Eratosthenes sieve ohlelweni

Izibalo isayensi eye yabonakala iminyaka eyizinkulungwane eziningana futhi isetshenziselwa ukusetshenziswa kakade eGrisi Yamandulo. Ngesikhathi esifanayo, izazi eziningi zemfundo ezazihlala ngaleso sikhathi zenza izinto ezitholakale zibe zikhulu futhi ziqhakazile, kodwa ukuqashelwa kwangempela kwamukelwa emakhulwini eminyaka kamuva, lapho ubuchwepheshe bwenza ukuthi kube lula ukuqonda ukukwazi okuphelele kokufundwa kwabafundi base-ancient arithmeticians. Kumele kuqashelwe ukuthi zonke izibalo ema-eras ezikude zenziwa "engqondweni" noma ziqukethe amarekhodi amakhulu amazinga okubala. Omunye wezazi ezidume kakhulu zamaGrisi kwakungu-Eratosthenes, obizwa ngokuyimfihlo ngokuthi umkhulu-omkhulu wezinhlelo. Ngokufika kwe-computer yesayensi, kwakuyizibalo zakhe, izinkomba kanye nezinkomba ezivame ukuguqulwa zibe "izilimi" zekhompyutha. Esigabeni semathematics kwakukhona ukutholakala okuthakazelisayo okuncane, kodwa okuvame kakhulu kwakuyi-sieve ye-Eratosthenes, okusiza ukuba uthole ngokushesha inomboro eyinhloko kusukela ngokulandelana okulandisiwe.

I-biography yososayensi

Naphezu kokuthi yonke imisebenzi yocwaningo yenzeke endaweni yaseGrisi lasendulo, ubuhlakani besikhathi esizayo bezalelwa e-Afrika ngekhulu lesithathu BC. Usosayensi wayefunda emadolobheni amakhulu kunawo wonke eGrisi, lapho ahlala khona njalo. Othisha bakhe babeyizimbongi ezidumile, izazi zefilosofi kanye nograma ngaleso sikhathi. Ngenxa yentuthuko eminingi kanye nenhlonipho kumbuthano wabantu abafana nomqondo, i-theorist ehlakaniphile imenywa esikhundleni se-librarian yase-Aleksandriya, lapho ekhonza khona kuze kube sekufeni kwakhe, edala ukuqhuma nokufunda okungenakwenzeka ngaleso sikhathi ezinkambeni ezihlukahlukene, kuhlanganise nesihluthulelo se-Eratosthenes. Isazi sesikhathi esizayo - i-Archimedes evelele - yakhuluma ngaye kuphela ngamazwi ahlabayo futhi yazinikela nomsebenzi wayo ohlukile.

Izimpumelelo

Isici esiyinhloko sosayense yasendulo kubhekwa njengendlela ehlukahlukene yokuqondisa iziqondiso. Cishe zonke izigaba, uthola imiphumela evelele. I-Philosophy, izinkondlo, izibalo, isayensi yezinkanyezi, umculo, philology, geography - ngenxa yokuzibonakalisa okungafani kwendawo yonke ekufuneni ulwazi, i-theorist yathola isiteketiso sePentatl, ngokubambisana nemidlalo yonke. Yiqiniso, akazange abe mkhulu kwenye yezindawo ezifundwayo, kepha kuzo zonke zazo kwakungenzeka ukufeza imiphumela emihle. Lokhu kuboniswa yizingcezu ezisekhona zemisebenzi kanye nezifundo zakhe. Naphezu kokuthola isithunzi somuntu ophila ngesikhathi sakhe, usosayensi waba nomthelela omkhulu emlandweni wezibalo, kanti isihluthulelo se-Eratosthenes esinamanani ambalwa awaziwa kahle saba yinto eyodwa ne-geometric edumile kanye nokutholakala kwe-arithmetic.

Umlando wegama nemininingwane yendawo

Ezikhathini zasendulo, wonke amarekhodi, kufaka phakathi izibalo zezibalo zenziwe ngamacwecwe akhethekile we-wax. Ngakho-ke, ngokubala kwe-algebraic kanye ne-arithmetical nature, ikakhulukazi ngenkathi kususwa izibalo ezilandelanayo, ososayensi "bawagcoba" ngezinto zokubhala. Ngemuva kwayo yonke imisebenzi, ithebhulethi yayifana nento yezindlu zasendlini, okwakubizwa ngalo isifundo - isihluthulelo se-Eratosthenes . Isisusa sokutholakala kwakungumqondo wekhono mayelana nokuthola izinombolo eziyinhloko emgqeni wemvelo. Umsebenzi wahlala ezinyangeni ezimbalwa, kuze kube yilapho umphumela wokugcina ufeziwe. Ekhulwini lesithathu BC kwaba impumelelo yangempela.

