Postulate Euclid sika yesihlanu: kumagama

Kukholakala ukuthi kwakukhona engu-10 000 edlule, impucuko wokuqala ongabantu. Kuqhathaniswa engu-iplanethi yethu, okuyinto, ngokusho ososayensi, kuyinto iminyaka eyizigidi ezingu-4,54 ubudala, lokhu nje emfushane. Ngenxa yalesi "umzuzwana" abantu baye bazenza eqa omkhulu kusukela amathuluzi bakudala itshe mkhathi interplanetary. Ubengeke kwenzeke, uma ngezikhathi emhlabeni bekungeke nhlobo ngizalwe ungungqondongqondo, isayensi iqhubekela phambili. Phakathi kwabo, yebo, libhekisela Euclid. imisebenzi yakhe yaba isisekelo yisisusa esinamandla sokuthuthukisa nesifundo sezibalo zanamuhla.

Lesi sihloko imayelana postulate wesihlanu Euclid nomlando wayo.

Kanjani i-geometry

Kusukela iziza zaba isihloko yerenti, ubungako bawo futhi indawo ukudayiswa kanye ukulethwa kudingeka, kulinganiswa kuhlanganise by izibalo. Ngaphezu kwalokho, izibalo ezinjengalezi sasidingeka ekwakhiweni izakhiwo ezinkulu, kanye lokulinganisa umthamo izinto ezahlukene. Konke lokhu isibe izimfanelo zeminyaka ayizinkulungwane 3-4 edlule eGibhithe naseBhabhiloni art wezokwakha. Kuye kwaba empirically futhi iqoqo izibonelo abangamakhulu amaningana zokuxazulula izinkinga ezithile, ngaphandle kobufakazi obuphathekayo.

Ngenxa ehlelekile isayensi geometry athuthukile e lasendulo Greece. Njengoba emuva enkulungwaneni yesithathu BC leminyaka kwakukhona supply elikhulu amaqiniso nezindlela ubufakazi. Nokho, kwakukhona umsebenzi ukuba afingqe eqoqwe impahla sasivumela olunzulu weJiyomethri a. Wazama ukuxazulula uHippocrates Fedii nezinye izazi zefilosofi yamaGreki asendulo. Nokho, kunengqondo ukuphetha abaqinisekisiwe yesayensi uhlelo Kwakukhona kuphela mayelana 300 eminyakeni BC. e. ne kunyatheliswa incwadi ethi "Principia".

Wayengubani Euclid

IGrisi yasendulo wanika emhlabeni eziningi zefilosofi enkulu kanye nososayensi. Enye yalezi okungukuthi Euclid, owaba umsunguli Aleksandriya esikoleni wezibalo. Mayelana usosayensi cishe lutho waziwa. Eminye imithombo ibonisa ukuthi uyise abasha ikusasa geometry yesimanje bafundelwa esidumile kaPlato e Athens, wabuyela e-Alexandria, lapho aqhubeka khona ukufunda isayensi yezibalo kanye yokukhanya, kanye ubhala umculo. Edolobheni lakubo wamisa esikoleni, lapho, kanye abafundi futhi wadala yakhe edumile ethi, okuyinto iminyaka engaphezu kwezinkulungwane ezimbili luyisisekelo iyiphi ebhukwinitifundvo kundiza geometry futhi geometry okuqinile.

"Imisuka" of Euclid

The main futhi kuqala kunazo umsebenzi ehlelekile ku-geometry siqukethe amavolumu 13. Izincwadi zokuqala ezine eyesithupha ukubhekana indiza geometry, futhi 11, 12 nele-13 - geometry okuqinile. Njengoba for nye amavolumu, zingabantu abazinikele izibalo, okuyinto kusukela iphuzu Ngenxa postulates weJiyomethri.

Indima eyinhloko umsebenzi Euclid okwalandela ukuthuthukiswa zezibalo wesayensi ayikwazi overestimated. Esekhona yepapyrus uhlu eziningana original, kanye imibhalo yesandla WaseByzantium.

NgeNkathi Ephakathi, "Imisuka" of Euclid abangu wafunda ngokuyinhloko ama-Arabhu, ngubani ababheke omunye wemisebenzi enkulu ukucabanga futhi usosayensi waseDamaseku. Esikhathini eside kamuva, le misebenzi abanesifiso baseYurophu. Njengoba sekunama zokunyathelisa isayensi, kuhlanganise i-geometry Euclidean kwenze ukuba angabe esasazi kuphela abakhethiweyo. Ngemva uhlelo lokuqala ngo-1533, "Imisuka" ayatholakala kuyo yonke abafisa ukuba uqonde izwe, futhi kukhona abaningi njalo ngonyaka. Isidingo idale ukuthengisela, ngakho-ke kukholakala ukuthi lo msebenzi wesibili kakhulu efundwa phakathi izikhumbuzo endala ngemva kokuba ukulotshwa kweBhayibheli.

ezinye izici

I "Izakhi" uchaza imethrikhi izakhiwo ngakuthathu, ezingenalutho, angenamkhawulo futhi isotropic isikhala, okuyinto Ivame ukubizwa Euclidean. It ubhekwa enkundleni lapho kukhona izenzakalo of physics zasendulo kukaGalileo Newton.

