Zonse Pentagon: mfundo osachepera

Ofotokozera Dictionary Ozhegova limanena kuti Pentagon ndi zojambula chithunzi, okha mizere asanu intersecting amapanga asanu kumathandiza kupeza ngodya zabwino mkati, komanso chinthu chilichonse cha mawonekedwe ofanana. Ngati mbali zonse ndipo kumathandiza kupeza ngodya zabwino za yemweyo mu polygon anapatsidwa, umatchedwa ufulu (ndi Pentagon).

Kodi chidwi zonse Pentagon?

Iwo anali mu mtundu umenewu zinamangidwa pa nyumba yotchuka ya United States silikhali. Buku la polyhedrons zonse yekha dodecahedron ali m'mphepete mwa mawonekedwe a Pentagon. Mu chikhalidwe palibe makhiristo pa onse, mbali yomwe anafanana ndi Pentagon zonse. Komanso, chithunzi ichi ndi polygon ndi mlingo wa kumathandiza kupeza ngodya zabwino, zomwe n'zosatheka matailosi m'deralo. Only chiwerengero cha diagonals a Pentagon mogwirizana ndi chiwerengero cha m'mbali mwake. Gwirizanani, ichi ndi chidwi!

katundu Basic ndi njira

Ntchito mitunduyi kwa polygon lililonse, mukhoza chimatanthauza magawo onse oyenera, amene ali Pentagon.

• Chapakati ngodya α = 360 / N = 360/5 = 72 °.
• Lamkati ngodya β = 180 ° * (n-2) / = 180 ° * 3/5 = 108 ° N. Choncho, Uwerenge kumathandiza kupeza ngodya zabwino mkati ndi 540 °.
• The chiŵerengero cha opendekera ku mbali lateral ndi wofanana (1 + √5) / 2, i.e. "Golden gawo" (pafupifupi 1,618).
• Kutalika kwa mbali, amene ali Pentagon zonse akhoza kuchita masamu ndi mmodzi mwa atatu mitunduyi, malingana ndi zomwe chizindikiro kale kuti:

• ngati limafotokoza mozungulila ndi kudziwika ndi utali wozungulira R, ndiye = 2 * R * tchimo (α / 2) = 2 * R * tchimo (72 ° / 2) ≈1,1756 * R;
• pamene m'ma bwalo utali wozungulira r Mukhoza alembedwa mu Pentagon wokhazikika, = 2 * r Mukhoza * tg (α / 2) = 2 * r Mukhoza * tg (α / 2) ≈ 1,453 * r Mukhoza;
• izo zimachitika kuti m'malo kudziwika ukulu radii opendekera D, ndiye malangizo anatsimikiza motere: a ≈ D / 1.618.

• M'dera la Pentagon zonse anatsimikiza, kachiwiri, malingana ndi zomwe chizindikiro amadziwika kuti:
• ngati pali linalembedwa kapena circumscribed bwalo, ndiye ntchito imodzi mwa mitunduyi awiri:

S = (n * ndi r Mukhoza * ) / 2 = 2,5 * ndi r Mukhoza * kapena S = (n * R ² machimo α) / 2 ≈ 2,3776 * R ^2;

• m'dera amathanso titsimikize podzindikira yekha mbali kutalika ndi:

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

Zonse Pentagon: nyumbayi

Izi mawonekedwe zojambula akhoza kumangidwa m'njira zosiyanasiyana. Mwachitsanzo, kuti zigwirizane ndi kukhala bwalo ndi utali wozungulira anakonzeratu zochokera anakonzeratu timakhala mbali. Zinayendera wakhala amafotokozedwa "Zochitika" wa Euclid mozungulira 300 BC Mulimonsemo, tiyenera kampasi ndi wolamulira. Yesani kuganizira kugwiritsa ntchito njira yomanga ndi circumference anakonzeratu.

1. Sankhani utali wozungulira lachabechabe, ndi jambulani chozungulira china, kutanthauza likulu lake mfundo O.

2. Pa mzere bwalo, sankhani mfundo imene adzatumikira monga mmodzi wa pinnacles a Pentagon wathu. Lolani iyi ikhale mfundo A. polumikiza mfundo O ndi gawo mzere.

3. Lembani mzere mwa mfundo perpendicular kwa mzere wolunjika o. Ikani mphambano za mzere uwu molunjika ndi chizindikiro bwalo monga mfundo B.

4. pakati pa mtunda wa pakati pa mfundo O ndi B kumanga mfundo C.

5. Tsopano jambulani chozungulira amene likulu ndi pa mfundo C ndi zomwe umadutsa mpaka A. Malo mphambano ake ndi molunjika mzere ob (zingakhale mwa bwalo yoyamba) akulozera D.

6. amange bwalo kudzera D, likulu la amene ali Area A a mphambano yake ndi bwalo oyambirira zothandiza kupeza mfundo E ndi F.

7. Tsopano kumanga bwalo amene likulu ndi ku E. Kuti tichite zimenezi m'pofunika kuti umadutsa A. Ndi malo ena mphambano ya bwalo choyambirira n'kofunika tisonyezeni mfundo G.

8. Pomalizira pake, kupanga bwalo ndi pakati mwa mfundo F. Mark mfundo ina mphambano za original bwalo H.

9. Tsopano muli ndi kulumikiza pamwamba A, E, G, H, F. Pentagon nthawi zonse adzakhala okonzeka!