Nzvimbo yePoindi maererano neDenderedzwa
Denderedzwa iri chimiro chejometri chakareruka uye chinowanzoonekwa muhupenyu hwezuva nezuva uye mumapazi akasiyana-siyana esainzi, akadai semasvomhu nefizikisi. Chimwe chinhu chinowanzo kurukurwa mumashoko edenderedzwa inzvimbo yepoindi ine chekuita nedenderedzwa. Nzvimbo yepoindi ine chekuita nedenderedzwa inogona kutsanangurwa nekureba kwayo kubva pakati pedenderedzwa, uye inogona kuva mukati, kunze, kana zvakananga padenderedzwa.
Kunzwisisa Kwekutanga kweMadenderedzwa
Tisati takurukura nezvenzvimbo yepoindi maererano nedenderedzwa, ngatitangei tanzwisisa tsananguro uye hunhu hwedenderedzwa. Denderedzwa iboka remapoindi ese ari mundege ine mativi maviri ari chinhambwe chakafanana kubva panzvimbo yakatarwa inonzi pakati. Daro iri rakagadziriswa rinozivikanwa seredhiyo yedenderedzwa.
Pamasvomhu, kana \( O \) iri pakati pedenderedzwa uye \( r \) iri radius yedenderedzwa, saka poindi yega yega \( P(x, y) \) iri padenderedzwa inogutsa equation:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
apo \( (a, b) \) ndiwo makoronesheni ari pakati pedenderedzwa.
Nzvimbo yePoindi maererano neDenderedzwa
Nzvimbo yepoindi \( P(x, y) \) padenderedzwa inogona kuzivikanwa nerubatsiro rwe equation yedenderedzwa. Pane nzvimbo nhatu dzinogona kuwanikwa papoindi iyi:
1. Pfungwa iri mukati medenderedzwa
2. Pfungwa iri padenderedzwa
3. Pfungwa iri kunze kwedenderedzwa
Kuti tizive nzvimbo yepoindi \( P(x, y) \), tinongoda kuenzanisa daro kubva papoindi kusvika pakati pedenderedzwa neradius yedenderedzwa, kureva \( r \).
1. Pfungwa iri mukati medenderedzwa
Poindi \( P(x, y) \) inonzi iri mukati medenderedzwa kana daro kubva panzvimbo kuenda pakati pedenderedzwa riri pasi pe radius yedenderedzwa. Pamasvomhu, izvi zvinoreva:
\[ (x – a)^2 + (y – b)^2 < r^2 \] Mukutaura kwejometri, kana poindi iri pedyo nepakati pedenderedzwa kupfuura daro rakatarwa neradius yedenderedzwa, poindi yacho inofanira kunge iri mukati medenderedzwa. 2. Mapoinzi Ari paDenderedzwa Poindi \( P(x, y) \) inonzi iri padenderedzwa chaipo kana daro kubva panzvimbo kuenda pakati pedenderedzwa rakaenzana neradius yedenderedzwa. Pamasvomhu: \[ (x - a)^2 + (y - b)^2 = r^2 \] Izvi zvinoreva kuti, poindi iri padenderedzwa rinogutsa equation yedenderedzwa yakatsanangurwa kare. 3. Mapoinzi Ari Kunze kweDenderedzwa Poindi \( P(x, y) \) inonzi iri kunze kwedenderedzwa kana daro kubva panzvimbo kuenda pakati pedenderedzwa rakakura kupfuura radius yedenderedzwa. Pamasvomhu: \[ (x - a)^2 + (y - b)^2 > r^2 \]
Muchiitiko ichi, pfungwa yacho iri kunze kwemiganhu inotsanangurwa nedenderedzwa.
Zvidzidzo zveNyaya uye Mashandisirwo
Ngatitorei mimwe mienzaniso kuti tinzwisise pfungwa iyi zviri nani.
Muenzaniso 1
Ngatitii tine denderedzwa rine pakati \( O(3, 4) \) uye radius \( r = 5 \). Tinoda kuona nzvimbo yepoindi \( P(6, 8) \) maererano nedenderedzwa.