Elementary into yejeyomethri, ngokuvumelana Euclid, iphuzu. Eyesibili umqondo obalulekile - infinity isikhala, okuyinto libhekene postulates yokuqala emithathu. Eyesine ezikhalweni nokulingana kwesokudla engeli. Ngokuphathelene postulate Euclid sika yesihlanu, khona-ke inquma izakhiwo kanye geometry ka Euclidean isikhala.

Ngokusho ososayensi, classical geometry uyise wadala incwadi ephelele, ukutadisha okuyinto ukubeka eceleni noma yikuphi ukungaqondi-material ngenxa yendlela isethulo sakhe. Ikakhulukazi, ngamunye umthamo "Imisuka" iqala kwencazelo imiqondo ihlangabezane ngokokuqala ngqá. Ikakhulukazi kusukela kweyokuqala Amakhasi we 1st ncwadi umfundi ethola ukuthi iphuzu, umugqa, iqonde nokunye. Sekukonke it has 23 izincazelo edingekayo ukuqonda main izinhlinzeko zoMthetho wamaZinga obekuxoxwa kule eliyisisekelo umsebenzi.

4 Axiom wokuqala futhi postulate Euclid

Ngemva kumbhali we "Imisuka" inikeza imiphumela zamukelwa ngaphandle kobufakazi. Wasezinikela lihlukana phakathi axioms futhi postulates. Iqembu lokuqala liqukethe izitatimende 11 Ngemva kwalokho lowo muntu aziwa intuitively. Ngokwesibonelo, Axiom 8th ukuthi wonke mkhulu ingxenye, futhi ngokuvumelana nenani ezimbili zokuqala, ngaphandle elilingana ezintathu, ilingana nomunye.

Ngaphezu kwalokho, 5 kubangela Euclid postulates. Ezine zokuqala ufunde kanje:

• ukusuka kunoma yiliphi iphuzu kunoma iyiphi enye, ungakwazi ukudweba umugqa oqondile;
• kusukela kunoma iyiphi sikhungo zonke engaba kungenzeka ukuchaza umbuthano;
• umugqa elinganiselwe ongalinikeza ngokuqhubekayo emgceni locondzile;
• zonke engele kwesokudla bayalingana.

postulate Euclid sika yesihlanu

Sekuyiminyaka engaphezu ezinkulungwaneni ezimbili, lesi sitatimende ngokuphindaphindiwe waba into ukunakwa zezibalo. Kodwa okokuqala, thina simazi kangcono okuqukethwe postulate Euclid sika yesihlanu. Ngakho, ekwakhiweni yesimanje kuzwakala sengathi indiza ezimpambanweni zomgwaqo ezimbili iqonde eyodwa emaceleni third-sum engele angaphakathi ngaphansi kuka-180 ° ke lezi imigqa ngenkathi ekuqhubekeni ngesinye ukuhlangabezana kuloluya hlangothi lapho le ubuningi (inani) engaphansi kuka-180 °.

postulate Euclid sika yesihlanu, kumagama elisetendeni emithonjeni ehlukene ngezindlela ezahlukene kusukela ekuqaleni wabangela ezemidlalo kanye nesifiso kwisi ku isigaba theorems ngokwakha ubufakazi umsindo. By endleleni, it is ngokuvamile kuphenduke ngenye inkulumo, eqinisweni, yasungulwa baqalekisiweyo futhi yaziwa nangokuthi Axiom ka Playfair. It sifundeka kanje: ebhanoyini ngokusebenzisa iphuzu ukuthi ingeyona elinikeziwe umugqa ozakuba yedwa nalowo aqonde umugqa ukufana phakathi kwalokhu.

ulimi

Njengoba sekushiwo, ososayensi abaningi baye bazama ezahlukene umqondo we postulate 5 Euclid. ukwakhiwa Ziningi sobala ngempela. Ngokwesibonelo:

• imigqa bebuthanela aphambana;
• kukhona okungenani eyodwa isikwele, okungukuthi, 4-square nge engele ezine kwesokudla;
• figure ngasinye kungenziwa kulingana owandiswayo;
• kukhona unxantathu nelincane, endaweni ezinqumela ezinkulu.

amaphutha

Euclidean geometry owayemkhulu kunabo bonke zezibalo imisebenzi endala futhi kuze kube 19 leminyaka, yilona elalingumakhonya mathematics. Naphezu kwakho konke lokhu, abanye amaphutha ayo Kuye kwaphawulwa ngisho bangesikhathi nombhali, futhi isazi lwesiGreki sakuqala, owayehlala kancane kamuva. Ikakhulu, ungeze entsha Archimedes Axiom, ezibizwa ngegama lakhe. Ithi kukhona n inamba, okuyinto n · [AB]> [CD] ngoba zonke izingxenye AB futhi CD.

