Kwegore idzva rechikoro

Vazhinji vaverengi vaive kune imwe nzvimbo pazororo - ingave munyika yedu yakanaka, munyika dzakavakidzana, kana pamwe mhiri kwemakungwa. Ngatitorei mukana weizvi apo miganho yakativhurira ... Ndeipi chiratidzo chaiwanzogara munzendo dzedu pfupi uye refu? Uyu museve unonongedza kunobuda kubva kumota, kuenderera kwenzira yegomo, mukova wemu museum, musuwo wemahombekombe, zvichingodaro zvichingodaro. Chii chinofadza pane zvese izvi? Masvomhu, kwete zvakanyanya. Asi ngatifungei: chiratidzo ichi chiri pachena kune vese ... vamiriri vebudiriro umo kupfura kwakambopfurwa. Chokwadi, hazvibviri kuratidza izvi. Hatizivi imwe budiriro. Zvisinei, iyo pentagon yenguva dzose uye shanduro yayo yakaita nyeredzi, iyo pentagram, inonyanya kufadza masvomhu.

Hatidi chero dzidzo kuti tiwane nhamba idzi dzinonakidza uye dzinonakidza. Kana, Muverengi, wanga uchinwa cognac yenyeredzi shanu muhotera ine nyeredzi shanu paPlace des Stars muParis, pamwe… Kana mumwe munhu akatikumbira kuti tiswedere nyeredzi, isu tinotora shanu-inonongedza tisingazeze, uye apo mutauri anoshamisika: "Ichi chiratidzo cheyaimbova USSR!", Tinogona kupindura: Stables!

Iyo pentagram, kana nyeredzi ine shanu-inonongedza, pentagon yenguva dzose, yakagoneswa nevanhu vese. Inosvika chikamu chimwe muzvina chenyika, kusanganisira iyo US uye yaimbova USSR, vakaisanganisira muzviratidzo zvavo. Sevana, takadzidza kudhirowa nyeredzi ine mativi mashanu pasina kusimudza penzura kubva papeji. Mukukura, anova nyeredzi yedu inotungamirira, isingachinji, iri kure, chiratidzo chetariro uye magumo, chirevo. Ngatizvitarise parutivi.

Nyeredzi dziri kutiudzei?

Vanyori vezvakaitika kare vanobvumirana kuti kusvika muzana remakore rechinomwe BC, nhaka yehungwaru yevanhu veEurope yakaramba iri mumumvuri wetsika dzeBhabhironi, Egypt neFenikiya. Uye kamwe kamwe zana remakore rechitanhatu rinounza rumutsiriro uye kukurumidza kukura kwetsika nesayenzi izvo vamwe vatori venhau (somuenzaniso, Daniken) vanoti - zvakaoma kutaura kana ivo pachavo vanotenda mune izvi - kuti izvi zvingadai zvisina kuitika pasina kupindira. yevasungwa. kubva muchadenga.

Kana zvasvika kuGreece, nyaya yacho ine tsananguro ine musoro: semugumisiro wekutama kwevanhu, vagari vePeloponnesian peninsula vanodzidza zvakawanda nezvetsika dzenyika dzakavakidzana (semuenzaniso, mabhii eFenikiya anopinda muGreece uye anovandudza alfabheti. ), uye ivo pachavo vanotanga kutora nzvimbo yeMediterranean. Aya ndiwo anogara akanakira mamiriro ekuvandudzwa kwesainzi: rusununguko rwakasanganiswa nekusangana nenyika. Pasina rusununguko, tinozvipa isu kune ramangwana renyika dzebhanana dzeCentral America; pasina vanobatika, kuNorth Korea.

Nhamba Inokosha

Muzana remakore rechitanhatu BC raive zana rinokosha munhoroondo yevanhu. Pasina kuziva kana kuti pamwe kusanzwa nezvemumwe nemumwe, vatatu vakuru vanofunga vakadzidzisa: Buddha, Confucius i Pythagoras. Zviviri zvekutanga zvakagadzira zvitendero nehuzivi zvichiripo nhasi. Basa rechitatu razvo rinongogumira pakuwanikwa kweimwe kana imwe pfuma yeimwe katatu here?

