Postulate shanaad Euclid ee: ereyada

Waxaa la rumeysan yahay in ay jiraan 10 000 oo sano ka hor, ilbaxnimada ugu horeysay ee aadanaha. Marka la barbar dhigo da'da dhulkeenna, taas oo, sida ay saynisyahano, wuxuu ku saabsan yahay 4,54 milyan oo sano jir ah, tani waxa keliya daqiiqad kooban. Waayo, kanu "daqiiqad" Dadka ayaa u boodboodi weyn ka qalabka dhagax heer hoose ah si ay u pride interplanetary. Isagu ma uu noqon doono in, haddii muddo la joogaba caalamka ayaa la dhalan lahaa hanad ka, sayniska hore ugu sii socoto. iyaga ka mid ah, dabcan, waxaa loola jeedaa Euclid. shuqulladiisa noqday aasaaska iyo wadadii awood leh ee horumarka ah ee xisaabta oo casri ah.

Maqaalkani waxa uu ku saabsan yahay postulate shanaad Euclid oo ay taariikhda.

Sidee joomateri ee

Tan iyo sirqoollada dalka hoos jiray kirada, ay size iyo bedka sale iyo dhalmada waxay u baahan yihiin in la qiyaasay, oo ay ku jiraan by xisaabinta. Intaas waxaa sii dheer, xisaabinta sida ay noqdaan loo baahan yahay in dhismaha dhismayaasha oo baaxad weyn, iyo sidoo kale cabbiraadda mugga waxyaabaha kala duwan. Waxaas oo dhan waxa uu noqday shuruudaha 3-4 kun oo sano ka hor ee Masar oo Baabuloon sahan tahay. Waxa ay siman ahayd oo waa a collection of dhowr boqol oo tusaale u ah xalinta dhibaatooyinka gaarka ah, iyada oo aan caddayn kasta.

Sida sayniska nidaamsan joomatari horumariyo Giriigii hore. Goor hore BC qarnigii saddexaad waxaa jiray sahayda badan oo ah xaqiiqooyinka iyo hababka caddayn. Si kastaba ha ahaatee, waxaa ka kacay dhibaatada ku filan ballaaran si ay u soo koobaan wax ka ururiyay joomateri. Waxay isku dayeen in ay xaliyaan Hippocrates Fedii iyo faylosuufiinta kale Giriigga ee hore. Si kastaba ha ahaatee, macquul xaqiijin nidaamka cilmiyaysan waxaa jiray oo kaliya oo ku saabsan 300 sano BC. e. la daabaco oo ka mid ah "Principia".

Kuwaas oo ahaa Euclid

Baydka Greece siiyey dunida badan oo ka mid ah faylosuufiinta weyn iyo aqoonyahanno. Mid ka mid ah kuwan waa Euclid, oo noqday aasaasihii dugsiga reer Iskanderiya ahaa ee xisaabta. About saynisyahan ah ficil ahaan waxba loo yaqaan. Ilo Qaar ka mid ah ayaa tilmaamaya in aabbihiis mustaqbalka dhallinyarada joomatari casriga bartay dugsiga caanka ah ee Plato ee Athens, ka dibna si Alexandria, halkaas oo uu sii waday in ay ka barato maaddooyinka xisaabta iyo optics, iyo sidoo kale music curinta soo laabtay. In magaalada hooyo ayuu asaasay dugsiga, halkaas oo, wada jir ah ula ardayda iyo abuuray shuqulkiisa caanka ah, kuwaas oo in ka badan laba kun oo sano waa aasaas u ah buugaagta wax on geometry diyaarad iyo joomatariga adag.

"Qaybaha" ee Euclid

The shaqo nidaamsan ugu weyn iyo kan ugu horeysay on geometry ka kooban yahay 13 Muga. joomatariga adag - The buugaagta ugu horeysay afar iyo lixaad leh geometry diyaarad, iyo 11-kii, 12-kii iyo 13-kii ka qabtaan. Sida ee Muga kale, iyagu waa u heelan yihiin inay xisaabta, taas oo ah ka barta of view of postulates joomateri.

