Incazelo algebra bokuthula. Umthamo sphere

Izwe elisizungezile, naphezu tintfo letehlukene kanye izenzakalo ezenzeka kubo, eligcwele ngokuvumelana Ngenxa umphumela ecacile imithetho yemvelo. Ahambisana Naleli inkululeko sobala ngawo imvelo udonsa zomhlangano kudala amafomu zezinto afihliwe imithetho ecacile futhi imithetho, yezimo abhekene kusikisela umqondo khona enqubeni yokwakha ezinye uhlobo emandleni aphakeme. On the esengozini isayensi pragmatic, enika incazelo imihlola ngokombono zezibalo kanye worldview theosophical, kukhona umhlaba, kusinike lonke kweqembu imizwa kanye nemigqondo kusukela ngokugcwalisa izinto zakhe futhi izenzakalo ezenzeka kubo.

Ball njengoba sibalo Jomethri iyona ifomu evamile zendalo ukuze zibe nemizimba yenyama. Iningi Izidumbu macrocosm futhi microcosm kukhona okwenyanga spherically, noma ukufuna zokusondelana ukuthi. Ngokuyisisekelo, ibhola yisibonelo ifomu enhle. Inchazelo owamukelwa for ibhola ubhekwa ngendlela elandelayo: umzimba weJiyomethri, sebuningini (sebuningini) wonke amaphuzu okuyizinto kude kusukela maphakathi ukuthi ayidluli kunani elicacisiwe. Ngo-geometry, ibanga eliye labizwa phezu kwazo engaba, futhi ngokuqondene nalo sibalo, ubizwa ngokuthi ihogela engaba. Ngamanye amazwi, umthamo ebiyelwe we sphere wonke amaphoyinti elele ibanga ukusuka enkabeni, esingeqile ubude engaba.

Ball namanje kubhekwa ngenxa ukujikeleza a umkhumbi ezungeze ubukhulu bayo, okuyinto ngaleyo ndlela uhlala umile. Ngakho izakhi ezifana nezinhlamvu njengoba engaba futhi ivolumu ibhola, eksisi ibhola sengezwe (ubukhulu fixed), nemikhawulo yomhlaba ibhola abizwa ngokuthi izingongolo. Ingaphezulu indilinga ngokuthi uyindilinga. Uma ubhekene naleso ibhola avaliwe, sizihlanganisa kule ndawo, uma evulekile, ke aqede ke.

Singafunda ngaphezu kwalokho elihlobene ne-ukuhlonza ibhola, kufanele ishiwo indiza ahlabayo. Kudlulwa maphakathi ibhola ukusika indiza ibizwa ngokuthi oyibanga. Kwabanye, izigaba indiza ka indilinga kwenziwa ukusebenzisa inkulumo ethi "imibuthano ezincane". Lapho kubalwa endaweni kwesiphambano-izigaba esetshenziswa ifomula πR².

Kubalwa ngevolumu indilinga, zezibalo ebhekene Imithetho kunalokho okuthakazelisayo futhi izici. Kwatholakala ukuthi lesi silinganiso noma izimpinda noma iyafana kakhulu indlela yokunquma ivolumu iphiramidi noma isilinda onciphisa ibhola. It kuvela ukuthi umthamo sphere ilingana ivolumu mbhoshongo, uma it has okufanayo isizinda ndawo njengoba ebusweni ibhola, futhi ukuphakama ilingane engaba ibhola. Uma sicabangela isilinda sphere onciphisa, kungenzeka ukubala iphethini owawuthi ivolumu sphere ingaphansi ivolumu ye isilinda ngesigamu.

Kubukeka indlela ekhangayo futhi yasekuqaleni bheke of sphere ivolumu usebenzisa Cavalieri isimiso. He is ukuthola umthamo kwanoma iyiphi sibalo ngokungeza endaweni wathola engu- yayo kwesigaba i isibalo esingapheliyo izindiza ngokulinganisa. Ukuze okukhipha ukuthatha Nenkabazwe ka engaba R emgqonyeni kokuba ukuphakama-R nge isizinda umbuthano engaba R (kumila Nenkabazwe futhi isilinda kukhona amaplanethi asendaweni). Ngo uMbhalo sizibhale Isigaxa nge vertex esikhungweni phansi kwesisekelo salo. Nihlola umthamo Nenkabazwe futhi uMbhalo kwesokunxele aphume Isigaxa kulula ukubala ivolumu uyindilinga. Formula kuthatha ifomu elilandelayo: ezine umkhiqizo wesithathu iqhuzu engaba ukuze π (V = 4 / 3R ^ 3 × π). Kulula ukufakazela, kokuba indiza ahlabayo ezivamile ngokusebenzisa Nenkabazwe futhi uMbhalo. Izikwele umbuthano amancane annulus iphahlwe ezinhlangothini ngaphandle kwe uMbhalo bese Isigaxa bayalingana. Futhi, besebenzisa Cavalieri isimiso, akunzima ukuza ifomula main ubufakazi ngalo ichaze ivolumu sphere.

Kodwa akukhona nje inkinga ekuhloleni imizimba natural is ngenxa ukuthola izindlela ukunquma izici zabo ezahlukene futhi izakhiwo. Lesi sibalo we-geometry okuqinile njengoba ibhola kabanzi lisetshenziswe umsebenzi womuntu esisebenzayo. amadivaysi IMisa lobuchwepheshe has imininingwane yayo ukwakhiwa hhayi kuphela ifomu eyindilinga kodwa futhi yakhiwa izakhi isitsha. Kukithi izixazululo enhle engokwemvelo inqubo umsebenzi womuntu inikeza ephezulu imiphumela.