Pakutanga kwezana remakore rechi624 nerechitanhatu (c. 546 - c. XNUMX BC) muMireto muAsia Minor yanhasi yaigara. Zvakadaro. Mamwe manyuko anoti akanga ari musayendisiti, mamwe kuti akanga ari mushambadzi akapfuma, uye vamwezve vanomudana kuti muzvinabhizimisi (sezviri pachena, mugore rimwe akatenga zvisviniro zvose zveoiri, ndokuzozvikwereta nokuda kwomubhadharo womubairo). Vamwe, maererano nefashoni yazvino uye muenzaniso wekuita sainzi, vanomuona, semubatsiri: sezviri pachena, akakoka vachenjeri, akavadyisa uye akavarapa, uye ipapo akati: "Zvakanaka, shandira mbiri ye ini neSainzi yese." Zvisinei, manyuko akawanda akakomba anoda kutaura kuti Thales, nyama neropa, akanga asipo zvachose, uye zita rake chete akashanda somunhu chaiwo pfungwa. Sezvazvaive, ndizvo zvazvaive, uye pamwe hatizombofa takaziva. Munyori wenhoroondo wemasvomhu E. D. Smith akanyora kuti dai pasina Thales, kwaisazova naPythagoras, uye hakuna akafanana naPythagoras, uye pasina Pythagoras paisazova naPlato kana mumwe akafanana naPlato. Zvimwe. Ngatisiyanei, zvisinei, chii chaizoitika dai.

Pythagoras (c. 572 - c. 497 BC) akadzidzisa paCrotone kuchamhembe kweItaly, uye ndipo pakazvarwa sangano renjere rakatumidzwa zita ratenzi: Pythagoreanism. Yakanga iri yehutsika-yechitendero kufamba uye kushamwaridzana kwakavakirwa, sezvatingazvidaidza nhasi, pazvakavanzika uye zvakavanzika dzidziso, tichifunga kudzidza kwesainzi seimwe yenzira dzekuchenesa mweya. Munguva yehupenyu hwechizvarwa chimwe chete kana zviviri, Pythagoreanism yakapfuura nematanho enguva dzose ekukura kwemazano: kukura kwekutanga nekuwedzera, dambudziko uye kuderera. Chokwadi mazano makuru haagumise hupenyu hwavo ipapo uye havafe zvachose. Dzidziso youngwaru yaPythagoras (iye amene akatanga shoko raakazvidana kuti: muzivi, kana kuti shamwari youchenjeri) uye vadzidzi vake vakadzora makare ose, ipapo vakadzokera kuRenaissance (pasi pezita rokuti vahedheni), uye chaizvoizvo tiri mupesvedzero yake. nhasi. Nheyo dzePythagoreanism dzakadzika midzi mutsika (kunyanya muEurope) zvekuti isu hatitomboziva kuti tinogona kufunga neimwe nzira. Isu tinoshamiswa saMolière's Monsieur Jourdain, uyo akashamiswa kuziva kuti akanga achitaura prose hupenyu hwake hwose.

Pfungwa huru yePythagoreanism yaiva yekutenda kuti nyika yakarongeka maererano nehurongwa hwakasimba uye kuwirirana, uye kuti basa remunhu nderokuziva kuwirirana uku. Uye ndiko kufungisisa kuwirirana kwenyika kunoumba dzidziso yePythagoreanism. MaPythagoras aive mashura uye masvomhu, kunyangwe zvirizvo nhasi izvo zviri nyore kuvaisa mumapoka akadaro. Vakagadzira nzira. Vakatanga zvidzidzo zvavo zvekuwirirana kwenyika, vakatanga kudzidza mimhanzi, nyeredzi, uye arithmetic.

Kunyange zvazvo vanhu vakakundwa nemashiripiti "nokusingaperi", chikoro chePythagorean chete ndicho chakaita kuti ive mutemo unoshanda. "Nhamba dzinotonga nyika" - sirogani iyi ndiyo yaive yakanakisa hunhu hwechikoro. Nhamba dzine mweya. Imwe neimwe yaireva chimwe chinhu, chimwe nechimwe chaifananidzira chimwe chinhu, chimwe nechimwe chairatidza kachikamu keiyi tsinhirano yeChisiko Chapose pose, i.e. nzvimbo. Shoko racho pacharo rinoreva “kurongeka, kurongeka” (vaverengi vanoziva kuti zvizorwa zvinopfavisa chiso uye zvinowedzera runako).

Nzvimbo dzakasiyana dzinopa zvirevo zvakasiyana izvo maPythagoras akapa kune imwe nhamba. Imwe nzira kana imwe, nhamba imwe chete inogona kufananidzira pfungwa dzakawanda. Akanyanya kukosha aive vatanhatu (nhamba yakakwana) i gumi - hwerengedzo yenhamba dzakatevedzana 1 + 2 + 3 + 4, inoumbwa nedzimwe nhamba, iyo chiratidzo chayo ichiripo nanhasi.

