Denderedzwa neUta
Denderedzwa iri nderimwe remaumbirwo ejometri akakosha uye anochinjika. Muhupenyu hwezuva nezuva, tinoona madenderedzwa mumhando dzakasiyana-siyana, kubva pawachi dzemadziro nematayi emotokari kusvika kutenderera kwemapuraneti muzuva. Muchinyorwa chino, tichaongorora denderedzwa zvakadzama uye tichaongorora chimwe chezvinhu zvakakosha: chord.
Tsanangudzo yeDenderedzwa
Panyaya yemasvomhu, denderedzwa muunganidzwa wemapoinzi ese ari mudenderedzwa ari kure zvakaenzana kubva panzvimbo yepakati. Daro iri rinonzi radius, uye nzvimbo yepakati inonzi pakati pedenderedzwa. Mafomula ekutanga edenderedzwa (C) nenzvimbo (A) yedenderedzwa ndeaya anotevera:
– Mupendero (C): \[ C = 2\pi r \]
- Nzvimbo (A): \[ A = \pi r^2 \]
apo \( r \) iri nharaunda yedenderedzwa uye \( \pi \approx 3.14159 \).
Zvinhu zveDenderedzwa
Kunze kwenharaunda nepakati, kune zvimwe zvinhu zvakakosha zviri mudenderedzwa:
1. Dhayamita: Mutsetse wakatwasuka unopfuura nepakati pedenderedzwa wobatanidza mapoinzi maviri padenderedzwa. Chinhu chakakosha chedhayamita ndechekuti kureba kwawo kunogara kuri kaviri radius: \( D = 2r \).
2. Arc: Chikamu chedenderedzwa redenderedzwa pakati pemapoinzi maviri. Arcs dzinogona kuyerwa mumadhigirii kana ma radians, zvichienderana nemamiriro adzinoshandiswa.
3. Chord: Chikamu chemutsetse chinobatanidza nzvimbo mbiri padenderedzwa. Chord inopfuura nepakati pedenderedzwa inozivikanwa sedhayamita.
Kunzwisisa Tambo dzeUta
Chord chimwe chezvinhu zvisinganyanyi kutariswa mu denderedzwa, asi ine basa rakakosha. Chord mutsetse wakatwasuka unobatanidza mapoinzi maviri padenderedzwa. Kusiyana ne radius kana dhayamita, iyo inogara ichipfuura nepakati pedenderedzwa, chord inogona kuva chero kupi chero bedzi mapoinzi maviri ainobatanidza ari pamucheto wedenderedzwa.
Hunhu hweStambo dzeBowstring
1. Kureba kwetambo yeuta: Kureba kwetambo yeuta kunogona kuverengerwa uchishandisa mafomula akasiyana-siyana, zvichienderana neruzivo rwakapihwa. Imwe fomura inowanzo shandiswa ndeiyi:
\[ c = 2 \cdot R \cdot \sin \left( \dfrac{\theta}{2} \right) \]
apo \( c \) iri kureba kwechord, \( R \) iri radius, uye \( \theta \) ndiyo kona yepakati inoumbwa ne radii mbiri dzinosangana panzvimbo dzechord.
2. Nzvimbo kubva Pakati: Chord refu ichave pedyo nepakati pedenderedzwa pane chord pfupi. Kutaura zvazviri, chord refu kwazvo mudenderedzwa ndiyo dhayamita yayo.
3. Kuenzana: Chord inokamura denderedzwa kuita zvikamu zviviri zvakaenzana. Kana tikadhirowa mutsetse wakatwasuka kubva pakati pedenderedzwa kuenda kuchord, nzvimbo yekusangana inokamura chord kuita zvikamu zviviri zvakaenzana.
4. Hukama neRadius: Kana chord neradius zvikaita triangle, tinogona kuverenga urefu hwechord nezvimwe zvinhu tichishandisa hwaro hwetrigonometry nemutemo wecosines.
Kushandiswa kweBowstring muhupenyu hwezuva nezuva
1. Uinjiniya neMagadzirirwo ezvivakwa: Mukugadzira zvivakwa nezvivakwa, machord anoshandiswa kutsanangura makomba kana maarches mukati mechivako. Semuenzaniso, mubhiriji rine arched kana dome.
2. Astronomy neKufamba: Mukuongorora nyeredzi, kuverenga arc chord kunobatsira pakuona nzira pfupi iri pakati penzvimbo mbiri pamusoro peNyika (daro guru redenderedzwa). Izvi zvakakosha zvikuru mukufambisa ndege nekufamba.
3. Kushandiswa Pakugadzira: Tambo dzehuremu dzinowanzo shandiswa muzvinhu zvakasiyana-siyana zvekugadzira, kubva pamifananidzo, hunyanzvi hwekuona kusvika kumafashoni kugadzira maumbirwo nemapatani erunako.
Hukama hweMasvomhu
Chord iyi haisiyaniswi nedzimwe pfungwa dzemasvomhu dzakadai seEuclidean geometry, trigonometry, uye kunyange calculus. Imwe nzira yekushandisa trigonometry maererano nechord ndeyekuverenga maangles ari mudenderedzwa uye kushandiswa kwayo mukuona hurefu hwechord kana nzvimbo yechikamu chakatenderera.
Semuenzaniso, kana tichiziva kureba kweradius (\(R\)) uye central angle (\(\theta\)) inoumbwa neradii mbiri, tinogona kushandisa trigonometric formulas kuti tione kureba kwechord. Uyu muenzaniso chaiwo wekuti masvomhu anogona kushandiswa sei kugadzirisa matambudziko chaiwo nenzira inoshanda zvikuru.
Muenzaniso weKuverenga
Ngatitii tine denderedzwa rine radius \( R = 10 \) cm uye central angle \( \theta = 60^\circ \). Tichishandisa fomura yehurefu hwechord, tinogona kuverenga seizvi:
\[ c = 2 \cdot R \cdot \sin \left( \dfrac{\theta}{2} \right) \]
\[ c = 2 \cdot 10 \cdot \sin \left( \dfrac{60^\circ}{2} \right) \]
\[ c = 20 \cdot \sin(30^\circ) \]
\[ c = 20 \cdot 0.5 \]
\[ c = 10 \, \chinyorwa{cm} \]
Saka, kureba kwetambo yeuta muchiitiko ichi i10 cm.
Mhedziso
Madenderedzwa nemachord zvinhu zviviri zvakakosha zvejometri zvine mashandisirwo akasiyana-siyana mune zvakasiyana-siyana zvesainzi uye muhupenyu hwezuva nezuva. Kunzwisisa hunhu hwemadenderedzwa nemachord kunotipa ruzivo rwakadzama pamusoro pekuti zvinhu zvinoshanda sei munzvimbo ine mativi maviri uye kunotibatsirawo kugadzirisa matambudziko akasiyana-siyana anoshanda.
Kuburikidza nechinyorwa chino, tinovimba kuti wanzwisisa zviri nani pfungwa dzemadenderedzwa nemachords, uye kuti angashandiswa sei mumamiriro ezvinhu chaiwo. Ungave uri mudzidzi, nyanzvi, kana munhu anofarira masvomhu, kugona pfungwa idzi kuchawedzera ruzivo rwako nehunyanzvi hwako hwekuongorora.
