Yuav ua li cas thiaj li nrhiav thaj tsam ntawm ib lub voos xwmfab?

Lub vib thab nyas muaj ntau yam khoom xyuam xim thiab paub txog cov neeg thaum ub thaum ub. Cov neeg sawv cev ntawm qee cov Greek cov tsev kawm ntawv ntseeg tau tias qhov elementary particles (atoms) ua rau peb lub ntiaj teb yog lub voos xwmfab, thiab mystics thiab esotericists txawm tias deified no daim duab. Thiab hnub no, cov neeg sawv cev ntawm parascience tus cuav rau cov zog ua zog.

Thawv muaj rau sab - nws yog ib tug zoo meej daim duab, ib tug ntawm tsib Platonic cov khib nyiab. Platonic lub cev yog Correct polyhedral daim duab satisfying peb cov neeg mob:

1. Tag nrho nws cov npoo thiab ntsej muag yog sib npaug.

2. Cov ces kaum ntawm cov ntsej muag yog sib npaug (rau ib lub voj voos rau cov ces kaum ntawm cov ntsej muag yog sib npaug li 90 degrees).

3. Tag nrho cov vertices ntawm daim duab kov lub npoo ntawm cheeb tsam uas tau piav txog nws.

Tus naj npawb ntawm cov duab no hu ua Ancient Greek mathematician Teethet Athenian, thiab tus thwj tim ntawm Plato Euclid nyob rau hauv phau ntawv 13 ntawm Origins muab lawv cov lus piav qhia ntau txog kev ua lej.

Cov Greeks qub, tau muab siab hlo nrog kev pab los ntawm ntau qhov los piav txog peb tus kheej lub ntiaj teb, muab Plato lub cev muaj lub ntsiab lus dawb huv. Lawv ntseeg tias txhua yam ntawm cov duab cim lub ntug pib: lub tetrahedron yog hluav taws, lub thawv yog lub ntiaj teb, octahedron yog huab cua, icosahedron yog dej, dodecahedron yog ether. Tus kheej piav nyob ib ncig ntawm lawv symbolized perfection, txoj cai divine.

Yog li ntawd, ib lub voos xwmfab, kuj hu ua ib tug hexahedron (los ntawm Greek "hex" -. 6), - ib tug peb-dimensional kev geometric zoo. Nws kuj yog hu ua quadrangular prism li qub los yog ib lub duab sib luag.

Lub voos xwmfab muaj 6 ntsej muag, kaum ob npoo thiab yim yim. Nyob rau hauv no daim duab, koj yuav tau nkag mus rau lwm yam kev polyhedra: tetrahedron (tetrahedron nrog sawv nyob rau hauv daim ntawv ntawm cov vajvoos peb sab), cov octahedron (octahedron) thiab cov icosahedron (icosahedron).

Thawv muaj rau sab kab pheeb ces kaum yog hu ua tus ya txuas ob tug symmetrical txheeb ze mus rau lub sab saum toj chaw. Paub txog lub voos xwmfab ntug ntev ib tug, koj yuav nrhiav tau qhov ntev ntawm kab pheeb ces kaum v: v = ^3.

Nyob rau hauv lub voos xwmfab, raws li tau hais los saum no, peb tuaj yeem nkag mus rau hauv ib cheeb, thiab lub vojvoog ntawm qhov sau nruab ntug (denoted by r) yuav ua kom ncaj ib nrab ntawm ntug qhov ntev: r = (1/2) a.

Yog hais tias tus kheej piav nyob ib ncig ntawm lub voos xwmfab, tom qab ntawd lub vojvoog ntawm cov lus piav qhia (peb qhia los ntawm R) yuav yog: R = (3/2) a.

Feem ntau hauv tsev kawm ntawv cov teeb meem: yuav ua li cas los xam lub cheeb tsam Qhov ntawm lub voos xwmfab? Nws yooj yim heev, nws 's kuj cuab kev xav txog ib lub voos xwmfab. Qhov saum npoo ntawm lub voos xwm txheej muaj rau ib sab rau hauv daim ntawv plaub fab. Thiaj li, nyob rau hauv thiaj li yuav nrhiav tau cov deg hauv cheeb tsam ntawm lub thawv muaj rau sab, nws yog thawj tsim nyog los nrhiav tau rau thaj tsam ntawm ib yam ntawm rau ib sab thiab kom lawv muaj pes tsawg: S _n = ^{2 6a.}

Cia li raws li peb tau pom cov deg hauv cheeb tsam ntawm lub thawv muaj rau sab, xam cov cheeb tsam ntawm nws cov sab: S _b = 4a ^2.

Los ntawm cov qauv no nws yog qhov tseeb tias ob lub ntsej muag ntawm lub voos xwm txheej yog cov hauv paus, thiab lwm yam plaub yog cov sab nraud.

Koj tuaj yeem nrhiav thaj tsam ntawm lub voos xwmfab ntawm lwm txoj hau kev. Xav txog qhov tseeb tias ib lub voos xwm txheej yog ib lub duab nrawm, ib qho siv tau lub tswv yim ntawm peb qhov chaw dim pa. Qhov no txhais tau tias lub voos xwmfab, yog daim duab peb sab, muaj 3 tsis: ntev (a), dav (b) thiab qhov siab (c).

Siv cov tsis, peb xam tag nrho deg hauv cheeb tsam ntawm lub voos xwmfab: S _n = 2 (b + ac + bc).

Los mus laij lub cheeb tsam ntawm lub sab nto ntawm lub thawv muaj rau sab, lub puag ncig ntawm lub hauv paus yuav tsum tau khoo los ntawm lub qhov siab: S _b = 2C (a + b).

Lub ntim ntawm ib lub voos xwm txheej yog ib yam khoom ntawm peb yam - qhov siab, ntev thiab qhov dav:
V = ABC los yog peb nyob ib sab npoo: V = ^3.