Doorka shaqada ugu weyn ee Euclid horumarinta xiga ee cilmiga xisaabta lama quudhsan karin. liisaska Extant caw dhowr ah oo asalka ah, iyo sidoo kale qoraal gacmeedyada Byzantine.

In qarniyadii dhexe, "Qaybaha" ee Euclid ayaa la bartay horrayn by baadiyaha ah, kuwaas oo iyaga ka mid ah, shuqullada weyn oo fikirka ah aadanaha iyo saynisyahan Dimishaq ka fiirsan. Inta badan dambe xagga shuqullada, kuwaas oo xiiseynaya Yurub. Iyada oo agaa of daabacaadda sayniska, oo ay ku jiraan geometry Euclidean mar dambe lama yaqaan oo kaliya in ay la doortay. Ka dib markii nuqulka kowaad ee 1533. "Qaybaha" ayaa diyaar u ah oo raba in la fahmo dunida oo dhan, oo waxaa jira wax dheeraad ah oo dheeraad ah sannad kasta. Dalabka dhaliyey in ay sahayda, sidaas darteed waxaa la rumeysan yahay in shaqadan waa kii labaad ee ugu ballaaran ka mid ah taxadiri Qarniyadii hore ka dib markii Kitaabka Quduuska ah akhriyo.

Tilmaamo qaar ka mid ah

The "Qaybaha" qeexayaa guryaha ton oo meel bannaan oo saddex geesood ah, oo madhan, limitless iyo isotropic, kaas oo sida caadiga ah loo yaqaan Euclidean. Waxaa la arkaa in ay saaxadda ah halkaas oo waxaa jira ifafaale of physics classical of Galileo oo Newton.

wax joomatari Hoose, sida ay Euclid, waa barta. Ra'yiga muhiim labaad - xad ee bannaan, taas oo ah waxa lagu gartaa saddexda postulates ugu horeysay. oo kii afraadna wuxuu ku saabsan sinnaanta ee xagal toosan. Iyadoo la tixgelinayo postulate shanaad Euclid ee, ka dibna waxa ay go'aamiso guryaha iyo joomatariga ee meel Euclidean.

Sida laga soo xigtay saynisyahano, aabbihiis geometry classical abuuray buugaagta kaamil ah, daraasadda of taas oo ka horjoogsanaya in is fahan mid ka mid ah waxyaabaha la, sababtoo ah sida uu soo bandhigayo. Gaar ahaan, mugga kasta oo ka mid ah "Qaybaha" bilaabmaa qeexidda fikradaha ay kala kulantay markii ugu horeysay. Gaar ahaan, ka bogagga ugu horreeya ee buugga 1aad akhristaha barto in hal dhibic, line, si toos ah iyo wixii la mid ah. Guud ahaan waxa ay leedahay 23 qeexitaan looga baahan yahay fahanka oo ka mid ah qodobada ugu muhiimsan ee wax lagu soo bandhigay this shaqada aasaasiga ah.

4 cadayn ugu horeysay oo postulate Euclid

Ka dib markii qoraa oo ka mid ah "Qaybaha" waxay bixisaa natiijada in la aqbalo oo aan caddayn. inuu kala qaybinaya galay axioms iyo postulates. Kooxdu waxay ugu horeysay waxay ka kooban tahay 11 statements in ninka aad maskax ahaan loo yaqaan. Tusaale ahaan, cadayn 8aad oo dhan ka wada weyn yahay qayb ka mid ah, iyo sida ay labada tiro marka hore, marka laga reebo siman saddex, loo siman yahay si kasta oo kale.