Ngaphezu kwalokho, ososayensi baye bafuna ukunciphisa simiso axioms Euclidean futhi postulates. Ukuze wenze lokhu, bathatha abanye babo kusukela ukuphumula.

Ngakho wakwazi "balahle" we postulate wesi-4 nokulingana engeli kwesokudla. Ngaye, ubufakazi azinabo watholakala, ngakho wathuthela isigaba theorems.

Umlando 5 postulate endulo futhi ekuqaleni kweNkathi Ephakathi

I classical ekwakhiweni kwalesi sitatimende Euclidean geometry kubonakala ingasaphathwa sobala kunamanye ezine. Kuyinto leli qiniso zezibalo haunted.

A isikhubekiso ukuba postulate Euclid sika yesihlanu kwakunguShamhuti kakhulu incazelo impindamqondo lemigqa amabili kanye b, othi isamba ezimbili eyodwa amakhona okuyinto akhiwa empambana a futhi b ngengxenye yesithathu umugqa c, kuyinto 180 degrees.

Umzamo wokuqala ukuba kufakazelwe njengendlela ifayela echaza ifomu senziwa geometer yamaGreki asendulo Posidonius. Wasikisela cabanga okunye okucishe kufane nalokhu ngqo indiza ye iqoqo zonke amaphuzu equidistant kakhulu kulokho eqale iyikho. Nokho, ngisho lokhu akazange avumele Posidonius yokuthola ubufakazi 5th postulate.

Noma akusizanga futhi imizamo nezinye zezibalo, kuhlanganise ephakathi, ezifana Arabhu Ibn Korra futhi Khayyam. Okuwukuphela into osekuzuziwe - ukuvela entsha postulates, okungaba afakazelwe Isekelwe ahlukahlukene ezizathwini.

Esikhathini 18-19-th eminyaka

geometry Classical aqhubeka nentshisekelo kwi-mathematics ne ekhulwini le-18. Ikakhulukazi, ngokwanele eduze ubufakazi postulate umfuziselo ukuza French sezibalo A. Legendre. Wabhala incwadi evelele ebhukwinitifundvo "Imisuka geometry", okusho okungukuthi cishe iminyaka engu-150 kwaba uthishanhloko yokufundisa izibalo Russian Empire izikole. Kuyo usosayensi wanika ezintathu ongakhetha afakazele Euclidean Axiom okufanayo, kodwa zonke, ekugcineni kwahlaluka ukuthi ayilungile.

Ngasekuqaleni kwekhulu le-19, umqondo ukudala i-geometry non-Euclidean. Incazelo yokuqala uhlelo, ukuzimela postulate yesihlanu, wahola unjiniyela lempi J. Bolyai. Kepha lalethukile ayekutholile futhi akazange aphishekele umbono, bekholelwa akulungile. Impumelelo uye wahluleka ukufeza nesazi sezibalo esikhulu German Gauss.

ukuphumelela

Sekuyiminyaka engaphezu kwengu-2000 we postulate Euclid sika yesihlanu, ubufakazi okuyinto wazama ukuthola amakhulu ososayensi, wahlala inkinga inombolo eyodwa kwi-mathematics. Breakthrough wenza sezibalo Russian NI Lobachevsky. Kuye kwezwe yokuqala wakwazi ukuchaza izakhiwo esikhaleni sangempela, efakazela ukuthi geometry Euclidean "isebenza" kuphela endabeni ethile kwesimiso sakhe.

N. I. Lobachevsky ekuqaleni wehla indlela efanayo ukuthi ozakwabo bafaka abantu. Ngizama ukubakhumbuza wesi-5 postulate, yena kodwa wangaphumelela. Khona-ke usosayensi wenqaba ukumelwa Euclidean, owawuthi engeli isizumbulu unxantathu elilingana 180 degrees. Ngokulandelayo, wazama ukuveza lokhu okwashiwo ukungqubuzana ngathola kulotshwe izwi nezwi entsha postulate yesihlanu. Manje, babevuma ukuthi ukhona imigqa eziningana ukufana phakathi kwalokhu, futhi edabula iphuzu amanga ngaphandle kulo mugqa.

geometry entsha

Kwenza akukho mqondo ukuxoxa okwenzele okuningi zezibalo. Indima Euclid futhi Lobachevsky ithonya engaqhathaniswa phezu ukubunjwa nokuthuthukiswa kwezinhlangano Newton kanye physics Einstein. Ngesikhathi esifanayo, lo omusha, i-geometry ngokuphelele kungenzeka ukuba babheke umqondo isikhala, breaking kude indlela classical "bakwazi ukuzwisisa lokho kungasilimaza singenakulinganiswa kuphela." Kodwa le ndlela yokukhuluma kujayezwe isayensi izinkulungwane zeminyaka.

