ndi mafilosofi omwe adakalipo mpaka pano. Kodi gawo lachitatu la iwo limangokhala pakupeza chinthu chimodzi kapena china cha makona atatu?

Kumayambiriro kwa zaka za m'ma 624 ndi 546 (c. XNUMX - c. XNUMX BC) ku Mileto ku Asia Minor yamakono. Zomwezo. Magwero ena amati iye anali wasayansi, ena kuti anali wamalonda wolemera, ndipo ena amamutcha iye wabizinesi (mwachiwonekere, m’chaka chimodzi anagula makina onse osindikizira mafuta, ndiyeno anawabwereka kuti abweze ngongole). Ena, malinga ndi kachitidwe kamakono ndi chitsanzo cha kuchita sayansi, amamuwona iye, nayenso, monga wosamalira: mwachiwonekere, iye anaitana amuna anzeru, kuwadyetsa ndi kuwachitira iwo, ndiyeno anati: “Chabwino, gwirani ntchito ku ulemerero wa ine ndi Sayansi yonse. ” Komabe, magwero ambiri aakulu amakonda kunena kuti Thales, thupi ndi magazi, panalibe konse, ndipo dzina lake anatumikira monga munthu wa malingaliro enieni. Monga izo zinali, kotero izo zinali, ndipo ife mwina sitidzadziwa konse. Wolemba mbiri wa masamu E. D. Smith analemba kuti kukanakhala kulibe Thales, sipakanakhala Pythagoras, ndipo palibe wonga Pythagoras, ndipo popanda Pythagoras sipakanakhala Plato kapena aliyense wonga Plato. Zowonjezereka. Tiyeni tisiye, komabe, zomwe zikanachitika ngati.

Pythagoras (c. 572 - c. 497 BC) anaphunzitsa ku Crotone kumwera kwa Italy, ndipo kumeneko kunali komwe gulu la aluntha lotchedwa mbuye linabadwa: Pythagoreanism. Inali gulu lachipembedzo-chipembedzo ndi mayanjano ozikidwa, monga momwe tingatchulire masiku ano, pazinsinsi ndi ziphunzitso zachinsinsi, poganizira kuti kuphunzira sayansi ndi imodzi mwa njira zoyeretsera moyo. Pa moyo wa m'badwo umodzi kapena iwiri Pythagoreanism anadutsa mu magawo mwachizolowezi kukula kwa malingaliro: kukula koyambirira ndi kukula, mavuto ndi kuchepa. Malingaliro abwino kwambiri samathera moyo wawo kumeneko ndipo sadzafa kosatha. Chiphunzitso chaluntha cha Pythagoras (iye mwiniyo anayambitsa liwu limene anadzitcha yekha: wanthanthi, kapena bwenzi lanzeru) ndi ophunzira ake analamulira zakale zonse, kenaka anabwerera ku Kubadwa Kwatsopano (m’dzina la chipembedzo chachipembedzo), ndipo kwenikweni tiri pansi pa chisonkhezero chake. lero. Mfundo za Pythagoreanism ndizokhazikika mu chikhalidwe (makamaka ku Ulaya) kotero kuti sitingazindikire kuti tikhoza kuganiza mosiyana. Tidadabwa kwambiri kuposa a Molière's Monsieur Jourdain, yemwe adadabwa kumva kuti wakhala akulankhula prose moyo wake wonse.

Lingaliro lalikulu la Pythagoreanism linali chikhulupiriro chakuti dziko lapansi limapangidwa motsatira ndondomeko yolimba ndi mgwirizano, ndi kuti ntchito ya munthu ndiyo kudziwa mgwirizano umenewu. Ndipo ndiko kulingalira kwa kugwirizana kwa dziko komwe kumapanga chiphunzitso cha Pythagoreanism. A Pythagoras analidi anthanthi komanso masamu, ngakhale kuti lero ndi zosavuta kuwagawa mwachisawawa. Iwo anakonza njira. Iwo anayamba maphunziro awo a mgwirizano wa dziko, choyamba kuphunzira nyimbo, zakuthambo, masamu, etc.

Ngakhale kuti anthu anagonja ku matsenga “kwamuyaya,” sukulu ya Pythagorean yokha ndiyo inaikweza kukhala lamulo logwiritsiridwa ntchito nthaŵi zonse. "Nambala zimalamulira dziko lapansi" - chiganizo ichi chinali chikhalidwe chabwino kwambiri cha sukulu. Manambala ali ndi moyo. Chilichonse chinkatanthauza chinachake, chilichonse chinkaimira chinachake, chilichonse chinkasonyeza kachigawo kakang’ono ka mgwirizano wa Chilengedwe Chonse, i.e. danga. Liwu lenilenilo limatanthauza “dongosolo, dongosolo” (owerenga amadziwa kuti zodzoladzola zimasalaza nkhope ndi kuwonjezera kukongola).

