Isikhundla Sephuzu Ngokuphathelene Nendilinga
Indilinga iyisimo sejiyometri esiyisisekelo kakhulu futhi ivame ukuhlangana nayo ekuphileni kwansuku zonke nasemagatsheni ahlukahlukene esayensi, njengezibalo kanye nefiziksi. Esinye isenzakalo esivame ukuxoxwa ngaso kumongo wezindilinga yindawo yephuzu elihlobene nendilinga. Indawo yephuzu elihlobene nendilinga inganqunywa yibanga layo ukusuka enkabeni yendilinga, futhi ingaba ngaphakathi, ngaphandle, noma ngqo endilinga.
Ukuqonda Okuyisisekelo Kwemibuthano
Ngaphambi kokuxoxa ngokuma kwephuzu maqondana nendilinga kabanzi, ake siqale siqonde incazelo kanye nezakhiwo eziyisisekelo zendilinga. Indilinga iyiqoqo lawo wonke amaphuzu endizeni enezinhlangothi ezimbili aqhelelene nephuzu eliqinile elibizwa ngokuthi isikhungo. Leli banga eliqinile laziwa ngokuthi i-radius yendilinga.
Ngokwezibalo, uma \( O \) iphakathi nendawo yendilinga futhi \( r \) iyirediyasi yendilinga, khona-ke yonke indawo \( P(x, y) \) endilinga yanelisa i-equation:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
lapho \( (a, b) \) kuyizixhumanisi zesikhungo sendilinga.
Isikhundla Sephuzu Ngokuphathelene Nendilinga
Indawo yephuzu \( P(x, y) \) esiyingini inganqunywa ngosizo lwe-equation yesiyingi. Kunezindawo ezintathu ezingaba khona zaleli phuzu:
1. Iphuzu lingaphakathi kwendilinga
2. Iphuzu lisendilinga
3. Iphuzu lingaphandle kwendilinga
Ukuze sithole indawo yephuzu \( P(x, y) \), sidinga nje ukuqhathanisa ibanga ukusuka ephuzwini kuya enkabeni yendilinga nerediyasi yendilinga, okungukuthi \( r \).
1. Iphuzu lingaphakathi kwendilinga
Iphuzu \( P(x, y) \) kuthiwa lingaphakathi kwendilinga uma ibanga elisuka ephuzwini liye enkabeni yendilinga lingaphansi kwerediyasi yendilinga. Ngokwezibalo, lokhu kusho ukuthi:
\[ (x – a)^2 + (y – b)^2 < r^2 \] Ngokwejiyometri, uma iphuzu liseduze nesikhungo sendilinga kunebanga elinqunywe yirediyasi yendilinga, iphuzu kumele libe ngaphakathi kwendilinga. 2. Amaphuzu Asendilinga Iphuzu \( P(x, y) \) kuthiwa lisendilinga ngqo uma ibanga elisuka ephuzwini liye enkabeni yendilinga lilingana nerediyasi yendilinga. Ngokwezibalo: \[ (x - a)^2 + (y - b)^2 = r^2 \] Lokhu kusho ukuthi, iphuzu lisendilinga egcwalisa isibalo sendilinga echazwe ngaphambilini. 3. Amaphuzu Angaphandle Kwendilinga Iphuzu \( P(x, y) \) kuthiwa lingaphandle kwendilinga uma ibanga elisuka ephuzwini liye enkabeni yendilinga likhulu kunerediyasi yendilinga. Ngokwezibalo: \[ (x - a)^2 + (y - b)^2 > r^2 \]
Kulokhu, iphuzu lingaphandle kwemingcele echazwe yindilinga.
Izifundo Zezimo kanye Nezicelo
Ake sithathe izibonelo ezithile ukuze siqonde lo mqondo kangcono.
Isibonelo 1
Ake sithi sinesiyingi esinesikhungo \( O(3, 4) \) kanye nerediyasi \( r = 5 \). Sifuna ukuthola indawo yephuzu \( P(6, 8) \) maqondana nesiyingi.
Isinyathelo 1: Bala ibanga ukusuka ku-\( P \) kuya ku-\( O \):
\[ (x – a)^2 + (y – b)^2 = (6 – 3)^2 + (8 – 4)^2 = 3^2 + 4^2 = 9 + 16 = 25 \]
Isinyathelo 2: Qhathanisa ne-\( r^2 \):
\[r^2 = 5^2 = 25 \]
Ngakho-ke, njengoba \( 25 = 25 \), iphuzu \( P(6, 8) \) lisendilinga ngqo.
