Nzira yekuverenga chikamu nzvimbo uye nharaunda yenharaunda

Ukuru hwemasvomhu yeharaunda iyi yave ichizivikanwa kubvira kare yeGreece. Kunyange munguva idzodzo dziri kure, vaGiriki vakaona kuti nzvimbo yacho inogara ichienderera mberi, iyo yakasungirirwa kumativi ose nehutambo hwakavharwa. Iyi inokosha nhamba, iyo inoyera mumakiromita masere. Nharaunda iyi inhamba nhamba yemhando yezvigadzirisiti zvemagetsi zvemagetsi (planimetric) uye zvisikwa zvemuviri muvhu (volume).

Parizvino, haisi kungowanikwa mune zvidzidzo zvekuchikoro mune zvidzidzo zve geometry uye mathematics, asiwo mune zvekuongorora nyeredzi, hupenyu hwezuva nezuva, mukuvaka, mukugadzirwa kweijiniya, mukugadzira uye mune dzimwe nzvimbo dzakawanda dzevanhu. Kazhinji kacho kuverenga nzvimbo dzezvikamu, tinoshandisa nzvimbo yekugadzira nzvimbo pakushongedza nzvimbo yemamiriro ekunze kana kana kugadzirisa zvigadziro zvemukati. Nokudaro, ruzivo rwemaitiro ekuverenga nzvimbo dzakasiyana-siyana dzemakemikari ejometri zvichave zvakanaka nguva dzose uye kwose kwose.

Kuti uverenge nzvimbo yerutenduru uye chikamu chepakati, zvakakosha kunzwisisa mitemo ye geometric inofanira kudiwa mukugadzirisa maitiro.

Chokutanga pane zvose, chikamu chendenderedzwa chikamu chechikwata chepandeti yepane ndege, iyo inenge iri pakati peArc yendenderedzwa uye chinyorwa chinochicheka. Usavhiringidza pfungwa iyi nemufananidzo wega. Izvi zvinhu zvakasiyana zvachose.

Chidimbu chikamu chinobatanidza pfungwa mbiri dziri penduru.

Iko kona yekona inoumbwa pakati pezvikamu zviviri - radii. Inoyerwa muzvidimbu ne-arc, pane imwe nzvimbo.

Nharaunda yacho inoumbwa apo chikamu chebato (sphere) chikabviswa neimwe ndege. Muchiitiko ichi, nheyo yechipfuva chemukati ndeyendenderedzwa, uye kukwirira ichinyorwa chinotenderera chinobva kubva pakati pechitenderera kusvika kumativi ose nechokudenga. Iyi nharo yepakati inonzi inonzi vertex yechikamu chebasa.

Kuti uone nzvimbo yechirongwa chemukati, unoda kuziva rutivi rwechikwata chakachekwa uye kukwirira kwebhora rega. Chigadzirwa chezvikamu zviviri izvi chichava nzvimbo yenharaunda yezvikamu: S = 2πRh, uko h kukwirira kwechikamu, 2πR ndiyo mhirizhonga, uye R iyo inharaunda yedenderedzwa guru.

Kuti uverenge nzvimbo yenhengo yedenderedzwa, munhu anogona kushandura kune mazano awa:

1. Kuti uwane chikamu chikamu nenzira yakareruka, zvakakosha kuverenga musiyano pakati penharaunda yemuganhu umo chikamu chacho chakanyorerwa uye nzvimbo ye isosceles katatu chinokwana chikamu chechikamu: S1 = S2-S3, apo S1 ndiyo chikamu chinzvimbo, S2 ndiyo inzvimbo yedunhu Uye S3 ndiyo nzvimbo yekatatu.

Mumwe anogona kushandisa fomu yakatarwa yekuverenga nzvimbo yerutenderedzwa: S = 2/3 * (a * h), pane imwe nheyo yekatatu kana urefu hwechidimbu, h ndiyo kukwirira kwechikamu, iyo inokonzerwa nekusiyana pakati pechikamu chedenderedzwa uye kukwirira kwesusceles katatu.

2. Chikamu chechikamu chinopesana nechimiro chechimiro chinoverengwa sezvinotevera: S = (π R2: 360) * α ± S3, apo π R2 ndiyo nzvimbo yedenderedzwa, α ndiyo chiyero chepakati chekona huru iyo ine arc yenhengo yedenderedzwa, S3 inzvimbo yekatatu , Iyo inoumbwa pakati pemarara maviri edenderedzwa uye nheyo ine kona panzvimbo yakakosha yedenderedzwa uye miviri miviri pamakona ekutaurirana pakati pemhepo uye denderedzwa.

Kana ikona α <180 degrees, chiratidzo chisina kushandiswa chinoshandiswa, kana α> 180 degrees, chiratidzo chikuru chinoshandiswa.

3. Verengai nzvimbo yenzvimbo inogona kuva nemamwe nzira kushandisa trigonometry. Sezvo mutemo, iyo katatu inotorwa sechikonzero. Kana iyo iyo yakakosha yakaenzana muzvidigiri, iyo inotevera inogamuchirwa inogamuchirwa: S = R2 * (π * (α / 180) - chivi α) / 2, uko R2 iyo yakareba yerusvingo rwegenderedzwa, α ndiyo chiyero chepakati chekona huru.

4. Kuverenga nharaunda yechikamu uchishandisa maitiro emagetsi, imwe shanduro inogona kushandiswa, kunze kwekuti ingiro yepakati inotaridzwa mumayera: S = R2 * (α-sin α) / 2, uko R2 iyo chikamu chemukati wechitenderedzwa, α ndicho chiyero chedigiri Pakati pekona.