Magwero osiyanasiyana amapereka matanthauzo osiyanasiyana omwe a Pythagoras anapereka kwa chiwerengero chilichonse. Mwanjira ina, nambala yomweyi imatha kutanthauza mfundo zingapo. Zofunika kwambiri zinali zisanu ndi chimodzi (nambala yabwino) i khumi - kuchuluka kwa manambala otsatizana 1 + 2 + 3 + 4, opangidwa ndi manambala ena, ophiphiritsa omwe adakalipo mpaka lero.

Kotero, Pythagoras anaphunzitsa kuti manambala ndi chiyambi ndi gwero la chirichonse, kuti - ngati mukuganiza - "amasakaniza" wina ndi mzake, ndipo timawona zotsatira za zomwe amachita. Zopangidwa, kapena m'malo mwake zopangidwa ndi Pythagoras, chinsinsi cha manambala alibe "chisindikizo chabwino" lero, ndipo ngakhale olemba ozama amawona apa osakaniza "njira ndi zopusa" kapena "sayansi, zinsinsi ndi kukokomeza koyera." N'zovuta kumvetsa momwe wolemba mbiri wotchuka Alexander Kravchuk analemba kuti Pythagoras ndi ophunzira ake anadzaza filosofi ndi masomphenya, nthano, zikhulupiriro - ngati sanamvetse kanthu. Chifukwa zimangowoneka ngati izi potengera zaka zathu za zana la XNUMX. A Pythagoras sanakakamize chilichonse, adapanga malingaliro awo mu chikumbumtima changwiro. Mwina m'zaka mazana angapo wina adzalemba kuti chiphunzitso chonse cha relativity chinalinso chopanda pake, chodzikuza komanso chokakamizidwa. Ndipo chizindikiro cha manambala, chomwe chinatilekanitsa ndi Pythagoras kwa kotala la miliyoni miliyoni, chinalowa kwambiri mu chikhalidwe ndipo chinakhala mbali yake, monga nthano zachi Greek ndi German, zolemba zakale zamatsenga, nthano zachi Russia za Kost kapena masomphenya a Juliusz Slovak. Papa wa Slavic.

Kusaganiza bwino kwachinsinsi

Mu geometry, a Pythagoras anadabwa kwambiri figurami-podobnymi. Ndipo kunali pakuwunika kwa chiphunzitso cha Thales, lamulo loyambira la malamulo ofananira, pomwe tsoka lidachitika. Magawo osayerekezeka adapezeka, motero manambala opanda nzeru. Ndime zomwe sizingayesedwe ndi mulingo uliwonse. Manambala omwe sali ofanana. Ndipo idapezeka mu imodzi mwa mawonekedwe osavuta: lalikulu.

Masiku ano, mu sayansi yakusukulu, timachilambalala mfundo imeneyi, pafupifupi osazindikira. Chigawo cha sikweya ndi √2? Chabwino, zingakhale zingati? Timakanikiza mabatani awiri pa chowerengera: 1,4142 ... Chabwino, tikudziwa kale kuti muzu wapakati wa awiri ndi chiyani. Chiti? Kodi ndizopanda nzeru? Mwina ndi chifukwa chakuti timagwiritsa ntchito chizindikiro chachilendo, koma pambuyo pake ndipotu ndi 1,4142. Kupatula apo, chowerengera sichinama.

Ngati owerenga akuganiza kuti ndikukokomeza, ndiye ... bwino kwambiri. Mwachiwonekere, sukulu za ku Poland sizili zoipa monga, mwachitsanzo, ku British, kumene chirichonse chiri kusayezeka penapake pakati pa nthano.

M'Chipolishi, mawu oti "zopanda nzeru" sali owopsa monga momwe amachitira m'zinenero zina za ku Ulaya. Manambala omveka pali zomveka, zomveka, zomveka, i.e.

Ganizirani mfundo yakuti √2 ndi nambala yopanda nzeru, ndiko kuti, si kachigawo kalikonse ka p/q, pamene p ndi q ali manambala. M'mawu amakono, zikuwoneka ngati izi ... Makamaka, onse p ndi q ndi osamvetseka. Tiyeni tione: 2q²=p². Nambala p singakhale yosamvetseka, kuyambira pamenepo p² zikanakhalanso, ndipo mbali yakumanzere ya kufanana ndi kuchulukitsa kwa 2. Choncho, p ndi even, i.e., p = 2r, choncho p.²= 4r². Timachepetsa equation 2q²= 4r². timapeza d²= 2r² ndipo tikuwona kuti q iyeneranso kukhala yofanana, zomwe timaganiza kuti sizili choncho. Adalandira kutsutsana umboni umatha - mutha kupeza njira iyi nthawi ndi nthawi m'buku lililonse la masamu. Umboni wokhazikika uwu ndi chinyengo chomwe amachikonda kwambiri a sophists.