Isibonelo 2
Manje, ake sithi sinendilinga enesikhungo \( O(0, 0) \) kanye nerediyasi \( r = 10 \). Sifuna ukuthola indawo yephuzu \( Q(3, 4) \) maqondana nendilinga.
Isinyathelo 1: Bala ibanga ukusuka ku-\( Q \) kuya ku-\( O \):
\[ (x – a)^2 + (y – b)^2 = (3 – 0)^2 + (4 – 0)^2 = 3^2 + 4^2 = 9 + 16 = 25 \]
Isinyathelo 2: Qhathanisa ne-\( r^2 \):
\[r^2 = 10^2 = 100 \]
Njengoba \( 25 < 100 \), iphuzu \( Q \) lingaphakathi kwendilinga. Isibonelo 3 Futhi, ake sithi sinesiyingi esinesikhungo \( O(1, 1) \) kanye nerediyasi \( r = 3 \). Sifuna ukuthola indawo yephuzu \( R(5, 6) \) maqondana nendilinga. Isinyathelo 1: Bala ibanga ukusuka ku-\( R \) kuya ku-\( O \): \[ (x - a)^2 + (y - b)^2 = (5 - 1)^2 + (6 - 1)^2 = 4^2 + 5^2 = 16 + 25 = 41 \] Isinyathelo 2: Qhathanisa ne-\( r^2 \): \[ r^2 = 3^2 = 9 \] Njengoba \( 41 > 9 \), iphuzu \( R \) lingaphandle kwendilinga.
Ukubaluleka Kokuqonda Indawo Yephuzu Ngokuphathelene Nendilinga
Ukwazi indawo yephuzu elihlobene nendilinga akubalulekile nje kuphela ku-geometry eyisisekelo kodwa futhi kunezinhlelo zokusebenza ezibanzi emikhakheni ehlukahlukene. Isibonelo, ku-computer graphics kanye nokucubungula izithombe, lokhu kuqonda kubalulekile ekunqumeni ukuthi i-pixel iwela ngaphakathi kwemingcele ethile. Ku-physics kanye nobunjiniyela, isetshenziswa nasekuhlaziyeni ukunyakaza kwezinto kanye nokulungiselela izindawo zokusebenza zomshini.
Izicelo kubuchwepheshe kanye nobunjiniyela
Kubuchwepheshe obufana nokubona ubuso, ukuthola izimo ezithile esithombeni kuncike kakhulu ekubaleni indawo yephuzu elihlobene nendilinga. Izinhlelo zokuzulazula ze-GPS nazo zisebenzisa lesi simiso ukunquma ibanga ukusuka kwisathelayithi ethile ukunquma indawo yento eMhlabeni.
Izinhlelo Zokusebenza Ezingaphakathi Kwegeyimu
Ekuklanyweni komdlalo, ukunquma ukuthi umlingiswa noma into ingaphakathi kwendawo ethile kusebenzisa isimiso esifanayo. Lokhu kungasetshenziswa ekutholeni ukushayisana, ekunqumeni izindawo zamakhono, njalo njalo.
Izicelo kuSayensi
Ku-astronomy, ukubala izikhundla zamaplanethi noma ezinye izidalwa zasezulwini emizuliswaneni yazo eyindilinga nakho kusebenzisa lo mqondo. Isimiso esifanayo sisetshenziswa ekuhlaziyeni okuhlukahlukene kwe-orbital ukuqonda ukunyakaza kwezidalwa zasezulwini.
Isiphetho
Indawo yephuzu elihlobene nendilinga iyindikimba eyisisekelo ku-geometry. Sisebenzisa i-equation yendilinga kanye nebanga elisuka ephuzwini liye enkabeni yalo, singanquma kalula ukuthi iphuzu lingaphakathi, ngaphandle, noma ngqo endilinga. Ukuqonda lo mqondo kuvula indlela yezinhlelo zokusebenza eziningi kubunjiniyela, isayensi, kanye nobuchwepheshe. Ngokufunda njalo nokusebenzisa lo mqondo, siyaqonda indilinga hhayi nje kuphela njengento ye-geometri kodwa futhi njengengxenye ebalulekile ekuhlaziyweni kwezibalo kanye nohlu olubanzi lwezinhlelo zokusebenza ezisebenzayo.