Ngeshwa, imibono Lobachevskii geometry akuzange kwamukelwe futhi aqondwe besikhathi sakhe. Ikakhulukazi, abafundi bakhe baqhubeka umsebenzi usosayensi, kanye nokuthuthukiswa geometry non-Euclidean esalibele amashumi eminyaka.

Ezinye izici inkolelo-mbono yokuziphendukela Lobachevsky

Ukuze siqonde geometry entsha, kubalulekile ukuba sicabangele infinity cosmic. Ngempela, kunzima ukucabanga ukuthi nobukhulu bendawo yonke yinani izikhala komugqa.

geometry Lobachevsky isetshenziselwa ukuchaza izikhala lwalugobile zidalwe izinkambu okudonsa zemithala. Wanika ukuba bamuke kulowo indlela ukunakwa zonke izibalo kuya "mayelana kwesokudla" isilinda, umbuthano, mbhoshongo, noma nanoma iyiphi inhlanganisela yalezi bobunjwa. Ukuze, isibonelo, eqinisweni, iplanethi yethu - akukho ibhola, futhi geoid, okungukuthi, sibalo okuyinto etholwe contouring ukunquma nentaba elingaphandle lithosphere (igobolondo kanzima) of the Earth ...

Ekuphileni okungokoqobo, kukhona analogue izikhala lwalugobile wendawo yonke, okuvumela ukuba ethule kungenzeka abe khona lemigqa eziningana parallel ngokudlula ngokusebenzisa iphuzu elifanayo. Ikakhulu, i-lwalugobile kobuso ezintathu izinhlobo, okuyinto abelwe by Italian geometer Beltrami futhi okuthiwa E. pseudosphere.

ukuqhubeka imfundiso yokuziphendukela Lobachevsky

Ezivelele Russian akuyena kuphela akufanele aphonsele absoluteness ka-geometry Euclidean. Ikakhulukazi, sezibalo Riemann ngo-1854 phambili umqondo kungenzeka abe khona izikhala ka-zero, ugobile emihle nemibi. Lokhu kwakusho ukuthi ungakha isibalo esingapheliyo amajiyomethri ezahlukene ze-non-classic.

On isikhundla Riemann sika, oye wacwaninga ikakhulu isikhala nge ugobile HIV, postulate 5 Euclid umsindo ngempela ngokungalindelekile. Ngokusho imibono yakhe, ngokusebenzisa iphuzu ngaphandle umugqa inikezwe alikwazi ukuphatha parallel umugqa kule.

Okuhluke kakhulu kunjalo izikhala zero, ugobile ezimbi futhi omuhle theory Klein sika. Ikakhulukazi, ukuthi icala lokuqala, bachazwa yi geometry parabolic, icala lakhe ikakhulukazi a classic, kwesibili - kuncike imibono Lobachevsky, kanti eyesithathu - uhambisane nalabo abachazwa yila Riemann.

Ukulandela ukushicilelwa Alberta Eynshteyna Awetiyori ye-Relativity, ukuhanjiswa izikhala ezinjalo zihambisana idatha acabangele ukhona kuncikene nokushintsha izilinganiso ezine - isisindo, amandla, isivinini kanye nesikhathi.

practice

Uma uya umbono womuntu isikhala, ngaphakathi orbit eMhlabeni ngoba unxantathu enkulu lemali elikhulu kunawo kungenzeka ukuphambuka kungenzeka engele ingaphakathi 180 degrees Classic kuyoba engu amane kuphela yomzuzwana. Lokhu value kakusekho amakhono homo Sapiens, ngakho "yasemhlabeni" funa kuba geometry Euclidean.

It uhlala balinde kuze izimo zidalwe ezivumela ukuthola idatha zokuhlola ukuqinisekisa noma ukuphikisa imfundiso yokuziphendukela N. Lobachevsky futhi Riemann yonkana galaxy.

Manje uyazi ukuthi usho postulate Euclid sika yesihlanu nomlando wayo, okuyinto ezifundisayo kakhulu, futhi sisivumela umkhondo ukuvela umqondo womuntu past 2300 iminyaka.