Incazelo ye-Circle
Indilinga ingenye yezimo zejiyometri eziyisisekelo kakhulu futhi iye yathumba isintu kusukela ezikhathini zasendulo. Ezibalweni, indilinga ichazwa njengeqoqo lawo wonke amaphuzu endizeni aqhelelene nephuzu eliqondile. Leli phuzu eliqondile libizwa ngokuthi isikhungo sendilinga, kanti ibanga elisuka enkabeni liye kunoma yiliphi iphuzu elisendilinga libizwa ngokuthi i-radius.
1. Incazelo yeSiyingi
Ukuze siqonde ngempela incazelo yendilinga, kumele sibheke izakhi zayo ngokuningiliziwe:
– Isikhungo Sendilinga: Iphuzu eliqondile lapho wonke amaphuzu esindilinga eqhelelene khona ngokulinganayo.
– Irediyasi (r): Ibanga ukusuka enkabeni yendilinga kuya kunoma iyiphi indawo endilinga.
– Ububanzi (d): Ibanga elide kakhulu phakathi kwamaphuzu amabili esindilinga esidlula phakathi nendawo. Ububanzi buphindwe kabili kune-radius, noma ngokwezibalo bungabhalwa njengo-\( d = 2r \).
2. Izakhiwo Zemibuthano
Imibuthano inezakhiwo ezithakazelisayo neziyingqayizivele:
– Wonke ama-radii esiyingi anobude obufanayo.
– Indilinga ilingana kahle phakathi nendawo yayo.
– Ububanzi ngabunye buhlukanisa indilinga ibe izingxenye ezimbili ezilinganayo.
– Indilinga iyigophe elivaliwe elingenasiqalo noma isiphetho.
3. Isilinganiso Sendilinga
Kuhlelo lwe-Cartesian coordinate, indilinga enesikhungo endaweni \((h, k)\) kanye ne-radius \(r\) ine-equation ejwayelekile:
\[ (x – h)^2 + (y – k)^2 = r^2 \]
Uma isikhungo sendilinga sisekuqaleni \((0,0)\), i-equation iba lula:
\[ x^2 + y^2 = r^2 \]
4. Ukujikeleza kanye nendawo yendilinga
Ukubala umjikelezo nendawo yendilinga kuyimisebenzi emibili eyisisekelo evame ukwenziwa nge-geometry.
– Ukujikeleza Kwendilinga: Ukujikeleza kwendilinga ubude bazo zonke izinhlangothi zangaphandle zendilinga. Ifomula yokujikeleza kwendilinga yile:
\[ K = 2\pir \]
Lapho i-\( \pi \) (pi) iyisimo esiqhubekayo sezibalo esicishe silingane no-3,14159.
– Indawo Yendilinga: Indawo yendilinga yisikhala esihlalwa yindilinga ngaphakathi kwendiza. Ifomula yendawo yendilinga yile:
\[ L = \pi r^2 \]
5. Umlando Nokubaluleka Kwemibuthano
Izindilinga ziyathakazelisa hhayi nje kuphela ezibalweni kodwa nasemlandweni namasiko abantu. Izindilinga zivame ukutholakala emvelweni, njengelanga, inyanga, nezinye izidalwa eziningi zasezulwini. Emasikweni abantu, izindilinga zivame ukuhlotshaniswa nokuphelela kanye nokuphelela.
– Izinkanyezi Namakhalenda: Ukunyakaza kwamaplanethi nezinkanyezi esikhaleni kuvame ukulandela izindlela eziyindilinga, noma ezicishe zibe yindilinga. Amakhalenda asendulo ayevame ukusekelwe emijikelezweni yenyanga neyelanga.
– Ukwakha Nobuciko: Izindilinga zisetshenziswa ezakhiweni eziningi zokwakha, njengezindonga nemibhoshongo, kanye nasemiklamo yobuciko kusukela kuma-mandala kuya kumasondo.
6. Izindilinga Empilweni Yansuku Zonke
Izindilinga nazo zinezindlela eziningi ezisebenzayo ekuphileni kwansuku zonke:
– Amasondo namaGiya: Isondo lingenye yezinto eziyisisekelo ezisungulwe ngabantu, ngesimo salo esiyindilinga. Amagiya asiza ekudluliseni amandla ngokunyakaza okujikelezayo.
– Amawashi: Isikhathi sivame ukuboniswa ngezindilinga, njengakuwashi odongeni nasemawashini esandla.