Intaas waxaa sii dheer, 5 sababa Euclid postulates. afar waxay marka hore la akhriyo sida soo socota:

• ka dhibic kasta oo kale oo kasta oo, waxaad sawiri kartaa xariiq toosan,
• xarunta mid ka mid ah gacan kasta oo suurto gal ah si ay u sharxaan goobo;
• line kooban kordhin karaa si joogto ah xariiq toosan,
• oo dhan xaglo xaq u siman yihiin.

postulate shanaad Euclid ee

In ka badan laba tobankii, bayaankan si joogta ah u noqday shayga of dareenka of xisaabyahannada. Laakiin marka hore, waxaan bartaan content ee postulate shanaad Euclid ee. Sidaas daraaddeed, in samaynta casriga ah waxa ay u muuqataa sidii diyaarad isgoyska laba toosan hal dhinac-wadarta saddexaad ee xaglo gudaha ka yar tahay 180 °, ka dibna khadadka halka si degdeg ah sii socdo ama ka dib la kulmi dhinac ku jira oo tiro this (lacagta) ka yar tahay 180 °.

postulate shanaad Euclid ee, taas oo ah erayada ku ilo kala duwan waa kala duwan bilowgaba sababay isboortiga iyo rabto in aad u turjumi category ee aragti by dhismaha Xujo dhawaaqa. By jidka, waxa badanaa ku badalay hadal kale, dhab ahaantii, Abuurtay habaaran oo sidoo kale loo yaqaan cadayn ee Playfair. Waxay u akhriya sida soo socota: diyaarad iyada oo hal dhibic oo aan ka tirsan line a siiyey qaban karo mid ka mid ah oo kaliya hal barbar line si toos ah u this.

afka

Sida hore u soo sheegnay, saynisyahano badan ayaa isku dayay kala duwan muujiyaan fikradda ah postulate 5aad ee Euclid. daawooyinka badan yihiin arrin cad. Tusaale ahaan:

• khadadka wada midaysan;
• waxaa jira ugu yaraan hal leydi, in uu yahay, 4-square afar xagal toosan;
• tiradaasi kasta la saami la kordhin karaa,
• waxaa jira saddex xagalka ah wax, meesha aan macquul ahayn oo waaweyn.

ceebaha

joomatariga Euclidean ahaa shuqullada weyn xisaabeed ee Qarniyadii hore iyo ilaa qarnigii 19aad, waxa boqor ka doodin in xisaabta. Iyadoo ay taasi jirto, qaar ka mid ah ceebaha ay la ogaaday xataa saffarro qoraaga, iyo aqoonyahan Giriigga ee hore, kaasoo xoogaa ku noolaa ka dib. Gaar ahaan, waxa uu intaa ku daray a cadayn cusub Archimedes, la odhan jiray ka dib. Waxa uu leeyahay waxaa jira n abyoonaha ah, taas oo n waa · [AB]> [CD] dhammaan qaybaha kala duwan ee AB iyo CD.

Intaa waxaa dheer, culumadu waxay dooneen si loo yareeyo habka of axioms Euclidean iyo postulates. Si arrintan loo sameeyo, waxay qaar ka mid ah inta kale ka soo qaadeen.

Sidaas waxaa u suurtagashay in ay "takhaluso" ee postulate 4aad ee sinaanta ee xagal toosan. Waayo, isaga, xujo adag laga helay, sidaas darteed wuxuu u dhaqaaqay category ee aragti.

Taariikhda 5 postulate ee Qarniyadii hore iyo qarniyadii dhexe hore

dejinta The classical of this hadal geometry Euclidean u muuqataa badan ka yar cad ka badan afar kale. Waa xaqiiqda xisaabyahannada dabataagan.

block ayaa lagu turunturoodo, waayo, postulate shanaad Euclidean ahaa qeexidda socotaa labada khadadka a iyo b, oo sheegaya in wadarta labada xaglood gooni taas oo loo sameeyay by isgoyska of a iyo b saddexaad oo isku xigta line c, si siman u 180 digrii.

