Polygon cheeb tsam

Geometry yuav rightly yuav hu ua ib tug ntawm cov hiob sciences, originating nyob rau hauv lub sij hawm ntawm Euclid.

Tab sis txawm ntau tshaj li 4000 xyoo dhau los, cov Iyi tau yooj yim geometrical ntsuam thiab siv zoo tib yam txoj kev uas zaum hnub no.

Neeg uas nyob ancient Babylon ua ntsuas yooj yim geometric duab siv square units.

Standard cheeb tsam ntsuas rau ib ntev lub sij hawm yog tus square - thiab tag nrho ua tsaug rau cov simplicity ntawm nws siv, sib npaug zos ces kaum thiab sab.

Txawm tias nyob rau hauv ancient Kievan Rus, qhov no kev ntsuas tsis tau muab rau ib tug ntev lub sij hawm. Ib tug interesting tseeb yog hais tias lub ancient Russians siv ib tug txawv kev ntsuas ntawm teb chaws cheeb tsam, uas tsis qhia cov kev ntsuas cov neeg thiab twb kiag arbitrary. Piv txwv li, nyob rau hauv lub xam ntawm cov se raws li ib qho kev ntsuas ntawm qhov chaw coj ib tug measured ua hauj lwm lub sij hawm, thiab hu ua nws "ib qho kev ntsuas ntawm txoj hauj lwm." Grasslands ntsuas haystacks - nws yog "fruitful" kev ntsuas. Lawm, tag nrho cov kev ntsuas yog subjective thiab arbitrary, Ntxiv, nyob rau hauv ntau yam principalities tej zaum kuj tsis sib haum mus rau txhua lwm yam, uas tshwm sim los loj txaav. Nyob ib ncig ntawm lub kawg ntawm lub 14th xyoo pua nyob rau hauv lub ancient writings nyob rau hauv Russia pib lo lus "them ib feem kaum". Nws tau txais nws lub npe vim yog lub fact, uas yog lub thib kaum ib feem ntawm lub square sib npaug zos ib mais.

Tag nrho cov no tsuas yog ib tug me me dimension ntawm voos thiab cov vajvoos peb sab. Tsuas yog tus Greeks paub yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib lub polygon. Txawm tias lub sij hawm "cheeb tsam" yog yeej tsis siv, raws li tau zoo raws li ib tug xov tooj tsis tau siv los mus txiav txim qhov chaw ntawm lub polygon.

Nyob rau hauv lub "Hais" ntawm Euclid kawm rau lo lus nug ntawm transformation ntawm ntau yam nuj nqis sib npaug zos loj, noj ib polygon rau lub feem ntawm lub dav hlau bounded los ntawm ib tug kaw nkhaus. Raws li qhov tseeb hais tias lub cheeb tsam ntawm tus duab yog tsis tau hloov yog hais tias nws yog tawg cia rau hauv tivthaiv qhov chaw thiab teem caij tsis muaj kev tshuam, nws muaj peev xwm mus tsim kom muaj hais tias cov cheeb tsam ntawm lub polygon yuav xam los ntawm summing lub cheeb tsam ntawm cov nuj nqis.

Cov kev tshwm sim ntawm nws ua hauj lwm tam sim no nyob rau hauv ntau cov tswv yim siv, piv txwv li, ntawm cov masters rau tso vuas. Rau thaj tsam ntawm lub polygon lawv ua ib lub phab ntsa ntawm complex configuration. Cia li suav cov xov tooj ntawm cov vuas siv rau nws ob sab phlu, thiab muab tso rau lawv cheeb tsam los nrhiav cov quadrature ntawm cov phab ntsa.

Los ntawm squaring lub rub cheeb tsam ntawm geometric nuj nqis. Yuav ua li cas tag nrho cov muaj nyob rau hauv lub ntsiab txhais ntawm lub cheeb tsam? Yuav kom muab tso rau tej yam yooj yim, nws yog ib tug xov tooj uas qhia yuav ua li cas muaj ntau yam plaub fab ntawm lub tib lub ib feem ntawm lub cev. Nco ntsoov tias qhov no yog tsis yog ib tug txhais, tab sis tsuas muaj ib tug dawb txhais lus. Lub tsev cheeb tsam no yog muab square nrog ib tug sab sib npaug zos rau ib tug kev ntsuas yuav luv. Yog hais tias qhov no ntsuas yog siv los 'meter', cheeb tsam, ntsig txog, yuav tsum xam nyob rau hauv square meters, yog piv hais tseg, thiab square centimeter, thiab lwm yam Lub cheeb tsam ntawm tag nrho cov geometric duab raws li ntsuas yog qhia los ntawm tus xov tooj muaj ib tug zoo nqi.

Yuav kom txiav txim seb lub cheeb tsam ntawm lub polygon, txhais los ntawm lub mis yog siv, raws li tau zoo raws li division rau hauv sib npaug zos daim duab peb sab. Yog hais tias ib tug polygon muaj ib tug complex zoo, koj muaj peev xwm sim phua nws mus rau hauv vaj huam sib daim, thiab los ntawm kev ntxiv rau lawv mus rau lub cheeb tsam los mus laij lub cheeb tsam ntawm lub Ameslikas teev zoo. Ib yam li ntawd convex polygon cheeb tsam no yog muab los xam.

Lub polygon yuav ua tau convex, yog ib tug ntawm cov nram qab no tej yam kev mob yog ntsib:

- nws cov lus dag nyob rau ib sab ntawm txoj kab txuas mus rau neighboring vertices;

- polygon yog cov kev tshuam ntawm ob peb dav hlau.

Ntawm lwm yam, ib tug convex polygon yuav ua tau kev hais tias tag nrho nws cov sab thiab cov ces kaum muaj sib npaug. Ib qho piv txwv ntawm no yog ib tug pentagon nrog sib npaug sab.

Tsuas yog ib tug hais tias: qhov chaw puag ncig peb yog hais tias koj saib ze ze, yog muaj li ntawm ntau geometric duab, thiab cov kev txawj ntse ntawm cov kev cai ntawm geometry thiab muaj peev xwm siv lawv kom haum txig rau hauv peb lub neej.