– Ezemidlalo: Ezemidlalo ezahlukahlukene, iziyingi zisetshenziswa ezinkundleni zokudlala, emabhola, nakwezinye izinto zemidlalo.
7. Imibuthano kuzibalo ezithuthukisiwe
Ezibalweni eziyinkimbinkimbi kakhulu, imibuthano idlala indima ebalulekile emagatsheni ahlukahlukene esayensi.
– I-Euclidean Geometry: Indilinga iyinto eyisisekelo esiza ekwakheni imibono eminingi ye-geometric.
– Ukuhlaziywa Okuyinkimbinkimbi: Kuzibalo eziyinkimbinkimbi, indilinga imelela isethi yawo wonke amaphuzu ebangeni elinikeziwe ukusuka enkabeni endizeni eyinkimbinkimbi.
– Ithiyori Yezinombolo: Ezinye izinkinga kuthiyori yezinombolo zihilela ukuthola amaphuzu esindilinga esinezimpawu ezithile.
8. Izindilinga kanye nezinye izigobe eziyindilinga
Indilinga iyisibonelo sejika eliyindilinga, kodwa kunezinye izijika ezifanayo, njenge-ellipse. I-ellipse isethi yamaphuzu lapho isamba samabanga awo ukusuka kumaphuzu amabili aqinile (i-foci) singaguquki. Indilinga ingacatshangwa njengesibonelo esikhethekile se-ellipse lapho izigxivizo ezimbili zihlangana khona endaweni eyodwa, isikhungo.
9. Izazi Zezibalo kanye Nocwaningo Ngemibuthano
Izazi zezibalo eziningi emlandweni ziye zafunda imibuthano futhi zanikela olwazini lwethu ngalesi simo. Isibonelo, u-Archimedes wayengusosayensi wezibalo ongumGreki owenza iminikelo eminingi ebalulekile, okuhlanganisa nokulinganisa inani le-pi ngokunemba okuphezulu.
UPierre-Simon Laplace, isazi sezibalo nesazi sezinkanyezi saseFrance, naye waba negalelo ekufundweni kwezindilinga ngokwesimo sokunyakaza kwamaplanethi kanye nenkolelo-mbono yokungenzeka.
10. Ubuchwepheshe Besimanje kanye Nezicelo
Enkathini yanamuhla, umqondo wemibuthano uthole izinhlelo zokusebenza ezahlukahlukene zobuchwepheshe. Isibonelo, kuma-computer graphics, imibuthano isetshenziselwa ukuklama izixhumi zomsebenzisi kanye nemidlalo. Kubunjiniyela bemishini, imibuthano isetshenziswa ekwakhiweni kwezingxenye ezihlanganisiwe ezidinga ukujikeleza okubushelelezi, njenge-bearings kanye ne-transmissions.
Ama-algorithms esimanje ekuqaphelweni kwamaphethini nasekuhlaziyweni kwezithombe nawo avame ukusebenzisa imibuthano ukuthola nokubona izimo ezithombeni zedijithali. Ngaphezu kwalokho, ekuxhumaneni okungenantambo, umqondo wombuthano usetshenziswa ekwakhiweni kwe-antenna kanye nokusatshalaliswa kwesignali.
11. Imfundo kanye Nemibuthano
Emfundweni, ukutadisha imibuthano kuqala besebancane. Ukwethula umqondo wemibuthano esikoleni samabanga aphansi kusiza ekwakheni isisekelo esiqinile ku-geometry kanye nezibalo ngokujwayelekile. Njengoba abafundi bengena emfundweni ephakeme, bazohlangana nemibuthano ezihlokweni ezahlukahlukene eziyinkimbinkimbi, njenge-calculus kanye ne-geometry yokuhlaziya.
Isiphetho
Indilinga iyisimo esilula kodwa esicebile kakhulu ngezakhiwo kanye nokusetshenziswa. Kusukela encazelweni yaso eyisisekelo kuya ezibalweni zezibalo, kusukela ekwakhiweni kwezakhiwo kuya kubuchwepheshe besimanje, indilinga idlala indima ebalulekile ezicini ezahlukene zokuphila. Ukuqonda indilinga akusizi nje kuphela ukuxazulula izinkinga zezibalo kodwa futhi kuvula ukuqonda ngobuhle nokuphelela okukhona emvelweni nasebuchwephesheni.