Danho 1: Verenga daro kubva pa \( P \) kusvika pa \( O \):
\[ (x – a)^2 + (y – b)^2 = (6 – 3)^2 + (8 – 4)^2 = 3^2 + 4^2 = 9 + 16 = 25 \]
Danho rechipiri: Enzanisa ne \( r^2 \):
\[r^2 = 5^2 = 25 \]
Saka, sezvo \( 25 = 25 \), poindi \( P(6, 8) \) iri padenderedzwa chaipo.
Muenzaniso 2
Zvino, ngatitii tine denderedzwa rine pakati \( O(0, 0) \) uye radius \( r = 10 \). Tinoda kuona nzvimbo yepoindi \( Q(3, 4) \) maererano nedenderedzwa.
Danho 1: Verenga daro kubva pa \( Q \) kusvika pa \( O \):
\[ (x – a)^2 + (y – b)^2 = (3 – 0)^2 + (4 – 0)^2 = 3^2 + 4^2 = 9 + 16 = 25 \]
Danho rechipiri: Enzanisa ne \( r^2 \):
\[r^2 = 10^2 = 100 \]
Sezvo \( 25 < 100 \), poindi \( Q \) iri mukati medenderedzwa . Muenzaniso 3 Zvakare, ngatitii tine denderedzwa rine pakati \( O(1, 1) \) uye radius \( r = 3 \). Tinoda kuona nzvimbo yepoindi \( R(5, 6) \) maererano nedenderedzwa. Danho 1: Verenga daro kubva \( R \) kusvika \( O \): \[ (x - a)^2 + (y - b)^2 = (5 - 1)^2 + (6 - 1)^2 = 4^2 + 5^2 = 16 + 25 = 41 \] Danho 2: Enzanisa ne \( r^2 \): \[ r^2 = 3^2 = 9 \] Sezvo \( 41 > 9 \), poindi \( R \) iri kunze kwedenderedzwa .
Kukosha Kwekunzwisisa Nzvimbo yePoint Kana Uchienderana neDenderedzwa
Kuziva nzvimbo yepoindi kana tichienzanisa nedenderedzwa hakungokoshi chete mu geometry yekutanga asiwo kune mashandisirwo akawanda muminda yakasiyana-siyana. Semuenzaniso, mumifananidzo yekombuta uye kugadzirisa mifananidzo, kunzwisisa uku kwakakosha pakuona kana pixel iri mukati memiganhu yakati. Mufizikisi neinjiniya, inoshandiswawo mukuongorora kufamba kwechinhu uye kugadzirisa nzvimbo dzebasa dzemuchina.
Zvikumbiro muTekinoroji neUinjiniya
Mumatekinoroji akadai sekuziva chiso, kuona maumbirwo chaiwo mumufananidzo kunoenderana zvakanyanya nekuverenga nzvimbo yepoindi kana tichienzanisa nedenderedzwa. Masisitimu ekufamba neGPS anoshandisawo musimboti uyu kuona daro kubva pane imwe satellite kuti aone nzvimbo yechinhu paPasi.
Mapurogiramu eMumutambo
Mukugadzira mutambo, kuona kana hunhu kana chinhu chiri munzvimbo yakati kunoshandisawo musimboti mumwe chete. Izvi zvinogona kushandiswa pakuona kurovana, kuona nzvimbo dzekugona, nezvimwewo.
Mashandisirwo muSainzi
Mukuongorora nyeredzi, kuverenga nzvimbo yemapuraneti kana mimwe mitumbi yekudenga mudenderedzwa rayo kunoshandisawo pfungwa iyi. Pfungwa imwechete inoshandiswa mukuongorora kwakasiyana-siyana kwemuchadenga kuti tinzwisise kufamba kwemitumbi yekudenga.
Mhedziso
Nzvimbo yepoindi kana tichienzanisa nedenderedzwa inyaya huru mu geometry. Tichishandisa equation yedenderedzwa uye daro kubva pane poindi kuenda pakati payo, tinogona kuona zviri nyore kana poindi iri mukati, kunze, kana zvakananga padenderedzwa. Kunzwisisa pfungwa iyi kunovhura nzira yekushandiswa kwakasiyana-siyana muinjiniya, sainzi, uye tekinoroji. Nekudzidza nguva dzose nekushandisa pfungwa iyi, tinonzwisisa denderedzwa kwete sechinhu che geometri chete asiwo sechinhu chakakosha mukuongorora masvomhu uye mashandisirwo akasiyana-siyana anoshanda.
