Yuav ua li cas mus nrhiav tau qhov ib ncig

Ib tug kaw txoj kab uas faib lub dav hlau mus rau hauv ob qhov chaw kawg (sab hauv - lub voj voog) thiab infinite (sab nraum kab), muab hais tias nws muaj ob peb txog kev zog, hu ua ib lub voj voog. Piv txwv li, qhov yuav tsum tau ua raws li equidistance ntawm cov ntsiab lus dag rau ntawm no, los ntawm ib tug taw tes ua qhov chaw ntawm lub voj voog. Rau ib lub dav hlau txhais los ntawm lub vajvoog, muaj ib co ntau yam ntxwv. Cov muaj xws li:

• voos kheej-kheej (qhov kev ncua deb ntawm tej taw tes dag rau nws, rau qhov chaw, R);
• txoj kab uas hla (kab faib ib lub voj voog rau hauv ob sib npaug zos qhov chaw, dhau los ntawm ob lub ntsiab lus thiab kos lub voj voog qhov chaw ntawm lub vajvoog, D);
• cheeb tsam txaus qhia qhov luaj li cas ntawm lub vajvoog, S;
• qhov ntev ntawm lub kaw txoj kab uas qhia txog ib lub voj voog (xaiv los ntawm tsab ntawv Ḻ).

Yog li, Ḻ tsis yog tsuas yog ib tug ntau cov yam ntxwv ntawm lub vajvoog, tab sis ib tug kaw kab, li ntawd, lo lus teb rau lo lus nug - yuav ua li cas kom paub qhov ib ncig, yog muaj feem xyuam rau cov geometrical tswv yim.

Qhov kev ncua deb khiav los ntawm ib tug sab nraud yam khoom dav hlau kaw nkhaus puag ncig zoo yog sib npaug zos rau qhov ntev ntawm txoj kab encircling nws. Qhov no ntau soj ntsuam ntawm lub ib ncig yog siv nyob rau hauv cov kev ntsuas ntawm lub cev khoom, tab sis kuj xav tias yuav thaum paub daws teeb geometric duab. Lub sij hawm muaj ib tug tshwj xeeb lub ntsiab lus rau geometric thiab trigonometric kev txawj ntse. Nws yog hais txog mus rau lub cev kom muaj nuj nqis, uas yog ib tug tshwj xeeb cov ntaub ntawv ntawm xws li ib tug tshaj plaws raws li ib tug perimeter. Nyob rau hauv Greek, lo lus suab «περίμετρον» ( «vajvoog») los yog «περιμετρέο» ( «ntsuas nyob ib ncig ntawm"). Puag ncig (dav hlau daim duab rau yam zoo) thiab qhov ib ncig (yeej zoo rau cov planar zoo) sib npaug tag nrho ntev ntawm tus ciam nrhiav. Tshwj xeeb cov ntaub ntawv (tus ciam ntawm lub voj voog) muaj tib lub dimension li qhov kev ncua deb los yog txoj kev. Yuav kom kawm lub npe "Yuav ua li cas los xam rau qhov ntev ntawm lub vajvoog", nws yog tsim nyog yuav tau nco qab cov chav nyob thiab lawv txhais lus.

Raws li lub thoob ntiaj teb system ntawm SI, tej txoj kev los yog deb ntsuas nyob rau hauv meters. Qhov no yog lub hauv paus, tab sis muaj kuj derivatives. Nws yog yog li ntawd tsim nyog rau cov neeg uas txiav txim siab mus theoretical thiab cov tswv yim muaj teeb meem rau "yuav ua li cas nrhiav tau qhov ntev ntawm lub ib ncig ntawm lub" ua lawv kev sib raug zoo:

• 1 kilometer = 1000 meters = 10000 = 100000 decimeters centimeters = 1000000 millimeters;
• 1 mile = 1,609344 kilometers = 1609,344 16093,44 meters decimeters = = = 160,934.4 Centimeters millimeters 1.609.344;
• 1 ft = 30,48 centimeters = 304,8 millimeters decimeters = 3,048 = 0,3048 = 0,0003048 meters kilometers.