Iyini i-algorithm?

Indlela esheshayo yokuthola zonke izinombolo eziyinhloko emgqeni wemvelo uye waba nesithakazelo ososayensi kusukela esikhathini esidlule. Phela, abanakho ukulandelana okuqinile futhi bahlelwe ngendlela ehlelekile ngokomzimba. Okwamanje, ochwepheshe baye baqaphela futhi bafunde indlela yokukhiqiza izibalo ezidingekayo masinyane. Kulokhu basiza i-algorithm elula - isihlungo se-Eratosthenes. Ubuhlakani basendulo bawuvula ngezigaba eziningana:

• Thatha uchungechunge lwemvelo kusuka komunye kuya kunoma iyiphi inamba (i-universal term N). Kumele kuqashelwe ukuthi eminkulungwaneni embalwa eyedlule i-unit yayibhekwa njengenombolo yokuqala. Manje ubhekiselwa ezinhlotsheni ezikhethekile ezingenayo incazelo eqondile.
• Ngaphezu kwalokho, zonke izinombolo ezihlukaniswa yi-deuce zisusiwe.
• Khona-ke owokuqala kokusele (kulokhu, kathathu) kuthathwa futhi zonke izinombolo ezihlukaniswe kulo zizosuswa.
• Ukubala kuyaqhubeka nenombolo yokugcina ngokulandelana.
• Uchungechunge olusele luzoqukatha izinkomba ezilula kuphela.

Lolu khetho luye lwacatshangwa ukuthi lusebenza kuphela, futhi lapho kufika ochwepheshe bezesayensi bekhompyutha bakwazi ukwenza izibalo zokulandelana okunzima kakhulu. Ngisho nobuchwepheshe obusha, isihluthulelo sika-Eratosthenes yiyona mbono ebaluleke kakhulu yezibalo.

Izilimi zokuhlela emkhakheni wezibalo ze-arithmetic

Ubuchwepheshe, amakhompiyutha kanye ne-informatics bavumela izibalo ukuba zifunde izinkolelo zama-algebra ukuze zifake isigaba esisha ekuthuthukiseni isayensi. Okokuqala, besebenzisa ithuba eliyingqayizivele, baqala ukuhlanganisa izibalo ezaziwa kakhulu ze-arithmetic kanye ne-geometric zibe izinhlelo. Esinye sezilimi ezithandwa kakhulu kwi-electronic-computational ngaleso sikhathi kwaba, kubalwa ukubalwa kwe-algorithm yesihlungo u-Eratosthenes, uPascal. Ngosizo lwaso emasekhondini ambalwa kwakungenzeka ukuthola izinombolo eziyinhloko ngokulandelana kwezinombolo zemvelo okwesikhathi eside zingenakutholakali noma zibalwa ngamarekhodi amakhulu, kuthatha isikhathi eside. Ngenxa yalokho, isisekelo esiwusizo sekhono elisha sesithuthukisiwe inguqulo yokutholakala yasendulo kanye namathuba okusebenza angenamkhawulo wokubala.

Sebenzisa kuma-Olympiad yanamuhla ku-Informatics

Okwamanje, umncintiswano wabafundi ezifundweni ezihlukahlukene uthola ukuthandwa futhi. Ukuncoma kanye nabanqobile izenzakalo ezinjalo kufinyelela izinga elisha lemfundo futhi bangathola amathemba omuhle emisebenzini eyengeziwe, kuhlanganise nezibonelelo zempahla. I-Olympiad e-Informatics ayihlanganisi izinkinga eziyinkimbinkimbi nje kuphela, kodwa futhi ithola imibono enjalo eyaziwayo njengezinombolo eziyinhloko. Isihlungi se-Eratosthenes sisetshenziswa njengendlela ehambelana kakhulu yokubala ukulandelana, ngokuhlanganisa i-axiom ibe ikhodi yohlelo. Naphezu kokudala kokutholakala, le ncazelo kusiza ukufunda ngokushesha futhi ngempumelelo ekubaleni okufinyeleleka kanzima.