Nzvimbo imwe equilateral Triangle

Pakati geometric nenhamba, izvo munyaya chikamu geometry, inonyanyoshandiswa nawo mhinduro matambudziko akasiyana-siyana pamwe chete Triangle. Zviri geometric mufananidzo inoumbwa pamitsara mitatu. Ivo pane imwe nguva regai piringisha uye vasina kuenderana. Zvinokwanisika kupa akasiyana Tsanangudzo: Triangle chinhu polygonal namahwindo munyonga zvinosanganisira vezvikwata nhatu umo mavambo ayo uye pakupedzisira chokuita pane imwe nguva. Kana mativi ose matatu munokosha vakaenzana, saka chinhu equilateral Triangle, kana, sezvo vachiti, ndizvo equilateral.

Sei isu kuona nzvimbo imwe equilateral Triangle? Kugadzirisa matambudziko aya zvakafanira kuziva zvimwe zvivako zviri geometric nenhamba. Chekutanga, mune ichi pamusoro netriangle mhando dzose pamakona vakaenzana. Chechipiri, kukwirira iyo kunotangira kubva kumusoro kusvikira nechigadziko, zvose evaMedhia uye kukwirira. Izvi zvinoratidza kuti kukwirira chakaderedzwa mutengo kuti Triangle rinokamukana huviri vakaenzana pamakona, uye negwara - huviri zvakaenzana zvikamu. Sezvo equilateral Triangle rinoumbwa maviri zvokuridza zvakanaka-angled, kana kusarudza zvinodiwa tsika vanofanira kushandisa Pythagorean theorem no.

Pakuverenga nzvimbo netriangle anogona kuitwa nenzira dzakasiyana, zvichienderana anozivikanwa kwazvo.

1. Funga equilateral netriangle pamwe anozivikanwa divi B kukwirira h. nzvimbo netriangle mune iyi ichava akaenzana mumwe-hafu kurutivi chigadzirwa uye kukwirira. In nzira yemaitiro zvingadai seizvi:

S = 1/2 * f * b

Mumashoko, mashoko equilateral Triangle nzvimbo akaenzana mumwe-hafu yayo divi basa uye kukwirira.

2. Kana uchiziva chete mutengo divi, asati kutsvaka nzvimbo, zvakakodzera exchange kukwirira kwayo. Nokuti ichi tikafunga hafu Triangle, inova kukwirira mumwe makumbo, iyo hypotenuse - kurutivi rwuno Triangle, uye yechipiri gumbo - hafu panhivi Triangle maererano ehupfumi ayo. isu tose kubva chete Pythagorean theorem no havatsananguri pakakwirira Triangle. Sezvazvakanyorwa anozivikanwa kubva, mativi ose hypotenuse unoenderana vakaverenga dzinoungana vanhu makumbo. Kana tikafunga hafu Triangle, muchiitiko ichi kudivi ndiye hypotenuse, divi hafu - iri gumbo, uye kukwirira - wechipiri.

(B / 2) ² + H2 = b², saka

h² = b²- (b / 2) ². Hechino chimwe dhinomineta:

h² = 3b² / 4,

H = √3b² / 4,

H = b / 2√3.

Sezvaunogona kuona, kureba mufananidzo pasi kufunga akaenzana zvibereko hafu chake uye mudzi zvitatu.

Dzinomiririra mu fomura uye ona: S = 1/2 * B * b / 2√3 = b² / 4√3.

Ndiko, nzvimbo isina equilateral netriangle akaenzana zvibereko divi rechina mativi uye muchivara mudzi zvitatu.

3. Pane vamwe mabasa apo unofanira kuona nzvimbo imwe equilateral netriangle pane imwe yakakwirira. Uye zviri nyore pane kare. Takatodzidza vakauya yapfuura nyaya, kuti h² = 3 b² / 4. Uyezve zvakakodzera pano yokubva divi uye kuchiiswa kupinda nzvimbo fomura. Zvichaita seizvi:

b² = 4/3 * h², saka b = 2h / √3. Dzinomiririra fomura kuti sikweya, tinowana:

S = 1/2 * f * 2h / √3, saka S = h² / √3.

Pane matambudziko kana zvakakodzera kuwana nzvimbo isina equilateral netriangle achitevedza nharaunda yacho yakanyorwa kana circumscribed denderedzwa. Nokuti kukarukureta ichi, panewo zvimwe Masvomhu ayo ndeinotevera: r = √3 * b / 6, R = √3 * b / 3.

Act kare zvaizivikanwa kwatiri musimboti. Aine anozivikanwa nharaunda, isu kuona kubva kurutivi Formula uye overenga parutivi dzinomiririra chinozivikanwa kukosha nharaunda. The vakawana ukoshi iri kuchiiswa mu nechakare payakavakirwa nokuti pakuverenga nzvimbo kurudyi Triangle kuita svomhu uye kuwana zvaida ukoshi.

Sezvaunogona kuona, kuti dzipedze zvinetso zvakafanana, unofanira kuziva kwete chete ehupfumi ane equilateral netriangle uye Pythagorean theorem no, uye, uye, uye nharaunda yacho yakanyorwa denderedzwa. Nokuti wakabata ruzivo mhinduro matambudziko akadaro haazorambi vavatore kumbondinetsa.