Yuav ua li cas mus nrhiav tau qhov chaw ntawm ib tug square rau ntawm nws sab thiab nws cov diagonals?

Niaj hnub no, ob peb uas tsis paub yuav ua li cas nrhiav tau cov cheeb tsam ntawm lub square. Thaum muaj, nws yog twb nyob rau hauv lub deb nag hmo ... Qhov ntawd yog, ib lub sij hawm thaum txhua leej txhua paub yuav ua li cas los mus laij lub cheeb tsam ntawm ib tug square, vim hais tias hnub no, raws li tab sis yog nws yuav sound absurd, cov teeb meem twb tas li tshwm nyob rau Internet. Nws yuav coj txawv txawv, hais qhov tsawg kawg yog - nws yog txaus ntshai.

Txawm nyob rau hauv tsev kawm ntawv yog qhia yuav ua li cas nrhiav tau cov square cheeb tsam. Tab sis koj yuav tsum xub kawm los paub txog cov cheeb tsam ntawm lub duab plaub (a square - tag nrho cov tib duab plaub, tab sis, nrog sib npaug zos sab).

Nws yog npaj los tsim kom tau rau ib tug tej yam square ntsuas ntawm lub cheeb tsam ntawm kev ntsuas - square centimeter los yog square meter. Qhov kev ntsuas no qhov chaw yog ib tug square nrog sab sib npaug los yog ib tug centimeter los yog ib tug 'meter'. Nyob ntawm seb qhov loj ntawm lub cheeb tsam yuav tsum tau ntsuas, nws yuav ua tau ib tug hectare (square kilometer), los yog ar (ib tug square nrog sab ntawm 100 meters, nyob rau hauv lwm yam lus - "tom hlab"). Cov squares thiab pw twj ywm rau hauv lub measured duab plaub.

Rau cov xyaum ua tej yam, yuav tsum tau me me duab plaub nrog sab ntawm, piv txwv li, sib npaug zos rau 3 thiab 5 centimeters. Rau clarity yau me nyuam kawm ntawv ua hauj lwm pab rau kos ib daim duab rau ntawm ib daim ntawv nyob rau hauv ib lub tawb, ces faib tus duab plaub thaum uas tig mus kab raws qhov ntev thiab dav, muab lawv nyob rau hauv lub cheeb tsam ntawm ob lub hlwb. Tej zaum, lub ob hlwb nyob rau hauv ib tug ib txwm lub tsev kawm ntawv phau ntawv sau sib haum mus rau ib tug centimeter. Yog li, nws zoo nkaus li uas lub duab plaub yog muab faib mus rau hauv square centimeters, uas yog muab tso rau hauv nws square centimeters - lub cheeb tsam ntawm kev ntsuas ntsuas.

Cov kauj ruam tom ntej yog suav lub squares ua ke rau hauv ib lub duab plaub nrog ib tug sab ntawm ib tug centimeter. Koj muaj peev xwm suav lawv ua ntej nyob rau hauv lub niaj zaus txoj kev, taw tes rau stick. Ces nco ntsoov siv ib tug unlearning npaug rooj: tau txais ib tug tsib txhua, txhua yam uas peb squares. Txawj lawv, peb tau yooj yim tau 15 square centimeters. Nyob rau hauv tej yam yooj yim cov ntsiab lus, cov cheeb tsam ntawm txhua duab plaub yog los ntawm txawj nws ntev thiab dav.

Hloov tus naj npawb 5 nyob rau lub "ib tug", thiab tus naj npawb 3 rau lub «b», cov me nyuam nrhiav tau yooj yim mus deduce tus duab plaub cheeb tsam mis. Yog li ntawd, nws hloov tawm hais tias S = taus b. Tab sis nws yog - ib tug noj mis nyuj tov rau tus duab plaub. Peb kuj yuav tsum coj ib tug txoj cai, piav qhia txog yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib tug square!

Nws yog heev yooj yim! Sab ntawm koj lub square yog muaj sib npaug, nws txhais tau tias koj yuav hloov lub sab "b" nyob rau hauv cov mis nyob rau hauv lub "ib tug". Ces koj saib cov nram qab qhia: S = taus zoo. Npaug ntawm ib tug xov tooj ntawm nws tus kheej tau txais lub square ntawm tus xov tooj los yog tus xov tooj ntawm lub thib ob degree.

Txawm li cas los, muaj lwm txoj kev los nrhiav tau qhov chaw ntawm lub square. Qhov no, ntawm chav kawm, muaj ntau lej teeb meem. Tab sis lawv kev txiav txim siab yuav tshwm sim tej yam mis. Piv txwv li, koj muab mus nrhiav yuav ua li cas nrhiav qhov chaw ntawm ib tug square tsis nyob rau sab thiab nyob rau hauv kab pheeb ces kaum.

Yuav kom daws tau qhov teeb meem no, muaj me ntsis kev paub ntawm thawj lub tsev kawm ntawv. Peb yuav tsum muaj cov Pythagorean theorem. Ua ntej, peb tsim ib tug square, e.g., NMOP kab pheeb ces kaum TSIS = m. Peb tau ob sib npaug zos ceskaum lub daim duab peb sab nrog rau lub hauv paus m.

Thov saum toj no hais theorem, peb nrhiav tau cov sab ntawm ib txoj cai daim duab peb sab. NM squared + MO = TSIS MUAJ nyob rau hauv lub square nyob rau hauv lub square. Tab sis raws li NM = MO, peb tau squared + NM NM = TSIS MUAJ nyob rau hauv lub square nyob rau hauv lub square. Li no NM 2 squared = TSIS MUAJ nyob rau hauv lub square. NM Nrhiav cov square yuav TSIS faib lub square rau hauv ob.

Tab sis NM nyob rau hauv lub square - qhov no yog cia li tau cov lus teb rau lo lus nug yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib tug square! Ib tug tsis muaj - yog kab pheeb ces kaum ntawm ib tug square. Yog li ntawd, peb yuav coj ib tug tshiab mis uas hais tias lub cheeb tsam ntawm lub square yog sib npaug zos rau ib nrab ntawm nws cov diagonals, tsa nyob rau hauv lub thib ob degree.

Nws yog ua tau rau neeg ib mis nrhiav ib tug square cheeb tsam raws tus voos kheej-kheej ntawm ib lub voj voog inscribed nyob rau ntawd los yog circumscribed nyob ib ncig ntawm nws. Tab sis tsis muaj teeb meem dab tsi teeb meem peb tsis tau solved, lub hauv paus yuav mus ib txhis kav hais tias peb kawm nyob rau hauv tsev kawm ntawv - uas txawj ob tog ntawm lub duab plaub, koj yuav nrhiav tau nws cheeb tsam.