Indlela yokuthola indawo ephindwe cube?

Cube enezinto eziningi izakhiwo ezithakazelisayo zezibalo futhi abantu eyaziwa kusukela ezikhathini zasendulo. Abamele ezinye izikole yamaGreki asendulo yokucabanga ukuthi izinhlayiya aphansi (ama-athomu) ezakha izwe lethu, abe ukuma cube, nezimfihlakalo kanye esoteric ngisho bakhuleka lesi sibalo. Namuhla abameleli parascience cube uyasho emangalisayo amandla izakhiwo.

Cube - kungcono sibalo ephelele, omunye ukudla okuqinile ezinhlanu kaPlato. umzimba kaPlato - ke efanele yehlukene kaningi okubalwa sibalo, eyanelisayo izimo ezintathu:

1. Zonke zihlangene emaceleni ayo nobuso bayalingana.

2. engeli phakathi facets kukhona (at engele phakathi ubuso cube bayalingana futhi 90 degrees).

3. Zonke izibalo ezihlobana ebusweni phezulu sphere circumscribed nxazonke.

Inani eliqondile lezi izibalo ngokuthi sezibalo ngesiGreki Theaetetus of Athens, bathi umfundi kaPlato, Euclid encwadini 13 ekuqaleni wabanika incazelo enemininingwane zezibalo.

AmaGreki asendulo zithambekele usebenzisa eziguquguqukayo ambalwa ukuchaza isakhiwo zezwe lethu, exhunywe ukudla okuqinile kaPlato ezijulile incazelo sacral. Babekholelwa ukuthi ngamunye izibalo limelela ekuqaleni jikelele: Tetrahedron - umlilo cube - emhlabeni, octahedron - emoyeni icosahedron - amanzi dodecahedron - ether. Ububanzi kuchazwa elibazungezile wabonakalisa ukuphelela, laphezulu.

Ngakho, cube, ebizwa nangokuthi i-hexahedron (kusukela lesiGreki "hex" -. 6), - a ngakuthathu njalo umumo weJiyomethri. Ibizwa nangokuthi njalo nezibhebhe quadrangular noma parallelepiped elingunxande.

A cube ubuso eziyisithupha, imiphetho nambili, futhi vertices eziyisishiyagalombili. Kulesi sibalo, ungafaka nezinye polyhedra njalo: Tetrahedron (Tetrahedron nge imiphetho ngesimo onxantathu), i-octahedron (octahedron) kanye icosahedron (icosahedron).

Cube idayagonali ubizwa ngokuthi ingxenye ohlanganisa isihlobo amabili ziyalingana enkabeni phezulu. Ukwazi cube onqenqemeni obuphelele a, ungathola ubude v idayagonali: v = ^3.

Ngo cube, hlaka njengoba kushiwo ngenhla, kungenziwa olotshiwe, lo engaba sphere elalibhalwe (r ezikhonjiswe) kulingana nengxenye ubude onqenqemeni: r = (1/2) a.

Uma kwenkululeko cube echazwe emhlabeni, lo engaba sphere (ezikhonjiswe R) ilingana: R = (3/2) a.

Izimo zethu zihluke kakhulu ezivamile izinkinga esikoleni umbuzo: kanjani ukuba abale endaweni ebusweni cube? Kulula kakhulu, nje ngeso lengqondo cube. Ingaphezulu cube inobuso eziyisithupha ngesimo izikwele. Ngenxa yalokho, ukuze uthole ndawo ubuso cube, kuba okokuqala kudingekile ukuthola indawo omunye ubuso futhi ukwandisa isibalo sabo: S _n = ^{2 6a.}

Njengoba nje siye sathola ndawo ubuso cube, ukubala indawo ubuso bayo lateral: S _b = 4a ^2.

Kule ifomula kuyacaca ukuthi ubuso ezimbili okuphambene cube - sekhaya, futhi kanti ezinye ezine - ohlangothini ebusweni.

Ukuze uthole i-surface area cube kungaba ngenye indlela. Sikhishwe yokuthi cube - a cuboid, ungasebenzisa umqondo zobukhulu amathathu ngekwendzawo. Lokhu kusho ukuthi cube, njengoba isibalo ngakuthathu has 3 nemingcele: ubude (a) futhi ububanzi (b) futhi ukuphakama (c).

Ukusebenzisa lezi nemingcele, esibala ngayo inani surface area cube: S _n = 2 (ab + ac + bc).

Ukuze abale endaweni ohlangothini ebusweni cube, azungezwe we base Wandisa babesazi ngokubheka ukuphakama: S _b = 2c (a + b).

Umthamo cube - iwumkhiqizo izingxenye ezintathu - ukuphakama, ububanzi nobude:
V = abc noma emaphethelweni ezintathu eduze: V = ^3.