Saka, Pythagoras akadzidzisa kuti nhamba ndiyo yekutanga uye tsime rezvose, kuti - kana iwe uchifungidzira - "vanosanganiswa" pamwe chete, uye tinoona chete migumisiro yezvavanoita. Yakagadzirwa, kana kuti yakagadziridzwa naPythagoras, kusanzwisisika kwenhamba hakuna "kudhindwa kwakanaka" nhasi, uye kunyangwe vanyori vakakomba vanoona pano musanganiswa we "pathos uye zvisina musoro" kana "sainzi, zvakavanzika uye kuwedzeredza kwakachena." Zvakaoma kunzwisisa kuti munyori wenhau dzakaitika akakurumbira Alexander Kravchuk anganyora sei kuti Pythagoras nevadzidzi vake vakazadza uzivi nezviratidzo, ngano, mashura - sokunge kuti haana kunzwisisa chinhu. Nekuti zvinongotaridzika seizvi kubva pakuona kwezana redu rechiXNUMX. VaPythagoreans havana kunetsa chero chinhu, vakagadzira dzidziso dzavo muhana yakakwana. Zvichida mumazana mashoma emakore mumwe munhu achanyora kuti dzidziso yese yehukama yaivewo isina musoro, yekunyepedzera uye yekumanikidzwa. Uye chiratidzo chenhamba, icho chakatiparadzanisa kubva kuPythagoras kwechikamu chechina chemirioni yemakore, chakapinda zvakanyanya mutsika uye chikava chikamu chayo, senge ngano dzeGreek neGerman, medieval knightly epics, ngano dzechiRussia nezve Kost kana chiratidzo chaJulius Slovak. Slavic Pope.

Kusanzwisisa kusinganzwisisike

Mune geometry, vaPythagoras vakashamiswa figurami-podobnymi. Uye kwaive mukuongorora kweThales theorem, mutemo wekutanga wemitemo yekufanana, iyo njodzi yakaitika. Zvikamu zvisingaenzaniswi zvakawanikwa, uye nokudaro nhamba dzisina musoro. Zvikamu zvisingagoni kuyerwa nechero chiyero. Nhamba dzisina kuenzana. Uye yakawanikwa mune imwe yemhando dzakareruka: square.

Nhasi, musainzi yechikoro, tinonzvenga chokwadi ichi, tisingazvioni. Diagonal yeskweya ndeye √2? Hongu, ingava yakawanda sei? Tinodzvanya mabhatani maviri pacalculator: 1,4142 ... Zvakanaka, isu tatoziva kuti square root yevaviri chii. Chii? Hazvina musoro here? Zvichida imhaka yekuti tinoshandisa chiratidzo chinoshamisa zvakadaro, asi shure kwezvose chokwadi iri 1,4142. Mushure mezvose, calculator hairevi nhema.

Kana muverengi achifunga kuti ndiri kuwedzeredza, saka ... zvakanaka kwazvo. Sezviri pachena, zvikoro zvePoland hazvina kushata senge, semuenzaniso, muBritish, uko kune zvese kusayera pane imwe nzvimbo pakati pengano.

MuchiPolish, izwi rekuti "zvisina musoro" harisi rinotyisa semumwe waro mune mimwe mitauro yeEurope. Rational nhamba dziripo dzine mufungo, ratidzo, dzine musoro, i.e.

Funga kufunga kuti √2 inhamba isina musoro, kureva kuti, hachisi chero chikamu chep/q, apo p na q ari manhamba. Mumazuva ano, zvinoita seizvi ... Ngatitii √2 = p / q uye kuti chikamu ichi hachichagoni kupfupiswa. Kunyanya, ose p uye q haana kujairika. Ngatienzane: 2q²=p². Nhamba p haigone kuve isinganzwisisike, kubva ipapo p² zvaizovawo, uye rutivi rworuboshwe rwekuenzana runowanda 2. Nokudaro, p is even, i.e., p = 2r, saka p.²= 4r². Isu tinoderedza equation 2q²= 4r². tinowana d²= 2r² uye tinoona kuti q inofanirawo kuenzana, zvataifungidzira kuti handizvo. Received kupokana humbowo hunopera - unogona kuwana iyi formula nguva nenguva mubhuku rega rega remasvomhu. Uhu humbowo hwemamiriro ekunze ndihwo hunyengeri hunodiwa hwemasophist.

Ini ndinosimbisa, zvisinei, kuti uku ndiko kufunga kwemazuva ano - vePythagoras vaive vasina zvigadzirwa zvealgebraic zvakagadziridzwa. Vakanga vachitsvaga chiyero chakafanana chemativi eskweya uye diagonal yaro, izvo zvakavatungamira kune imwe pfungwa yekuti hapaigona kuve nechiyero chakafanana. Kufungidzira kwekuvapo kwayo kunotungamirira kune kupesana. Ivhu rakaoma rakatsvedza kubva pasi petsoka dzangu. Zvinhu zvose zvinofanira kukwanisa kurondedzerwa nenhamba, uye diagonal yechikwere, iyo chero ani zvake anogona kutora netsvimbo pajecha, haina urefu (kureva, inoyerwa, nokuti hapana dzimwe nhamba). “Kutenda kwedu kwakanga kusina maturo,” vaPythagoraan vaitaura kudaro. Kuita sei?

