Ntawm lub perimeter ntawm daim duab peb sab: lub tswvyim, tus yam ntxwv, txoj kev rau kev txiav txim

Daim duab peb sab yog ib tug ntawm cov yooj yim geometric duab sawv cev peb kev sib tshuam kab theem. Qhov no xam tau paub kawm siab ntawm ancient tim lyiv teb chaws, ancient Greece thiab Tuam Tshoj, uas tau coj feem ntau ntawm cov qauv thiab cov qauv siv los ntawm kws tshawb fawb, engineers thiab designers kom deb li deb.

Lub ntsiab tivthaiv qhov chaw ntawm daim duab peb sab yog:

• ncov - lub taw tes rau ntawm kev sib tshuam ntawm cov kab txiav.

• tog - sib tshuam kab theem.

Raws li cov kev Cheebtsam, formulate tswv yim xws li lub perimeter ntawm lub daim duab peb sab, nws cheeb tsam, inscribed thiab circumscribed lub voj voog. Los ntawm tsev kawm ntawv peb yeej paub hais tias ntawm lub perimeter ntawm daim duab peb sab yog ib tug hais txog zauv qhia txog lub sum ntawm tag nrho cov peb ntawm nws cov sab. Nyob rau tib lub sij hawm cov qauv rau kev nrhiav cov nqi no yog lub npe hu ib tug ntau, nyob ntawm seb cov nqaij nyoos cov ntaub ntawv uas soj ntsuam muaj nyob rau hauv ib tug cov ntaub ntawv.

1. Qhov yooj yim txoj kev uas yuav nrhiav tau ntawm lub perimeter ntawm daim duab peb sab yog siv nyob rau hauv lub rooj plaub thaum txog zauv qhov tseem ceeb yog lub npe hu rau tag nrho peb ntawm nws cov sab (x, y, z), raws li ib tug tsim nyog tau:

P = x + y + z

2. Lub puag ncig ntawm ib tug equilateral triangle nrhiav tau, yog hais tias peb nco ntsoov hais tias qhov no daim duab rau tag nrho cov tog, txawm li cas los, raws li tag nrho cov ces kaum muaj sib npaug. Paub qhov ntev ntawm lub sab ntawm ib tug equilateral daim duab peb sab puag ncig yog xam raws li nram no:

P = 3x

3. ceskaum daim duab peb sab, nyob rau hauv sib piv rau equilateral, tsuas yog ob tug sab muaj tib lub zauv tus nqi, Txawm li cas los nyob rau hauv rooj plaub no tus puag ncig nyob rau hauv lub dav dav daim ntawv no yuav tsum tau raws li nram no:

P = 2 x + y

4. Cov nram qab no txoj kev yog tsim nyog nyob rau hauv tus neeg mob qhov twg lub npe hu hais txog zauv qhov tseem ceeb yog tsis yog txhua txhua ob tog. Piv txwv li, yog hais tias tus txoj kev tshawb no yog cov ntaub ntawv nyob rau hauv ob sab, thiab tseem paub lub therebetween, ntawm lub perimeter ntawm daim duab peb sab yuav pom los ntawm kev txiav txim rau peb tog thiab paub lub. Nyob rau hauv cov ntaub ntawv no, lub thib peb tog yuav tsum pom los ntawm cov mis:

z = 2 x + 2y-2xycosβ

Raws li, ntawm lub perimeter ntawm daim duab peb sab yog sib npaug zos rau:

P = x + y + 2 x + (2y-2xycos β)

5. Nyob rau hauv lub rooj plaub uas lub chiv muab ntev tsis ntau tshaj ib sab ntawm lub duab peb sab thiab lub npe hu hais txog zauv tseem ceeb ntawm cov ob ces kaum uas nyob ib sab thereto, ntawm lub perimeter ntawm daim duab peb sab yuav xam rau lub hauv paus ntawm lub sine theorem:

P = x + sinβ x / (kev txhaum (180 ° -β)) + sinγ x / (kev txhaum (180 ° -γ))

6. Muaj mob qhov twg yuav nrhiav lub perimeter ntawm lub daim duab peb sab siv lub npe hu tsis vajvoog inscribed nyob rau ntawd. Qhov no mis yog zoo dua lub npe hu rau ntau tseem nyob rau ntawm lub tsev kawm ntawv:

P = 2s / r (S - cheeb tsam ntawm lub vajvoog, whereas r - lub voos kheej-kheej).

Ntawm tag nrho cov saum toj no nws yog tseeb hais tias tus nqi ntawm lub perimeter ntawm ib tug peb tog muaj peev xwm yuav nrhiav tau nyob rau hauv ntau txoj kev, nyob rau hauv lub hauv paus ntawm cov ntaub ntawv nyob rau ntawm tus kws tshawb fawb. Nyob rau hauv tas li ntawd, muaj ib tug ob peb tshwj xeeb no, nrhiav cov nqi no. Yog li, tus puag ncig yog ib tug ntawm cov tseem ceeb tshaj plaws qhov tseem ceeb thiab cov yam ntxwv ntawm txoj cai-angled daim duab peb sab.

Raws li yog lub npe hu, hu li ntawd daim duab peb sab zoo lawm, ob tog ntawm uas tsim ib txoj cai kaum sab xis. Ntawm lub perimeter ntawm ib txoj cai daim duab peb sab yog lub sum ntawm ib tug numeric qhia los ntawm ob lub ob txhais ceg thiab lub hypotenuse. Nyob rau hauv cov ntaub ntawv uas, yog tias tus kws tshawb fawb paub ntaub ntawv tsuas yog nyob rau ob sab, tseem yuav tshuav yuav xam siv lub zoo-paub Pythagorean theorem: z = (x2 + y2), yog hais tias paub, ob txhais ceg, los yog x = (Z2 - y2), yog hais tias paub hypotenuse thiab txhais ceg.

Nyob rau hauv cov ntaub ntawv uas, yog hais tias peb paub tus hypotenuse ntev thiab uas nyob ib sab ib tug ntawm cov nyob rau hauv nws cov ces kaum, qhov ob sab yog muab los ntawm: x = z sinβ, y = z cosβ. Nyob rau hauv cov ntaub ntawv no, ntawm lub perimeter ntawm ib txoj cai daim duab peb sab yog sib npaug zos rau:

P = z (cosβ + sinβ +1)

Tsis tas li ntawd, ib tug tshwj xeeb cov ntaub ntawv yog muab xam rau ntawm qhov tseeb puag ncig (los yog equilateral) daim duab peb sab, uas yog, xws li ib tug duab nyob rau hauv uas tag nrho cov sab thiab tag nrho cov ces kaum muaj sib npaug. Muab xam los ntawm lub perimeter ntawm lub daim duab peb sab ntawm cov paub ces yog tsis muaj teeb meem, txawm li cas los, soj ntsuam ntawm feem ntau paub ib co lwm cov ntaub ntawv. Yog li, yog hais tias tus paub voos kheej-kheej ntawm lub inscribed vajvoog, ntawm lub perimeter ntawm ib tug tsis tu ncua daim duab peb sab yog muab los ntawm:

P = 6√3r

Yog hais tias muab tus nqi ntawm lub voos kheej-kheej ntawm lub circumscribed lub voj voog, ib tug equilateral daim duab peb sab puag ncig yog pom raws li nram no:

P = 3√3R

Qauv yuav tsum nco ntsoov rau ntse priment nyob rau hauv xyaum.