Pentagon ejwayelekile: ulwazi ubuncane

Esishoyo Dictionary Ozhegova uthi pentagon kuyinto sibalo Jomethri, kungagcini imigqa emihlanu intersecting ezakha engele zangaphakathi amahlanu, kanye nanoma yikuphi into ukuma okufanayo. Uma zonke izinhlangothi futhi engeli okufanayo endaweni ipholigoni unikezwa, ubizwa ngokuthi ngakwesokudla (nePentagon).

Kuyini ezithakazelisayo pentagon njalo?

Kwakuthinta kuleli fomu selakhiwe phezu isakhiwo odumile wase-United States Wezokuvikela. Umthamo polyhedrons njalo dodecahedron kuphela has onqenqemeni ngesimo pentagon. Emvelweni azikho zinhlayiya nhlobo, izici eyayizobadabulisa lalifana pentagon njalo. Ngaphezu kwalokho, lesi sibalo a ipholigoni ngenombolo ubuncane engeli, okuyinto engenakwenzeka ukuba Tile ndawo. Kuphela inani diagonals we pentagon ilingane nesibalo lwaso. Ngiyavuma, lokhu kuthakazelisa!

izakhiwo Eyisisekelo kanye formula

Ukusebenzisa amafomula nganoma yisiphi ipholigoni njalo, ungakwazi ukuchaza zonke nemingcele ezidingekayo, okuyinto nePentagon.

• Emaphakathi engela α = 360 / n = 360/5 = 72 °.
• I kwangaphakathi engela β = 180 ° * (n-2) / n = 180 ° * 3/5 = 108 °. Ngakho, isamba engeli elingaphakathi 540 °.
• Isilinganiso idayagonali kuse ecaleni lateral uyalingana (1 + √5) / 2, isb le "ngxenye osemqoka" (cishe 1,618).
• Ubude ohlangothini, okuyinto has a pentagon njalo kungenzeka ibalwa ngomunye ezintathu amafomula, okuya ngokuthi yikuphi ipharamitha isivele eyaziwa:

• uma uchaza indulungu eyaziwa futhi engaba R, ke = 2 * R yesono (α / 2) = 2 * R yesono (72 ° / 2) ≈1,1756 * R;
• lapho c umbuthano engaba r alotshiwe a pentagon elivamile, = 2 * r * TG (α / 2) = 2 * r * TG (α / 2) ≈ 1,453 * r;
• kwenzeka ukuthi esikhundleni aziwayo ezidlula radii D idayagonali ke isiqondiso kunqunywa kanje: a ≈ D / 1.618.

• Kwendawo pentagon njalo uzimisele, futhi, kuye ngokuthi yiziphi ipharamitha yaziwa kithi:
• uma kukhona eqoshwe noma circumscribed embuthanweni, bese usebenzisa elinye amafomula ezimbili:

S = (n * a r * ) / 2 = 2,5 * a r * noma S = (n * R ² yesono α) / 2 ≈ 2,3776 * R ^2;

• endaweni ingaphinda kunqunywa ukwazi kuphela ohlangothini obuphelele a:

S = (5 * ² * tg54 °) / 4 ≈ 1,7205 * ^2.

pentagon ejwayelekile: isakhiwo

Lokhu ukuma weJiyomethri lingakhiwa ngezindlela ezahlukene. Ngokwesibonelo, ukuze uvumelane kube umbuthano engaba predetermined esekelwe predetermined Yakha ohlangothini. Ukulandelana iye yachazwa ezinhlwini ezingu le "Imisuka" of Euclid azungeze 300 BC Kunoma ikuphi, sidinga ikhampasi nombusi wezwe. Cabanga usebenzisa indlela yokwakha umuntu selilonke kusengaphambili.

1. Khetha engaba kabi amandla akhe, futhi ukudweba indilinga, elisho isikhungo salo iphuzu O.

2. Emgqeni mbuthano, khetha iphuzu oluzosiza njengoba omunye elineziqongo ka pentagon yethu. Ake lokhu kube A. iphuzu Xhuma amaphuzu O no ingxenye umugqa.

3. Dweba umugqa ngokusebenzisa iphuzu perpendicular umugqa oqondile OA. Beka empambana lo mugqa iqonde nge uphawu umbuthano njengoba iphuzu B.

4. Ngesikhathi phakathi ibanga phakathi kwezindawo O B Yakha iphuzu C.

5. Manje ukudweba indilinga ogama nendawo endaweni C no okuyinto sidlula iphuzu A. Isikhundla empambana yayo nge umugqa oqondile OB (kuyoba ngaphakathi umbuthano wokuqala) kuyinto ukhombe D.

6. Yakha umbuthano ngokusebenzisa D, maphakathi okuyinto Area A empambana yayo nge emjikelezweni yasekuqaleni kuyadingeka ukuhlonza amaphuzu E F.

7. Manje ukwakha umbuthano kabani isikhungo ungaphakathi E. Ukuze wenze lokhu kubalulekile ukuze sidlula A. Kuyinto omunye esikhundleni empambana emjikelezweni yasekuqaleni kuyadingeka ekhethwe iphuzu G.

8. Ekugcineni, ukwakha umbuthano isikhungo A ngokusebenzisa iphuzu F. Mark elinye iphuzu empambana emjikelezweni H. yasekuqaleni

9. Manje kuphela ukuxhuma phezulu A, E, G, H, F. pentagon qobe uzolunga!