Ndikutsindika, komabe, kuti izi ndi malingaliro amakono - a Pythagoras analibe zida zopangira algebraic. Iwo anali kufunafuna muyeso wamba wa mbali ya lalikulu ndi diagonal, zomwe zinawatsogolera ku lingaliro lakuti sipangakhale muyeso wamba wotero. Lingaliro la kukhalapo kwake limabweretsa kutsutsana. Malo olimbawo anatsetsereka pansi pa mapazi anga. Chilichonse chiyenera kufotokozedwa ndi manambala, ndipo diagonal ya square, yomwe aliyense angathe kujambula ndi ndodo pamchenga, alibe kutalika (ndiko kuti, ndi yoyezera, chifukwa palibe manambala ena). “Chikhulupiriro chathu chinali chachabechabe,” akutero a Pythagoras. Zoyenera kuchita?

Kuyesayesa kunapangidwa kuti adzipulumutse okha mwa njira zamagulu. Aliyense amene angayerekeze kupeza kukhalapo kwa ziwerengero zopanda nzeru adzaphedwa, ndipo, mwachiwonekere, mbuye mwiniyo - mosiyana ndi lamulo la kufatsa - amachita chiganizo choyamba. Ndiye chirichonse chimakhala chotchinga. Malinga ndi Baibulo lina, a Pythagoreans anaphedwa (pena anapulumutsidwa ndipo chifukwa cha iwo lingaliro lonse silinatengedwe kumanda), malinga ndi wina, ophunzira okha, omvera, amathamangitsa mbuye wopembedzedwayo ndipo kwinakwake amathera moyo wake ku ukapolo. . Gulu lampatukoli likutha.

Tonsefe timadziwa mawu a Winston Churchill akuti: "N'zosatheka m'mbiri ya anthu kuti azimenyana ndi anthu omwe ali ndi ngongole zambiri kwa ochepa." Zinali za oyendetsa ndege omwe adateteza England ku ndege za Germany mu 1940. Ngati tisintha "mikangano ya anthu" ndi "malingaliro aumunthu", ndiye kuti mawuwa akugwira ntchito kwa ochepa a Pythagoreans omwe adathawa (pang'ono kwambiri) kuchokera ku pogrom kumapeto kwa XNUMXs. Zaka za m'ma XNUMX BC.

Kotero "lingalirolo linadutsa popanda vuto." Chotsatira ndi chiyani? M'badwo wagolide ukubwera. Agiriki akugonjetsa Aperisi (Marathon - 490 BC, Malipiro - 479). Demokalase ikukula. Malo atsopano a malingaliro afilosofi ndi masukulu atsopano akubwera. Otsatira a Pythagoreanism akukumana ndi vuto la manambala opanda nzeru. Ena amati: “Sitingamvetse chinsinsi ichi; titha kungolingalira ndikusilira Uncharted." Otsatirawa ndi anzeru kwambiri ndipo salemekeza Chinsinsi: “Ngati pali china chake cholakwika ndi ziwerengerozi, tiyeni tizisiye, pakatha zaka 2500 chilichonse chidzadziwika. Mwina manambala salamulira dziko? Tiyeni tiyambe ndi geometry. Sizinalinso manambala omwe ali ofunikira, koma kuchuluka kwawo ndi ma ratios.

Othandizira njira yoyamba amadziwika kwa akatswiri a mbiri yakale a masamu ngati mawu omveraIwo anakhala kwa zaka mazana angapo ndipo ndi zimenezo. Omalizawo amadzitcha okha masamu (kuchokera ku mathein achi Greek = kudziwa, kuphunzira). Sitiyenera kufotokozera aliyense kuti njira iyi yapambana: yakhala zaka mazana makumi awiri ndi zisanu ndikuchita bwino.

Kupambana kwa masamu pa auzmatics kunasonyezedwa, makamaka, mu maonekedwe a chizindikiro chatsopano cha Pythagoreans: kuyambira tsopano chinali pentagram (pentás = zisanu, galamala = chilembo, zolemba) - pentagon yokhazikika mu mawonekedwe a nyenyezi. Nthambi zake zimadutsana molingana kwambiri: yonse nthawi zonse imatanthauza gawo lalikulu, ndipo gawo lalikulu ndi laling'ono. Iye anayitana gawo laumulungu, kenako osakhala achipembedzo ku golide. Agiriki akale (ndi kumbuyo kwawo dziko lonse la Eurocentric) ankakhulupirira kuti chiwerengerochi chinali chokondweretsa kwambiri m'maso mwa munthu, ndipo chinakumana nacho pafupifupi kulikonse.

(Cyprian Camille Norvid, Prometidion)

Ndimaliza ndi ndime ina, nthawi ino kuchokera mu ndakatulo "Faust" (yomasuliridwa ndi Vladislav August Kostelsky). Chabwino, pentagram ndi chithunzi cha mphamvu zisanu ndi "phazi lamatsenga" lodziwika bwino. Mu ndakatulo ya Goethe, Dr. Faust ankafuna kudziteteza kwa mdierekezi pojambula chizindikiro ichi pakhomo la nyumba yake. Anachita mwachisawawa, ndipo izi ndi zomwe zinachitika:

Faust

M epistopheles

Faust

Ndipo zonsezi ndi za pentagon wamba kumayambiriro kwa chaka chatsopano cha sukulu.