Yadda za a sami surface yankin na shigen sukari?

A shigen sukari yana da yawan sha'awa ilmin lissafi Properties da aka sani zuwa ga mutane tun lokacin da. Wakilai daga wasu daga cikin tsoho Greek mazhabobin cewa na farko barbashi (kwayoyin halitta) cewa yin up mu duniya, da siffar wani shigen sukari, da kuma Sufi da esoteric ko bauta wa wannan adadi. Yau wakilan parascience yaba shigen sukari ban mamaki makamashi Properties.

Cube - yana da cikakken adadi, daya daga cikin biyar Platonic daskararru. Platonic jiki - shi dace Multi-faceted adadi, gamsarwa uku yanayi:

1. Duk da gefuna da kuma fuskokin su daidaita.

2. A kusassari tsakanin fuskoki dabam-dabam ne (a kusassari tsakanin shigen sukari fuskoki ne daidai da 90 digiri).

3. All Figures lãbartãwa a saman surface na Sphere circumscribed a kusa da shi.

A daidai adadin wadannan Figures kira Greek lissafi Theaetetus na Athens, kuma daliba Plato, Euclid a cikin 13th littafin na farkon ba su da wani cikakken ilmin lissafi bayanin.

A zamanin d Helenawa masu yiwuwa ga yin amfani da gwada yawa canji don bayyana tsarin da mu duniya, a haɗe zuwa Platonic daskararru zurfin sacral ma'anar. Sun yi imani da cewa kowane daga cikin Figures wakiltar farkon na duniya: tetrahedron - wuta shigen sukari - duniya, octahedron - iska icosahedron - ruwa dodecahedron - ether. Bigiren da aka bayyana a kusa da su nuna alamar kamala, allahntaka.

Saboda haka, wani shigen sukari, wanda kuma ake kira mai hexahedron (daga Girkanci "hex" -. 6), - wani mai hawa uku na yau da kullum na lissafi siffar. Haka kuma an kira yau da kullum quadrangular Prism ko wani rectangular parallelepiped.

A shigen sukari shida fuskoki goma sha biyu gefuna, da kuma takwas vertices. A wannan adadi, za ka iya shiga sauran yau da kullum polyhedra: tetrahedron (tetrahedron da gefuna a cikin nau'i na triangles), da octahedron (octahedron) da kuma icosahedron (icosahedron).

Cube diagonal ne ake kira da rabi a haɗa da biyu tsakaitã dangi zuwa saman cibiyar. Sanin shigen sukari baki tsawon wata, za ka iya samun tsawon diagonal v: v = wani ^3.

A wani shigen sukari, kamar yadda aka tattauna a sama, za a iya rubũtacce Sphere, da radius daga cikin rubũtacce Sphere (denoted r) shi ne daidai rabin gefen tsawon: r = (1/2) a.

Idan da ikon yinsa, daga cikin shigen sukari da aka bayyana a kusa, da radius daga cikin Sphere (denoted R) ne, sunã daidaita: R = (3/2) a.

Quite na kowa a makaranta matsaloli da tambaya: yadda za a lissafta da wuri surface na shigen sukari? Very sauki, kawai ganin wani shigen sukari. A surface na shigen sukari yana shida fuskoki a cikin nau'i na murabba'ai. Sanadiyar haka ne, domin ya sami surface yankin na shigen sukari, shi ne na farko zama dole a samu a yankin na daya daga cikin fuskokin, kuma don su kara yawan: S _n = ^{2 6a.}

Kamar yadda muka samu da surface yankin na shigen sukari, lissafi da yankin na ta kaikaice fuskoki: S _b = 4A ^2.

Daga wannan dabara a fili yake cewa biyu daura da fuskoki na wani shigen sukari - mai tushe, da kuma sauran hudu - gefen surface.

Don samun da surface yankin na shigen sukari na iya zama wata hanya dabam. Ganin cewa a cikin shigen sukari - a cuboid, za ka iya amfani da ra'ayi na uku na sarari girma. Wannan yana nufin cewa shigen sukari, kamar yadda wani mai hawa uku adadi yana 3 sigogi: tsawon (a) da kuma fadin (b) da kuma tsawo (c).

Amfani da wadannan sigogi, da muka lissafta jimlar surface yankin na shigen sukari: S _n = 2 (ab + ac + bc).

Don lissafi da yankin na gefen surface na shigen sukari, da kewaye daga cikin tushe da za a yawaita da tsawo: S _b = 2c (a + b).

A girma daga cikin shigen sukari - ne samfurin na uku aka gyara - da tsawo, nisa da tsawon:
V = ABC ko uku m gefuna: V = wani ^3.