Regular Pentagon: m bayanai

Bayani Dictionary Ozhegova ya furta cewa, Pentagon ne na lissafi adadi, iyakance zuwa biyar intersecting Lines da yin sama da biyar ciki kusassari, kazalika da wani abu na irin wannan siffar. Idan duk bangarorin da kusassari da wannan a cikin wani da aka ba polygon, shi ne ake kira a dama (Pentagon).

Mene ne ban sha'awa yau da kullum Pentagon?

Yana da aka a wannan nau'i da aka gina a kan shahara gini na Amurka Tsaro. Na girma na yau da kullum da polyhedrons kawai dodecahedron yana gefen a cikin nau'i na Pentagon. A yanayi babu lu'ulu'u a duk, fuskoki dabam-dabam na wanda za sun yi kama da na yau da kullum Pentagon. Bugu da ƙari kuma, wannan adadi ne mai polygon tare da m yawan kusassari, wanda shi yiwuwa a tayal yankin. Kawai a cikin yawan diagonals na Pentagon dãce da adadin daga sãsanninta. Yarda, wannan shi ne mai ban sha'awa!

Basic kaddarorin da kuma na dabara

Amfani da dabarbari ga wani yau da kullum polygon, za ka iya ayyana dukan zama dole sigogi, wanda yake shi ne Pentagon.

• A tsakiyar kwana α = 360 / n = 360/5 = 72 °.
• A ciki kwana β = 180 ° * (n-2) / n = 180 ° * 3/5 = 108 °. Haka kuma, da Naira Miliyan Xari da ciki kusassari ne 540 °.
• A rabo daga cikin diagonal zuwa a kaikaice gefen shi ne daidaita (1 + √5) / 2, Ina nufin da "zinariya sashe" (kamar 1,618).
• A tsawon gefe, wanda yana da wani yau da kullum Pentagon iya lasafta ta daya daga uku dabarbari, dangane da wanda siga da aka riga aka sani:

• idan ta bayyana a da'irar a kusa da aka sani da radius R, sa'an nan a = 2 * R * zunubi (α / 2) = 2 * R * zunubi (72 ° / 2) ≈1,1756 * R;
• idan c da'irar radius r rubũtacce a yau da kullum Pentagon, a = 2 * r * KU (α / 2) = 2 * r * KU (α / 2) ≈ 1,453 * r.
• ta faru da cewa maimakon a san girma radii diagonal D, sa'an nan da shugabanci aka ƙaddara kamar haka: a ≈ D / 1.618.

• A yankin na yau da kullum Pentagon aka ƙaddara, sake, dangane da wanda siga da aka sani a gare mu:
• idan akwai aka rubũtacce ko circumscribed da'irar, sa'an nan kuma amfani da daya daga biyu dabarbari:

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

• yankin iya tabbatarwa a sanin kawai gefe tsawon wata:

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

Regular Pentagon: gini

Wannan lissafi siffar za a iya gina hanyoyi daban-daban. Alal misali, don shige shi a cikin wani da'irar da wani qaddara radius bisa qaddara ginawa gefe. Jerin da aka bayyana a cikin "Abubuwa" na Euclid a kusa da 300 BC A cikin wani hali, muna bukatar wani kamfas kuma mai mulki. La'akari da yin amfani da wata hanyar da gina wani qaddara karkara.

1. Zaɓi wani sabani radius, kuma zana da'ira, denoting ta cibiyar batu O.

2. A cikin da'irar line, zaɓi wani batu da za su bauta a matsayin daya daga cikin pinnacles na mu Pentagon. Bari wannan zama wani batu A. Haša maki Ya kuma A line kashi.

3. zaro wani layi ta hanyar batu perpendicular zuwa mike layin OA. Sanya mahada wannan mike layin tare da da'irar alama kamar yadda aya B.

4. A tsakiyar nesa tsakanin maki Ya kuma B ginawa batu C.

5. Yanzu zana da'ira wanda cibiyar ne a auna C da kuma wanda ya wuce ta nufi A. Matsayi na ta rarrabawa tare da mike layin likitan mata (zai zama a cikin ta farko da'irar) ne nuna D.

6. Ku gina wani da'irar ta hanyar D, cibiyar da ke cikin Area A na ta rarrabawa da asali da'irar wajibi ne don gane da maki E da F.

7. Yanzu gina wata da'ira wanda cibiyar ne a E. Don yin wannan shi wajibi ne don haka da cewa shi ya wuce ta A. Shi ne wani wuri na rarrabawa da asali da'irar zama dole designate batu G.

8. A karshe, yi da'ira tare da cibiyar A ta cikin aya F. Mark wani mahada batu na asali da'irar H.

9. Yanzu ku ne kawai da a haɗa shi da saman A, E, G, H, F. Our yau da kullum Pentagon zai kasance a shirye!