Muaj ntau ntau lwm yam units ntawm kev ntsuas: lub British (los yog American), cov laus Lavxias teb sab, Greek, Japanese thiab lwm tus neeg. Nyob rau hauv kev txiav txim rau lawv ua suav, nws yog pom zoo kom siv cov lus qhia background.

Rau tag nrho lub voj voog yus muaj los ntawm ib tug tshaj plaws nyob rau hauv ntau, uas yog tsim los ntawm zaum ntawm antiquity. Piv ntawm ntev mus txoj kab uas hla ntawm ib lub voj voog yog ib txwm ib qhov xov tooj. Rau ib ntev lub sij hawm zaum siv ntau txoj kev (thiab tam sim no tshwj xeeb software thiab computer technology), yog sim mus nrhiav kom tau lub caij nyoog muaj nqis ntawm tus xov tooj. Nws yog feem ntau yog denoted los ntawm cov Greek tsab ntawv «π» (pronounced li pi). Lub approximate muaj nqis nyob rau txawv sij hawm varied, tab sis muaj ib txwm ib tug me ntsis ntau tshaj peb. Tus xov tooj π yog dimensionless. Niaj hnub no, zaum twb tau mus nrhiav kom tau tom qab tus zauv point kaum trillion tias. Qhov no yog cov neeg yog tsim nyog rau txoj zauv. Tab sis nyob rau hauv kev daws geometric teeb meem, nyob qhov twg yuav tsum tau teb cov lus nug - yuav ua li cas nrhiav tau qhov ib ncig, nce siv no tus xov tooj mus rau tsib los yog ob tug cim: π ≈ 3,14159 ≈ 3,14.

Nws yog lub npe hu hais tias Ḻ / d = π = 3,14 los yog Ḻ / 2 R = π = 3,14. Yog li ntawd nws yog ib qho yooj yim los teb rau lo lus nug - yuav ua li cas nrhiav tau qhov ntev ntawm qhov ib ncig ntawm ib lub vojvoog ntawm 1 Meter los yog 2 decimeter, los yog ib lub cheeb ntawm 5 centimeters. Suffice khoo ob npaug ntawm voos kheej-kheej los yog txoj kab uas hla ntawm tus xov tooj π. Rau tag nrho peb tus neeg mob los ntawm cov mis Ḻ = π • D = 3,14 • D los Ḻ = 2 • π • r = 2 • 3,14 • R kev tshwm sim tau li nram qab no suav:

1. Ḻ = 3.14 • 2 • 1 = 6.28 m;
2. Ḻ = 3.14 • 2 • 2 dm = 12,56;
3. Ḻ = 3,14 • 5 = 15.7 cm.

Cov hauj lwm ntawm muaj cov nqe lus nug - yuav ua li cas nrhiav tau qhov ntev ntawm lub ib ncig, yog tias paub, nws voos kheej-kheej los yog txoj kab uas hla, tab sis cov paub cheeb tsam ntawm ib lub voj voog, ib tug me ntsis nyuab, tab sis nws muaj peev xwm kuj yuav daws tau. Rau ib ntev lub sij hawm nws yog lub npe hu hais tias ib tug yeej cheeb tsam sib npaug zos rau cov khoom ntawm π thiab cov square ntawm lub voos kheej-kheej los yog txoj kab uas hla ntawm ib tug plaub ntawm ib tug square: S = π • ṟ² los yog S = π • D ² / 4.

Xam ib tug thawj voos kheej-kheej r = √ (S / π) los yog txoj kab uas hla D = √ (4 • S / π), thiab ces tus xam circumferential ntev. Koj yuav saib tau ib qho piv txwv ntawm ob tus neeg twg lub cheeb tsam ntawm ib lub voj voog yog sib npaug zos rau 12,56 m² thiab 78,5 cm²:

1. R = √ (12,56 / 3,14) = 2 m, whereas Ḻ = 3.14 • 2 • 2 = 12.56 m los yog d = √ (4 • 12,56 / 3,14) = 4 m, ces Ḻ = 3,14 • 4 = 12.56 m.
2. R = √ (78,5 / 3,14) = 5 cm, ces Ḻ = 3.14 • 5 • 2 = 31.4 cm los yog d = √ (4 • 78.5 / 3.14) = 10 cm ces Ḻ = 3,14 • 10 = 31.4 cm.