Imibuthano ye-Euler: izibonelo namathuba

Izibalo ziyisayensi engabonakali, uma sisuka emibhalweni yokuqala. Ngakho-ke, kwi-apula yama-apula amathathu ungabonakala ngokucacile imisebenzi eyisisekelo ehambisana nezibalo, kodwa njengoba indiza yomsebenzi ikhula, lezi zinto azikwazi ngokwanele. Ukhona oke wazama ukukhombisa ukusebenza kumaqoqo angapheli kuma-apula? Lokho nje iphuzu, ukuthi cha. Njengoba kunzima kakhulu ukucabanga ukuthi izibalo zisebenza ezikwahlulelweni zayo, kube nzima ukuthi kubonakale kuyinkimbinkimbi yokubona, okuzokwenziwa ukuze kube lula ukuqonda. Kodwa-ke, ngenjabulo yabafundi besimanje nesayensi njengamanje, imibuthano ye-Euler isuselwe, izibonelo kanye namathuba esizoxoxa ngazo ngezansi.

Umlando omncane

Ngo-Ephreli 17, 1707, izwe lanikeza isayensi kuLeonhard Euler, ososayensi ophawulekayo owenzela izibalo, i-physics, ekwakhiweni kwemikhumbi ngisho nangomqondo wezingoma akuzange kuvezwe. Imisebenzi yakhe iyabonakala futhi iyadingeka kulolu suku emhlabeni wonke, naphezu kokuthi isayensi ayimi. Okuthakazelisayo ikakhulukazi ukuthi uMnu. Euler uthathe ingxenye eqondile ekwakheni isikole saseRussia semathematika aphezulu, ikakhulukazi njengoba ephindelela kabili ezweni lethu ngentando yesikhathi esizayo. Usosayensi unekhono eliyingqayizivele lokwakha ama-algorithms ebalazweni lakhe, ukusika konke okungadingekile nokunyuka kusuka jikelele kuya esikhathini esincane kunazo zonke. Ngeke sibhale konke okuhle kwakhe, ngoba kuzothatha isikhathi esiningi, bese uphendukela ngokuqondile esihlokweni salesi sihloko. Nguye owayephakamisile ukusebenzisa ukumelela okucacile kokusebenza kumaqoqo. Imibuthano ye-Euler isinqumo sanoma yikuphi, ngisho nomsebenzi onzima kakhulu, singaboniswa ngokubonakalayo.

Kuyini okuyisisekelo?

Ngokwenzayo, u- Euler ubuthana, uhlelo oluboniswa ngezansi, lungasetshenziswa kuphela kwizibalo, ngoba imiqondo "yokusetha" ayitholakali kuphela kulolu luleko. Ngakho, ziyasebenza ngempumelelo ekuphathweni.

Umdwebo ongenhla ukhombisa ubudlelwano bama-sets A (izinombolo ezingenangqondo), B (izinamba ezingenangqondo) no-C (izinombolo zemvelo). Imibuthano ibonisa ukuthi isethi C ifakiwe kusetjenziswa B, kanti isethi A ayifaki nayo nganoma iyiphi indlela. Isibonelo esilula, kepha uchaza ngokucacile ukuthi "ukusebenzisana kwamasethingi" akuphi, okungabonakali kakhulu ekuqhathaniseni kwangempela, uma kungenxa yokuthi bangaphasi.

I-Algebra ye-logic

Le ndawo ye-logic yezibalo isebenza ngezitatimende ezingaba zingamanga futhi zingamanga. Isibonelo, kusukela ephansi: inombolo 625 ihlukaniswe ngu-25, inombolo 625 ihlukaniswe ngu-5, inombolo 625 ilula. Isitatimende sokuqala nesesibili siyiqiniso, kuyilapho leli qembu lingamanga. Yiqiniso, ekusebenzeni konke kunzima kakhulu, kodwa okusemqoka kuboniswa ngokucacile. Futhi, impela imibuthano ye-Euler iphinde ihileleke esixazululweni, izibonelo ngokusetshenziswa kwazo zilula kakhulu futhi zibonakala zingenandaba.

Inkolelo encane:

• Vumela i-A no-B ikhona futhi ingabi nalutho, ngakho-ke imisebenzi elandelayo ye-intersection, inyunyana kanye nokuhlukunyezwa kuchazwa.
• I-intersection yamasethingi A no-B aqukethe izinto ezihambisana naso kokubili i-A ne-B.
• Ukubambisana kwamasethingi A neB kubandakanya izinto ezise-set A noma kwi-set B.
• Ukulahla isethi A kuyisethi esakhiwe ngezinto ezingekho zeqoqo A.

Konke lokhu kuphinda kubonise imibuthano ka-Euler enengqondo, ngoba ngosizo lwabo inkinga ngayinye, kungakhathaliseki ukuthi yinkimbinkimbi kangakanani, iba sobala futhi iyabonakala.

Ama-algumra we-logic

Ake sithi 1 no-0 zikhona futhi zichazwe kusetjenziswa A, bese:

• Ukwehluleka kokulahlwa kwe-A kuyisethi A;
• Ukubambisana kwe-A isethi nge-non-A kungu-1;
• Iminyango ye-A isethi ene-1 ingu-1;
• Ukubambisana kwe-A ngokwakho kuyisethi A;
• Ukubambisana kwe-A isethi ene-0 kuyisethi A;
• I-intersection ye-A ene-A ayi-0;
• I-intersection ye-A ngokwayo yi-A isethi;
• I-intersection ye-A ene-0 ngu-0;
• I-intersection ye-A isethi ene-1 yisethi A.

Impahla eyisisekelo ye-Algebra ye-Logic

Ake sithi i-A ne-B ikhona futhi ayinalutho, ke:

• Ngokwesigatshana kanye neminyango yamasethingi A no-B, umthetho ohambayo usebenza;
• Ngendlela yokuhlangana nokuhlanganiswa kwamasethingi A no-B, umthetho wokuhlanganisa usebenza;
• Ngokwesigaba sokuhlangana nokuhlanganiswa kwamasethingi A no-B, umthetho wokusabalalisa usebenza;
• Ukunganaki kwe-intersection yamasethingi A no-B kuyindlela yokunciphisa izintambo A no-B;
• Ukwehluleka kwezinyunyana zamasethingi A neB kubumbano lwezinhlupho ze-A no-B.

Ngezansi sibonisa imibuthano ka-Euler, izibonelo ze-intersection kanye nenyunyana yamasethingi A, B no-C.

Amathemba

Umsebenzi kaLeonard Euler ucatshangelwa ukuthi uyisisekelo semathematika zanamuhla, kodwa manje asetshenziswe ngempumelelo emkhakheni wezenzo zomuntu ezivele zamuva, ukuthatha okungenani ukubusa kwezinkampani: imibuthano ye-Euler, izibonelo kanye namagrafu kuchaza izindlela zokuthuthukiswa kwamamodeli, kungakhathaliseki ukuthi isiRussia noma isiNgisi noma isiNgisi .