Pentagon rhoqo: ulwazi oluncinci

Lencazelo Dictionary Ozhegova ithi lepentagoni a umzobo zejiyometri, kuphelele ezintlanu sibezilayini ezidibanayo ezakha engile ezintlanu yangaphakathi, kwakunye nayiphi na into semilo efanayo. Ukuba onke amacala nee-engile ye ezifanayo buyimilo elinikiweyo, oko kuthiwa ilungelo (i-ntlanu).

Yintoni umdla rhoqo pentagon?

Kuye kule fomu eyakhiwe esi sakhiwo adumileyo United States Defense. Of umthamo polyhedrons rhoqo dodecahedron kuphela ngohlangothi ngohlobo pentagon. Endalweni akukho ziikristale konke, iinkalo ekwakumele ukuba zifana pentagon rhoqo. Ngapha koko, lo mzobo yepholigoni ubuncinane inani engile, nto leyo engenakwenzeka okugquma ndawo. Kuphela inani idayagonali lepentagoni lisi kunxibelelana nenani emacaleni aso. Uyavuma, oku kubangela umdla!

iimpawu ezingundoqo kunye nefomula

Ukusebenzisa iifomyula nayiphi yipolygon, uyakwazi ukuchaza zonke iparameters eziyimfuneko, oko kukuthi i-ntlanu.

• I angle α engundoqo = 360 / n = 360/5 = 72 °.
• Le yangaphakathi angle β = 180 ° * (n-2) / n = 180 ° * 3/5 = 108 °. Ngako oko ke, inani engile elingaphakathi-540 °.
• Umlinganiselo idiagonal ukuya kwicala osecaleni ilingana (+ 1 √5) / 2, ngamanye i "kwicandelo yegolide" (malunga 1,618).
• Ubude icala, nto leyo iba pentagon rhoqo ukuze ubalwe ngomnye kwabathathu ifomula, ngokuxhomekeke kuyo parameter sele yaziwa:

• ukuba uchaza kwisangqa eyaziwa kunye radius R, ngoko a = 2 * R * isono (α / 2) = 2 * R * isono (72 ° / 2) ≈1,1756 * R;
• xa r c circle radius abhaliwe a pentagon rhoqo, a = 2 * r * kubatshaba- (α / 2) = 2 * r * kubatshaba- (α / 2) ≈ 1,453 * r;
• kwenzeka ukuba endaweni owaziwa ubukhulu radii oxwesileyo D, ngoko ulwalathiso kubalwa ngolu hlobo lulandelayo: a ≈ D / 1.618.

• Ummandla a pentagon rhoqo imiselwa, kwakhona, ngokuxhomekeke kuyo parameter yaziwa kuthi:
• ukuba kukho libhalwe okanye nezisekelwe isangqa, ngoko sebenzisa enye ifomula ezimbini:

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

• indawo kwakhona imiselwe ukwazi kuphela ubude ecaleni a:

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

pentagon rhoqo: isakhiwo

Le milo lwezibalo zingakhiwa ngeendlela ezahlukeneyo. Umzekelo, ukuba ilingane ube kwisangqa radius kwangaphambili esekelwe kwicala yokwakha kwangaphambili. Ukulandelelanisa iye yachazwa kwi "Elements 'of Euclid malunga 300 BC Enoba kunjalo, kufuneka sibe ikhampasi kunye nomlawuli. Cinga usebenzisa indlela ngolwakhiwo ojikeleyo kwangaphambili.

1. Khetha radius ngendlela engaqondakaliyo, kwaye bazobe isangqa, ebonisa indawo yaso O.

2. On line isangqa kulo, khetha ingongoma eya kusebenza njengomnye uqoqo ka pentagon wethu. Makube oku kube ngongoma A. Dibanisa amanqaku O kunye A ingxenye line.

3. Krwela umgca kwindawo nkqo ukuya kumgca ngqo OA. Beka kuhlangana le kumgca othe ngqo nge mark isangqa njengoko point B.

4. phakathi umgama phakathi amanqaku O kunye B ukwakha indawo C.

5 Ngoku ke zoba isangqa iziko ondlu kwindawo C kwaye udlula kwindawo A. Indawo yonqumlo yalo OB umgca othe ngqo (bekuya kuba ngaphakathi kwisangqa lokuqala) yingongoma D.

6. construct isangqa ngenxa D, embindini leyo Area A ekudibaneni kwawo kwisangqa original kuyimfuneko ukuchonga iingongoma E kunye F.

7. Ke kaloku, ukwakha isangqa iziko na E. Ukwenza oku ukuze udlula A. Kuyinto enye indawo yonqumlo kwisangqa yokuqala ogama kuyimfuneko kuyimfuneko akhethe ingongoma G.

8 Elokugqiba, ukwakha onale kwiziko A kwindawo F. Mark kwikona ingongoma kwisangqa H. yokuqala

9. Ngoku kufuneka kuphela ukudibanisa encotsheni A, E, G, H, F. pentagon kwethu rhoqo uya kuba ukulungele!