Madenderedzwa neArcs
Madenderedzwa neArc ipfungwa huru mumasvomhu dzine mashandisirwo akapararira munzvimbo dzakasiyana-siyana, kubva pakugadzira michina kusvika kumifananidzo yemakombiyuta. Chinyorwa chino chichakurukura zvakadzama tsananguro, hunhu, uye mashandisirwo emadenderedzwa neArc.
Tsanangudzo yeDenderedzwa
Denderedzwa iboka remapoinzi ese ari mudenderedzwa ari kure zvakanyanya kubva panzvimbo yakapihwa inonzi pakati. Daro iri rinozivikanwa se radius. Pamasvomhu, denderedzwa rinogona kuratidzwa se equation:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
apo \((a, b)\) ari makoronesheni ari pakati pedenderedzwa uye \(r\) ari radius yedenderedzwa.
Muhupenyu hwezuva nezuva, tinowanzo sangana nechimiro chedenderedzwa, kubva pamavhiri emotokari kusvika kumawachi emadziro kusvika kumidziyo yakasiyana-siyana yemumba. Chimiro ichi chedenderedzwa hachingofadzi chete asi chinoshandawo mumabasa akawanda.
Zvikamu zviri mudenderedzwa
Kuti unzwisise madenderedzwa zvakadzama, zvakakosha kuziva zvimwe zvezvinhu zvikuru:
1. Nzvimbo yepakati:
Nzvimbo yepakati ndiyo nzvimbo iri pakati pedenderedzwa. Ndiyo nzvimbo huru yekutarisa nharaunda uye chimiro chedenderedzwa rese.
2. Nharaunda (Minwe):
Radiyumu idaro rinobva pakati pedenderedzwa kusvika chero panzvimbo yakatenderedzwa yedenderedzwa. Mitsetse yese inotorwa kubva pakati kuenda kudenderedzwa ine radiyumu uye ine urefu hwakaenzana.
3. Dhayamita:
Dhayamita (diameter) mutsetse wakatwasuka unobatanidza nzvimbo mbiri padenderedzwa uye unopfuura nepakati paro. Dhayamita yacho yakapetwa kaviri kureba kweradius (D = 2R).
4. Kutenderera:
Denderedzwa ndiro hurefu hwemativi ese edenderedzwa. Denderedzwa rinogona kuverengerwa uchishandisa fomura iyi:
\[ K = 2\pir \]
apo \(r\) iri nharaunda yedenderedzwa uye \(\pi\) iri nhanho yemasvomhu inenge yakaenzana ne3.14159.
5. Nzvimbo:
Nzvimbo yedenderedzwa inzvimbo yedunhu rakaganhurirwa nedenderedzwa uye inogona kuwanikwa uchishandisa fomura:
\[ A = \pi r^2 \]
Denderedzwa Arc
Arc chikamu chemucheto wedenderedzwa chinochekwa nepfungwa mbiri padenderedzwa. Kune mhando mbiri huru dzearcs: arcs huru nearcs diki. Kana tikadhirowa denderedzwa tosarudza pfungwa mbiri padenderedzwa, mutsetse wakakombama unobatanidza pfungwa mbiri idzodzo iarc. Kana arc ikafukidza isingasviki hafu yedenderedzwa, inonzi arc diki; kana ikafukidza inopfuura hafu, inonzi arc diki.
Kuverenga Hurefu hweArc
Kureba kwearc kunoenderana nekona iri pakati pema radii maviri anopindirana nedenderedzwa panzvimbo mbiri. Kureba kwearc kunogona kuverengerwa uchishandisa fomura iyi:
\[ s = r \theta \]
apo \(s\) iri kureba kwearc, \(r\) iri radius, uye \(\theta\) iri kona yepakati muma radians. Kana kona ikapihwa mumadhigirii, kureba kwearc kunogona kushandurwa uchishandisa:
\[ s = \frac{\theta}{360} \kawa 2\pir \]
Nzvimbo yeSector
Chikamu (sector) idunhu riri mukati medenderedzwa rakaganhurirwa nemaradhi maviri nearc. Nzvimbo yechikamu inogona kuwanikwa uchishandisa fomura:
\[ L = \frac{1}{2} r^2 \theta \]
apo \(L\) iri nzvimbo yechikamu, \(r\) iri radius, uye \(\theta\) iri central angle muma radians. Kana angle yakapihwa mumadhigirii:
\[ L = \frac{\theta}{360} \times \pi r^2 \]
Mashandisirwo eMadenderedzwa neMaArcs
Madenderedzwa nema arc ane basa rakakosha muminda yakasiyana-siyana inoshanda, mune zvese sainzi netekinoroji.
