Sida loo helo bedka of saaraayo ah?

saaraayo waxa uu leeyahay tiro ka mid ah guryaha xisaabeed oo xiiso leh iyo waxaa lagu yaqaan in ay dad tan iyo wakhtiyadii hore. Wakiilada qaar ka mid ah dugsiyada Giriigga ee hore oo fikirka ah in qayb ka hoose (atamka) uu ka samaysan yahay dunida, waxay leeyihiin qaab a of sedjibeke, iyo mysticism iyo fahmayn xataa caabudeen tiradaasi. Maanta wakiilada parascience saaraayo tiriyey guryaha tamarta la yaab leh.

Cube - waa tiradaasi kaamil ah, mid ka mid ah shan adkaha kiciyo. jirka kiciyo - waxaa tiradaasi kala weji duwan ku habboon, dheregto saddex xaaladaha:

1. Dhammaan geesaha iyo weji siman yihiin.

2. xagal u dhexeeya saabsan yihiin (at xaglo dhexeeya wejigooda saaraayo waa loo siman yahay iyo 90 degrees).

3. tirooyinka oo dhan la xidhiidha in ay dusha sare ee ka howgala duruufaysnaa ku wareegsan.

tirada saxda ah ee tirooyinkan loo yaqaan xisaab Greek Theaetetus ee Athens, iyo ardayga ee Plato, Euclid kitaabkii 13aad ee bilowgii wuxuu iyagii siiyey a description xisaabeed faahfaahsan.

Giriigtu waxay qadiimiga ah u nugul iyagoo isticmaalaya doorsoomayaal taranta in lagu qeexo qaab dhismeedka of our dunida, ku lifaaqan adkaha kiciyo macnaha qoto dheer sacral. Waxay rumeysan yahay in mid kasta oo ka mid ah tirooyinka ka dhigan tahay bilowga ah ee caalamiga ah: tetrahedron - saaraayo dab - dhulka, octahedron - icosahedron hawada - dodecahedron biyo - ether. Baaxadda waxaa lagu tilmaamay ku wareegsan oo iyaga kaamil ah calaamad, rabaani ah.

Sidaas daraaddeed, sedjibeke, sidoo kale loo yaqaan hexahedron ah (ka Giriigga ah ee "hex" - ka. 6), - saddex geesood ah oo joogto ah qaab joomateri. Waxaa sidoo kale loo yaqaannaa soo askunmay quadrangular joogto ah ama parallelepiped ah qaab.

saaraayo A lix weji, iyo toban geesaha, iyo siddeed iyo geesaha. Sawirkaan this, waxaad geli kartaa kale polyhedra joogto ah: tetrahedron (tetrahedron la geesaha ee foomka of saddexagal), octahedron (octahedron) iyo icosahedron (icosahedron) ah.

Cube dadab waxaa lagu magacaabaa qeybta xira laba qof qaraabo ah symmetrical xarunta top. Ogaanshaha dherer ah ku laayeen saaraayo ah, waxaad ka heli kartaa dhererka v dadab: v = ^{3 a.}

In sedjibeke, ka howgala sida kor looga hadlay, in la Isasaaray karaa, gacan ah ee ka howgala Isasaaray (r muujinaysaa) waa loo siman yahay si ay u bar dhererka ku laayeen: r = (1/2) a.

Haddii baaxadda saaraayo ku wareegsan tilmaamay, gacan ah ee ka howgala (R muujinaysaa) waa loo siman yahay si: R = (3/2) a.

Wax caadi ah in dhibaato dugsiga su'aasha ah: sida loo xisaabiyo degaanka dusha sare ee saaraayo ah? Mid aad u fudud, kaliya arki sedjibeke. dusha sare ee saaraayo uu leeyahay lix wejigooda ee foomka of god. Sidaa darteed, si aad u hesho bedka of saaraayo ah, marka hore loo baahan yahay in la helo aagga of mid ka mid ah Wajiyadooda iyo in la kordhiyo tiradooda: S _n = ^{2 6a.}

Sida aan ka heli bedka of saaraayo ah, xisaabi degaanka ee weji lateral: S _b = 4a ^2.

From formula this waxaa iska cad in laba weji oo iska soo horjeeda ee sedjibeke - saldhig, iyo afar kale oo ka - side dusha.

Si aad u hesho bedka of saaraayo ah waxay noqon kartaa hab kale. Marka la eego xaqiiqada ah in saaraayo ah - ama bulukeetiga guryaha, waxaad isticmaali kartaa fikradda ah sadex dhinac da'ayeen. Taas macnaheedu waa in saaraayo ah, sida tirada saddex geesood ah ayaa 3-beegyada, oo dhererkiisu (a) iyo width (b) iyo height (c).

Isticmaalka koobin, waxaan xisaabiyo aagga guud ee dusha saddex jibaaranaha ah: S _n = 2 (ac ab + + bc).

Si loo xisaabiyo degaanka ee dusha ka dhisan ee saaraayo ah, wareega saldhigga si loo laablaabi by height ah: _b S = 2c (a + b).

mugga sedjibeke ah - waa wax soo saarka ee saddex qaybood - height ah, width iyo dhererka:
V = abc ama saddex geesaha xiga: V = ^{3 a.}