Inkcazelo algebra ukuvumelana. Umthamo we sphere

Ihlabathi elisingqongileyo, nangona iindidi zezinto ngezimanga kwenzeka kubo, zizele Maz nobunye nempembelelo ecacileyo imithetho yendalo. Ngaphaya inkululeko okubonakala ngayo indalo uzoba kucacile kwaye kudala iintlobo zinto ifihlakeleyo imithetho ecacileyo kunye nemithetho, engathandi lubonisa ingcamango phambi kwinkqubo yokwakha ezinye uhlobo amandla aphezulu. Ngomhla kumqukumbelo inzululwazi ebambekayo, ukunika inkcazo nesenzeko ngokwembono iifomyula zemathematika kunye inqubo theosophical, kukho ihlabathi, asinike lonke iqela iimvakalelo kunye gca evela ngokugcwalisa izinto kunye neziganeko ezenzeka kubo yakhe.

Ibhola njenge inani zejometri yeyona lolona hlobo luqhelekileyo zendalo ukuze imizimba. Uninzi Izidumbu macrocosm kunye sekuba zime spherically, okanye bafune ukufumana kufutshane nto. Ngokwesiseko, ibhola ngumzekelo ifomu efanelekileyo. Le nkcazelo eyamkelekileyo ukuba ibhola uthathwa ngolu hlobo lulandelayo: umzimba zejometri, a nobuninzi (Ukuba kwisininzi) kuzo zonke iingongoma ayindalo kumgama ukusuka kwiziko ukuba ayidluli ixabiso elichaziweyo. Geometry, umgama uye wabizwa embindini, kwaye ngokubhekiselele kulo mzobo, ibizwa ngokuba sphere of radius. Ngamanye amazwi, xa umthamo sethi sphere zonke iingongoma elele kumgama ukusuka kwiziko, esingadlulanga ubude radius.

Ibhola kuseyinto ngenxa njengokujikeleza kwisangqa ngeenxa ububanzi balo, nto leyo ke ishiyeke izinzile. Ngaloo izakhi neempawu ezifana embindini kunye nomthamo ibhola, esqwini ibhola kongezwe (ubukhulu esisigxina), kunye iziphelo ibhola zibizwa ngokuba nezibonda. Phezu sphere ekuthiwa sphere. Ukuba sisebenzisana ibhola evaliweyo, ubhala kule ndawo, ukuba evulekileyo, akubikho nto.

Ukuqwalasela enxulumene isebe ngokuchonga ibhola, kufuneka enokuthethwa ukuzilimaza moya. Edlula embindini ibhola yokusika moya kuthiwa sisangqa enkulu. Kwabanye, amacandelo moya ka sphere wenza ukuba asebenzise ibinzana elithi "izangqa ezincinane". Xa kubalwa indawo lomnqamlezo-amacandelo kusetyenziswa ifomula πR².

Ukubala umthamo sphere, zezibalo senze Imithetho kunokuba umdla neempawu. Kwacaca ukuba eli xabiso nokuba uphinda okanye efana kakhulu indlela yokuqingqa umthamo yephiramidi okanye itankana circumscribing ibhola. Kubonakala ukuba umthamo kwisigaba lilingana ivolyum yephiramidi, ukuba unalo indawo isiseko efanayo njengoko phezu ibhola, ukuphakama elingana kwirediyasi ibhola. Xa siqwalasela itankana sphere circumscribing, kunokwenzeka ukuba ukubala ngokomfuziselo ngokwendlela apho umthamo sphere ingaphantsi kwe umthamo itankana ngesiqingatha.

Likhangeleka indlela enomtsalane original ukuba Ukuveliswa kwe sphere of ivolyum usebenzisa umgaqo Cavalieri. Nguye ukufumana umthamo yiyiphi ngokudibanisa ndawo wafumana icandelo layo umnqamlezo inani engenasiphelo -moya ngaxeshanye. Kwimveliso uthathe ikhweyitha of radius R kunye umphanda kokuba umphakamo-R kunye nesiseko isangqa radius R (isiseko ikhweyitha kunye lombhobho ke loo moya efanayo). Xa lombhobho sizibhale ikhowuni enekona kwi kumbindi emazantsi nesiseko saso. Ebonakalalisa ukuba lo mqulu we-ikhweyitha kunye lombhobho ekhohlo ngaphandle cone kulula ukubala umthamo sphere. Ifomula kuthatha le fomu ilandelayo: ezine imveliso sesithathu amagaqa radius ukuba π (V = 4 / 3R ^ 3 × π). Kulula ukuba ubungqina, ukuba isithole moya iqhelekileyo ikhweyitha kunye nesilinda. Izikwere isangqa encinane annulus lirhangqwe emacaleni ngaphandle lombhobho kunye cone bayalingana. Kwaye, esebenzisa umgaqo vayimeri, akukho nzima ukuza ifomyula engundoqo ubungqina ngazo thina ezichaza umthamo kwisigaba.

Kodwa akukho nje ingxaki kophononongo lwemizimba yendalo ngenxa ukufumana iindlela ukumisela iimpawu zazo ezahlukeneyo kunye neepropati. Eli nani we geometry eziqinileyo njengoko ibhola lisetyenziswa kumsebenzi yabantu pfunaka. izixhobo Mass technical anayo iinkcukacha zalo zokwakha hayi kuphela ifomu ungqukuva kodwa yakhiwa izakhi isitya. Kuyinto up izisombululo efanelekileyo yendalo kwinkqubo zezinto ezenziwa luluntu inika iziphumo aphezulu umgangatho.