Kuedza kuzviponesa kwakaitwa nemitoo yamasekete. Ani naani anotsunga kuwana kuvapo kwenhamba dzisina mufungo achaurawa, uye, sezviri pachena, tenzi pachake—anopesana nomurayiro wokupfava – anoita mutsara wokutanga. Zvadaro zvinhu zvose zvinova keteni. Maererano neimwe vhezheni, maPythagoreans vakaurayiwa (vakaponeswa uye nekutenda kwavari iyo pfungwa yese haina kuendeswa kuguva), sekureva kwemumwe, vadzidzi ivo pachavo, vachiteerera, vanodzinga tenzi anonamatwa uye iye kumwe anopedzisa hupenyu hwake mukutapwa. . Kapoka kachirega kuvapo.

Isu tose tinoziva chirevo chaWinston Churchill: "Hazvina kumboitika munhoroondo yekurwisana kwevanhu kune vanhu vakawanda vane chikwereti kune vashomanana." Yakanga iri pamusoro pevatyairi vakadzivirira England kubva kuGermany ndege muna 1940. Kana tikatsiva "makakatanwa evanhu" ne "pfungwa dzevanhu", saka chirevo chinoshanda kune vashoma vePythagoras vakapukunyuka (zvishoma) kubva papogrom pakupera kwemaXNUMXs. XNUMXth century BC.

Saka "pfungwa yakapfuura isina kugadzikana." Chii chinotevera? Nguva yegoridhe iri kuuya. MaGiriki anokunda vaPezhiya (Marathon - 490 BC, Muripo - 479). Democracy iri kuwedzera kusimba. Nzvimbo itsva dzepfungwa dzehuzivi uye zvikoro zvitsva zviri kubuda. Vateveri vePythagoreanism vakatarisana nedambudziko renhamba dzisina musoro. Vamwe vanoti: “Hatichazivi chakavanzika ichi; isu tinogona kungozvifungisisa uye kuyemura Uncharted." Iwo ekupedzisira ane pragmatic zvakanyanya uye haaremekedze Chakavanzika: "Kana chimwe chinhu chisina kunaka nenhamba idzi, ngatizvisiyei, mushure memakore 2500 zvese zvichange zvazivikanwa. Pamwe nhamba hadzitonge pasi rose? Ngatitange ne geometry. Haisisiri nhamba dzakakosha, asi zviyero uye zviyero.

Vatsigiri vegwaro rekutanga vanozivikanwa kune vanyori venhoroondo yemasvomhu se acousticsVakararama kwemamwe mazana emakore mashoma uye ndizvo zvazviri. Vekupedzisira vakazviti masvomhu (kubva muchiGiriki mathein = kuziva, kudzidza). Hatifaniri kutsanangurira ani zvake kuti nzira iyi yakakunda: yakararama kwemazana makumi maviri nemashanu uye inobudirira.

Kukunda kwemasvomhu pamusoro pe auzmatics kwakaratidzwa, kunyanya, mukuonekwa kwechiratidzo chitsva chePythagoras: kubva zvino zvichienda mberi yaive pentagram (pentás = shanu, girama = tsamba, chinyorwa) - pentagon yenguva dzose muchimiro che star. Matavi aro anopindirana zvakanyanya kuenzana: iyo yose inogara ichireva chikamu chikuru, uye chikamu chikuru kune chikamu chidiki. Akafona chiyero choumwari, ndokuzoitwa zvechitendero ku ndarama. VaGiriki vekare (uye nyika yose yeEurocentric shure kwavo) vaidavira kuti chikamu ichi ndicho chakanyanya kufadza ziso revanhu, uye chakasangana nacho kwose kwose.

(Cyprian Camille Norvid, Prometidion)

Ndichapedzisa neimwe ndima, panguva ino kubva munhetembo "Faust" (yakashandurwa naVladislav August Kostelsky). Zvakanaka, iyo pentagram zvakare mufananidzo wepfungwa shanu uye yakakurumbira "tsoka yen'anga". Munhetembo yaGoethe, Dr. Faust aida kuzvidzivirira kubva kuna dhiyabhorosi nokudhirowa chiratidzo ichi pachikumbaridzo chemba yake. Akazviita zvakasununguka, uye izvi ndizvo zvakaitika:

Faust

M epistopheles

Faust

Uye izvi zvese nezve pentagon yakajairwa pakutanga kwegore idzva rechikoro.