Isku daygii ugu horeysay si ay u caddeeyaan sida Aragtida ahayd by geometer ee qadiimiga ah ee Giriiga Posidonius. Wuxuu soo jeediyay in la tixgeliyo isku midka ah si toos ah diyaarad of set oo dhan dhibcood in ay yihiin meelsha asalka ah. Si kastaba ha ahaatee, xataa waxaas uma ay oggolaan Posidonius heli caddayn postulate 5aad.

Nor ay u ma anfacdo iyo isku day ah xisaabyahannada kale, oo ay ku jiraan Dr Makumbe, sida ibn Carbeeda Korra iyo Khayyam. Waxa kaliya oo uu soo gaaray - bixitaanka postulates cusub, taas oo lagu caddayn karo oo ku salaysan fikrado kala duwan.

In qarniyadii 18-19-th

joomatariga classical sii waday in ay xiiseynayaan in xisaabta iyo qarnigii 18aad. Gaar ahaan, ku filan u dhow postulate ku caddayn barbar iman kara xisaabyahan Faransiis A. Legendre. Waxa uu ku qoray buugga aad u fiican "Qaybaha joomatari", taas oo ku saabsan 150 sano ahaa maamulaha barayay xisaabta ee dugsiyada Ruush Empire. In waxa saynisyahan siiyey saddex doorasho cadeeyo cadayn ah Euclidean isku midka ah, laakiin oo dhan ay soo baxday in aan sax ahayn.

By bilawgii qarnigii 19aad, fikradda ah abuuraya a geometry non-Euclidean. description koowaad ee nidaamka, madax banaan postulate shanaad, hogaaminayo injineer ciidamada J. Bolyai. Laakiin wuu cabsi uu helay oo mana ay ka daba fikradda, Mu'minaadka ah u qaldan. Guusha ayaa aan awoodin in ay gaaraan iyo xisaab weyn Jarmal Gauss.

horumar degdeg ah

In ka badan 2000 sano ee postulate shanaad Euclid ee, caddeynta ah oo isku dayay in la helo boqolaal saynisyahano, ay weli tahay dhibaato koowaad ee xisaabta. Breakthrough dhigay xisaab Ruush NI Lobachevsky. isaga u adduunka ee ugu horeeyay ee u suurtagashay in ay sharaxaad ka sifooyinka meel dhabta ah, isagoo caddaynaya inuu geometry Euclidean "shaqeeya" oo kaliya in kiiska gaar ah oo uu nidaamka.

N. I. Lobachevsky hore hoos ugu tegey, Jidka la mid ah sida in of saaxiibadii. Isku dayga in la caddeeyo postulate 5aad, uusan ku guulaysteen. Markaas saynisyahan diiday matalaad Euclidean, sida laga soo xigtay oo ah xaglo wadarta xagal si siman u 180 digrii. Next, inuu isku dayay inuu cadeeyo caddaynta this by khilaaf iyo helay ereyada cusub postulate shanaad. Haddaba, ayuu qirtay jiritaanka dhowr khadadka isku midka ah in ay this, iyo marayay hal dhibic ka been ka baxsan line this.

joomatariga cusub

Waxaa macno lahayn in ay ka munaaqashoodaan kii sameeyey ka badan xisaabta. Doorka Euclid iyo Lobachevsky saamayn u dhiganta on the formation iyo horumarinta Newton iyo physics Einstein ee. Isla mar ahaantaana, cusub, joomateri waadaxa waxaa suurtagal ah in ay fikirin fikradda ah ee meel, ka go'ay habka classical iska "fahmi kartaa oo keliya waxa la qiyaasi karin." Laakiin hab noocan ah ku dhaqma sayniska kumanaan sanadood.

Nasiib darro, fikradaha joomatari Lobachevskii aan la aqbali iyo fahamsan yahay by saffarro uu. Gaar ahaan, ardayda lama sii shaqo ee cilmiga, iyo horumarinta geometry non-Euclidean ayaa dib dhowr sano ee.

