Perimeter yekatatu: pfungwa, maitiro, nzira dzokutsunga

Iko katatu ndiyo imwe yenhamba dzepamusoro dzejometri, dzinomiririra zvikamu zvitatu zvekudzivirira kwemigwagwa yakarurama. Iyi nhamba yaizivikanwa nevanodzidza vekare veEgypt, Ancient Greece neAkare China, avo vakawana maitiro akawanda nemitemo yakashandiswa nevasayendisiti, injinki nevagadziri kusvikira nhasi.

Izvo zvikamu zvakanyanya zvechanhatu ndezvi:

• Vertices ndiwo mapurisa emakwikwi ezvikamu.

• Mativi acho ndiwo mapoka akasiyana-siyana.

Kuenderera mberi kubva kune izvozvi zvikamu, kuumba pfungwa dzakadaro sepakati pemutatu, nzvimbo yaro, yakanyorwa uye yakatenderedzwa sedenderedzwa. Kubva kuchikoro inozivikanwa kuti rutivi rwekanyararo ndeyekuverenga nhamba yemari yemativi ose matatu. Panguva imwecheteyo, nhamba yakawanda yemafungiro inozivikanwa nekuwana kukohwa kwakapiwa, zvichienderana nemashoko ekutanga ayo muongorori ane mune imwe kana imwe nyaya.

1. Nzira yakareruka yekuwana yakaenzana nekatatu inoshandiswa munyaya iyo nhamba dzepamusoro dzezvikamu zvayo zvitatu (x, y, z) dzinozivikanwa, sechigumisiro:

P = x + y + z

2. Chimiro chekufananidza katatu chinogona kuwanikwa kana tichiyeuka kuti mumufananidzo uyu mativi ose, zvisinei, semakumbo ose, akaenzana. Kuziva urefu hwemutivi urwu, chiyero chekanyengeri chekufananidza chinogona kutsanangurwa neshoko:

P = 3x

3. Mune isosceles katatu, kusiyana nemakondohwe akafanana, maviri chete gareal ane mativi akaenzana nenhamba, saka munyaya iyi mhepo inowanzove yakaita seyiyi:

P = 2x + y

4. Nzira dzinotevera dzinodiwa mumamiriro ezvinhu apo nhamba dzenhamba dzisiri dzose dzinozivikanwa. Semuenzaniso, kana chidzidzo chacho chine dhamoni pamativi maviri, uye iyo yakaenzana pakati pavo inozivikanwa, ipapo mhirizhonga yekatatu inogona kuwanikwa nekutsanangurira rutivi rwechitatu uye inozivikanwa engona. Muchiitiko ichi, iyi yechitatu iyo inowanikwa nemurairo:

Z = 2x + 2y-2xycosβ

Kuenderera mberi kubva pane izvi, chiyero chekatatu chichave chakaenzana ne:

P = x + y + 2x + (2y-2xycos β)

5. Muchiitiko chacho kana urefu hwepakati pekona katatu huripo uye huwandu hunoenderana nehuwandu hwemakona maviri akaenzana nawo hunenge huchizivikanwa, chiyero chekatatu chinogona kuverengwa kubva pane sine theorem:

P = x + sinβ x / (sin (180 ° -β)) + sinγ x / (sin (180 ° -γ))

6. Pane zviitiko apo zvizivo zvinozivikanwa zvependeredzwa zvakanyorwa mairi zvinoshandiswa kuwana rutivi rwetatu. Uyu maitiro anozivikanwawo nevanhu vazhinji kubvira zuva rechikoro:

P = 2S / r (S inharaunda yedenderedzwa, iyo r inharaunda yayo).

Kubva pane zvose zvataurwa pamusoro apa, zvinogona kuonekwa kuti rutivi rwekanyararo runogona kuwanikwa nenzira dzakasiyana-siyana, zvichienderana nemashoko iyo muongorori ane. Mukuwedzera, pane dzimwe mimwe mimwe mamiriro ekuwana kuwana chipo chapiwa. Nokudaro, chiyero chacho chimwe chezvinhu zvakakosha zvikuru uye zvigadziro zvekatenderedzwa yakarurama.

Sezvinozivikanwa, katatu yakadaro ndeye chimiro chine mapande maviri akaita sendima yakarurama. Nhamba yekona katatu yakarurama inowanika kuburikidza nenhamba dzekutaura kwehuwandu hwemakumbo ose uye nehuwandu. Kana muongorori achiziva mapoka maviri chete, iyo yakasara inogona kuverengwa kuburikidza nedzidziso yakakurumbira yePythagoras: z = (x2 + y2) kana makumbo acho ose achizivikanwa, kana x = (z2 - y2) kana chikonzero uye kati ichizivikanwa.

Muchiitiko chekuti urefu hwenheyo uye imwe yemakona ari pedo neyo inozivikanwa, iyo imwe nhengo mbiri inopiwa nemazwi: x = z sinβ, y = z cosβ. Muchiitiko ichi, chiyero chekatatu chinotenderera chichave:

P = z (cosβ + sinβ + 1)

Uyewo chiitiko chakakosha ndiko kuverenga kwehuwandu hwekanguva (kana kuti equilateral) katatu, kureva, chimiro umo mativi ose nemakona ose akaenzana. Kuenzanisa kwepakati pekatatu yakadaro pane ruzivo rwunozivikanwa hakuiti dambudziko chero ripi zvaro, zvisinei, kazhinji muongorori anoziva imwe dheinhe. Saka, kana ruzivo rwechikwata chakanyorwa ruchizivikanwa, rutivi rwekatatu rinowanikwa runowanikwa nemurairo:

P = 6√3r

Uye kana ruzivo rwechikwata chakatenderedzwa runopiwa, chiyero chekatatu chinowanikwa chinotevera:

P = 3√3R

Mafomu anofanira kuchengetwa nepamusoro kuti ave nekubudirira kushandiswa mukuita.