Kanjani ukubala kwendawo ingxenye ye ingxenye eyindilinga futhi endaweni

Inani zezibalo kwendawo yaziwa kusukela ezikhathini yaseGrisi yasendulo. Emuva ngalezo zinsuku amaGreki wathola ukuthi endaweni iyingxenye okuqhubekayo we ebusweni, okuyinto iphahlwe nxazonke by iluphu avaliwe. Lena inani lenombolo ukuthi kukalwa amayunithi sikwele. Le ndawo kuwuphawu zezinombolo njengoba izibalo flat yejeyomethri (planimetric) kanye evele zemizimba emkhathini (umthamo).

Okwamanje, yena kutholakala hhayi kuphela kukharikhulamu esikoleni eemfundweni geometry nezibalo ezingamaGreki, imfundo kodwa futhi ukufunda izinkanyezi, ukuphila ekwakheni, ukuthuthukiswa ubunjiniyela, ukukhiqiza futhi kwezinye eziningi zokukhulekela yomuntu. Isikhathi esining impela, ukubala kumasegmenti endaweni thina iphendukele ngesakhiwo ekuklanyweni landscape izindawo noma umsebenzi wokulungisa design sesimanje isikhala. Ngakho-ke, izindlela kokubala indawo ulwazi ahlukene zeJiyomethri ewusizo noma nini nanoma kuphi.

Ukuze abale kwendawo ingxenye isiyingi futhi ingxenye sphere kuyadingeka ukubhekana imigomo weJiyomethri, okuyinto kuyodingeka uma inqubo Computing.

Okokuqala, isinqamu ibizwa ngokuthi ingxenye wombuthano umbuthano indiza sibalo okuyinto ngokufanele phakathi arc isiyingi futhi kuzithinta yayo cutoff. Hhayi kunomvuzo kudidaniswe nomqondo wemboni sibalo. Lezi yizinto ezahlukene ngokuphelele.

Kuzithinta ibizwa ngokuthi ingxenye exhumanisa amaphuzu amabili umbuthano.

A engela emaphakathi obakhiwa imigqa emibili - radii. It is kulinganiswa amazinga arc, lapho kwamasabatha.

sphere ingxenye kwakhiwa ukusika indiza ye (iindulungu) by. etholwe Ngakho eyindilinga base ingxenye umbuthano, futhi ukuphakama perpendicular lovela isikhungo indingilizi ezimpambanweni zomgwaqo kobuso sithombe. Lokhu iphuzu kuhlangana ngokuthi vertex ingxenye ibhola.

Ukuze yokubona ukwenaba komusa endaweni ingxenye, odinga ukukwazi ubude selilonke we uhla ushayiwe futhi ukuphakama ibhola. Umkhiqizo kulezi zingxenye ezimbili futhi kuyoba kwendawo ingxenye eyindilinga: S = 2πRh, lapho h - ukuphakama ingxenye, 2πR - selilonke, futhi R - lo engaba oyibanga.

Ukuze abale kwendawo ingxenye mbuthano, ungakwazi iphendukele amafomula ezilandelayo:

1. Ukuze athole endaweni ingxenye ngendlela elula, kubalulekile ukubala umehluko phakathi endaweni wemboni ku eqoshwe ingxenye kanye endaweni unxantathu isosceles kabani base liyingxenye kuzithinta: S1 = S2-S3, lapho S1 - ingxenye endaweni, S2 - wemboni endaweni futhi s3 - endaweni unxantathu.

Kungenzeka ukusebenzisa eseduze ifomula ukubala kwendawo ingxenye isiyingi: S = 2/3 * (a h *), lapho - kumila unxantathu noma ka kuzithinta obuphelele, h - ukuphakama ingxenye ukuthi kuwumphumela umehluko phakathi embuthanweni engaba futhi ukuphakama unxantathu isosceles.

2. Le ndawo ingxenye, okuyinto ihlukile umkhumbi ibalwa kanje: S = (π-R2: 360) * α ± S3, lapho π-R2 - endaweni embuthanweni, α - degree elithile engela emaphakathi, okuhlanganisa i ingxenye arc wombuthano, S3 - unxantathu endaweni kwakhiwa okuyinto phakathi ezimbili radii wombuthano futhi kuzithinta ubambe engela endaweni maphakathi circle vertices ezimbili ngesikhathi amaphuzu lokuxhumana radii nge selilonke.

Uma α engela <180 degrees, uphawu lokususa isetshenziswa uma α> 180 degrees, uphawu lokuhlanganisa isetshenziswa.

3. Sebenzisa ikhompyutha endaweni ingxenye kungaba, kanye nezinye izindlela usebenzisa trigonometry. Njengomthetho, ngesisekelo unxantathu. Uma engela emaphakathi kukalwa ngama-degree, uyamukeleka uma le ndlela elandelayo: S =-R2 * (π * (α / 180) - isono α) / 2, lapho u-R2 - umbuthano engaba yisikwele, α - degree elithile engela emaphakathi.

4. Ukuze abale kwendawo ingxenye besebenzisa imisebenzi Trigonometric, futhi angasebenzisa obunye ifomula kuncike ekutheni engela emaphakathi kukalwa ngama-radians: S =-R2 * (α - isono α) / 2, lapho u-R2 - umbuthano engaba yisikwele, α - degree isilinganiso engela emaphakathi.