MuUinjiniya neMagadzirirwo ezvivakwa
Madenderedzwa anowanzo shandiswa mumapazi akasiyana-siyana einjiniya nekuda kwechimiro chawo chakaenzana uye chakakodzera. Semuenzaniso, mavhiri emotokari akagadzirwa muchimiro chedenderedzwa kuti ave nechokwadi chekufamba kwakanaka uye kwakanaka. Muinjiniya yezvivakwa, maarches kana maarcs anogona kutsigira mitoro nekupararira kwakaenzana kwekumanikidza, sezvinoonekwa mumabhiriji akakombama kana maarches ezvivakwa.
Mukugadzira Mifananidzo uye Mifananidzo
Munyika yekugadzira mifananidzo nemifananidzo, madenderedzwa nemitsara yakatenderera zvine basa rakakosha zvakaenzana. Madenderedzwa anoshandiswa sezvinhu zvakakosha zvezvinhu zvakasiyana-siyana nemagadzirirwo. Semuenzaniso, pakugadzira mavara ane mifananidzo kana malogo ekambani, madenderedzwa anowanzo shanda sechimiro chikuru chezvinhu zvakasiyana-siyana.
MuAstronomy
Mukuongorora nyeredzi, madenderedzwa epasi anowanzoonekwa sedenderedzwa kana kuti denderedzwa. Kunzwisisa madenderedzwa kwakakosha pakufanotaura kufamba kwemapuraneti nezvimwe zvinhu zvemudenga. Johannes Kepler, mumutemo wake wechitatu wekufamba kwemapuraneti, akashandisa pfungwa dzemadenderedzwa nema ellipses kutsanangura madenderedzwa emapuraneti ari mu solar system.
Mukufambisa uye Jogirafi
Mukufamba netsoka, kunyanya mugungwa nendege, madenderedzwa anoita basa guru pakuronga nzira. Pfungwa yedenderedzwa guru, denderedzwa rine pakati paro riri pakati peNyika uye rinoyambuka pamusoro peNyika, ndiyo inokosha pakufamba nendege munyika dzakasiyana.
Denderedzwa Masvomhu muDzidzo
Madenderedzwa inyaya huru muzvidzidzo zvemasvomhu pasi rose. Pakutanga kwedzidzo, madenderedzwa anobatsira vadzidzi kunzwisisa nekuona pfungwa dzejometri dzepakutanga. Sezvo vadzidzi vachifambira mberi mudzidzo, pfungwa idzi dzinowedzera kuita ongororo yakaoma, kusanganisira trigonometry necalculus.
Zvikamu zvemasvomhu zvakakosha, zvakaita setrigonometry, zvine hukama zvakananga nedenderedzwa reyuniti (denderedzwa rine radius 1). Pfungwa dzesine, cosine, uye tangent dzakavakirwa pakuratidzwa kwemapoinzi padenderedzwa reyuniti.
Mhedziso
Madenderedzwa nema arcs ipfungwa huru mu geometry dzine mashandisirwo akapararira muminda inotangira painjiniya nekuvaka kusvika pakugadzira mifananidzo nenyeredzi. Kunzwisisa zvakakwana hunhu hwemadenderedzwa nema arcs hakungokoshi chete muzviitiko zvemasvomhu asiwo kune kukosha kunoshanda muhupenyu hwezuva nezuva nemabasa akasiyana-siyana. Izvi zvinoratidza kukosha kwepfungwa idzi mukusimudzira ruzivo netekinoroji.