Tilmaamo Qaar ka mid ah aragtida Lobachevskii ah

Si loo fahmo geometry cusub, waxaa lagama maarmaan ah in la tixgeliyo xad la'aan ah runtan. Indeed, waa ay adag tahay in la qiyaaso in waasicinnay ee caalamka waa wadarta meelaha toosan.

joomatariga Lobachevsky waxaa loo isticmaalaa in lagu qeexo meelaha qalooca in loo abuuray by beerihii gravitational of falagyada. Waxay ogol yahay in ay ka habka of dareenka tirooyinka oo dhan tago in ay "ku saabsan xaq" dhululubo, goobada, Ahraamta, ama isku mid ka mid ah qaababka kuwan. Waayo, tusaale ahaan, in dhab, dhulkeenna - kubada lahayn, iyo geoid ah, ie, tirada a kaas oo la helay contouring dusha sare ee lithosphere (qolof adag) ee Dhulka ...

Nolosha dhabta ah, waxaa kale oo jira analogues meelaha qalooca ee caalamka, kaas oo u ogolaanaya inay soo bandhigto waxaa macquul ah jiritaanka dhowr khadadka isku midka ah ee ku dhaco iyada oo hal dhibic ka mid ah. Gaar ahaan, tani waxay dusha qalooca oo ka mid ah saddex nooc oo loo qoondeeyey geometer Talyaani Beltrami oo la odhan jiray E. pseudosphere.

horumarinta dheeraad ah oo aragtida ah ee Lobachevsky

Heer Ruush ma ahaa qofka kaliya ee aan u malaynay absoluteness joomatari Euclidean. Gaar ahaan, Riemann xisaab ee 1854 ee horey fikradda ah waxaa macquul ah jiritaanka meelaha of eber, dhaf togan iyo kuwa taban. Taasi waxay keentay in aad ka abuuri karaan tiro aan la koobi karayn of geometries non-classical kala duwan.

On booska Riemann ee, kaasoo bartay inta meel la dhaf wanaagsan, postulate 5aad ee Euclid codadka arrin lama filaan ah. Sida ay fikradaha uu, iyada oo hal dhibic ka baxsan line a siiyey ma qaban karto wax kasta oo barbar line in this.

kiiska la eber meelaha, dhaf xun ama fiican oo ka mid ah aragtida Klein ayaa yara duwan yahay. Gaar ahaan, in qofkii ugu horreeyey ee ay ku tilmaamay by geometry saxan a, kiis gaar ah taas oo ku classical, kii labaadna wuxuu ahaa - adeeca fikrado Lobachevskian, iyo kii saddexaad - waafaqsan kuwa ku tilmaamay by Riemann.

Ka dib markii la daabaco ee Alberta Eynshteyna Aragtida of Relativity, soo gudbinta of meelaha sida xogta in ay tixgeliyaan jiritaanka afar cabbir isku xidhan oo la beddelo - miisaanka, awood, xawaaraha iyo waqtiga.

ku dhaqanka

Haddii aad tagto aragtida aadanaha ee meel gudahood kastana falagiisuu dhex Earth ee Rafaa xagalka ugu weyn ee suurto galka ah ee weecasho suurto galka ah ee wadarta xaglo gudaha of 180 digrii samaynaysaa classical afar millionths ee labaad ah. Qiimaha Tani waa ka baxsan awoodaha ee sapiens homo, sidaas "dunida" dalabka waa joomateri Euclidean.

Waxaa weli in ay sugaan illaa shuruudaha loo abuuray oo u oggolaan in la helo xogta tijaabo ah si loo xaqiijiyo ama ku doodeen aragtida ah ee N. Lobachevsky iyo Riemann guud ahaan Galaxy ah.

Hadda aad ogtahay in leeyahay postulate shanaad Euclid iyo taariikhda, taas oo ah mid aad u Waano, oo noo ogolaanaya si loo raad raaco horumar ah ee maskaxda aadanaha ka badan 2300 sano ee la soo dhaafay.