Yuav ua li cas mus nrhiav tau qhov chaw ntawm ib tug rhombus?

Yuav ua li cas mus nrhiav tau qhov chaw ntawm ib tug rhombus? Yuav kom muab ib lub teb, koj yuav tsum xub to taub dab tsi peb xav txog ib pob zeb diamond.

Firstly, ib tug quadrangle. Secondly, nws muaj plaub sib npaug zos sab. Peb, nws diagonals yog perpendicular ntawm cov kev tshuam taw tes. Plaub, cov kab pheeb ces kaum sib tshuam taw tes yog muab faib mus rau hauv sib npaug zos qhov chaw. Fifthly, tib qhia kab pheeb ces kaum ces kaum ntawm lub rhombus rau hauv ob sib npaug zos qhov chaw. Sixth, nyob rau hauv lub sum ntawm ob ces kaum uas yog nyob ib sab mus rau ib sab, ua li cov unwrapped lub, i.e. 180 degrees. Thiab yog hais tias koj hais kom yoojyim, tus pob zeb diamond - ib tug sloping square.

Yog hais tias koj noj ib square uas nws sab yog fastened flexibly thiab yooj yim rub nws nyob rau hauv ob opposite lub, lub square yuav poob nws squareness thiab tig mus rau hauv ib tug pob zeb diamond. Yog li ntawd, cov pob zeb diamond nrog txoj cai ces kaum - qhov no yog ib tug tiag tiag square.

Tus thawj kom paub lub tswvyim ntawm cov pob zeb diamond Hero thiab Pappus ntawm Alexandria, Greek lej. Lo lus "cov pob zeb diamond" ntawm lub Greek yuav muab txhais raws li "lub nruas".

Yuav nrhiav tau cov cheeb tsam ntawm ib tug rhombus, yog tsim nyog xav tias cov pob zeb diamond - yog ib tug parallelogram. Thiab lub cheeb tsam ntawm lub parallelogram yuav pom los ntawm txawj ntawm ib lub hauv paus, uas yog cov kev taw qhia thiab qhov siab.

Los ua pov thawj no, nws yuav tsum tau rho los ntawm cov saum toj kawg nkaus ntawm lub sab sauv ces kaum ntawm lub rhombus perpendiculars. Piv txwv li, muab ib pob zeb diamond QWER. Los ntawm cov vertices ntawm lub sab sauv ces kaum Q thiab W perpendiculars QT thiab WY. Thiab perpendicular QT ntog nyob rau sab ntawm RE, thiab perpendicular WY yog nyob rau hauv continuation ntawm no sab.

Yog li, tshiab muab QWYT quadrilateral nrog thaum uas tig mus sab thiab txoj cai ces kaum, uas, raws li nyob rau hauv lub foregoing, nws yog ua tau rau lub npe ua siab loj duab plaub.

Lub cheeb tsam ntawm no duab plaub yog txawj sab thiab siab. Tam sim no peb yuav tsum tau los ua pov thawj hais tias cov cheeb tsam ntawm lub resulting duab plaub cheeb tsam raws li ib tug muab kev mob ntawm ib pob zeb diamond.

Xav tau los ntawm constructing ntxiv cov vajvoos peb sab QYR thiab NTUB, peb yuav hais tias lawv nyob rau ntawm ib tug ceg thiab ib tug hypotenuse. Tom qab tag nrho ob txhais ceg ntawm cov vajvoos peb sab yog ua perpendiculars, uas nyob rau tib lub sij hawm no yog ob sab ntawm lub resulting duab plaub. Ib tug hypotenuse - qhov no sab ntawm cov pob zeb diamond.

Rhombus yog lub sum ntawm cov square ntawm daim duab peb sab thiab Trapezoid QYR QYEW. Cov uas ua duab plaub yog muaj li ntawm cov tib daim duab peb sab thiab Trapezoid QYEW NTUB, nws lub cheeb tsam yog sib npaug zos rau cov cheeb tsam ntawm ib tug daim duab peb sab QYR. Li no tus xaus qhia nws tus kheej: QWER rhombus cheeb tsam tus nqi sau raws nkaus Ii mus rau lub cheeb tsam ntawm ib tug duab plaub QWYT.

Tam sim no nws yog ib qhov tseeb yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib tug rhombus ntawm sab thiab nws qhov siab: lawv yuav tsum tau muab.

Koj yuav nrhiav tau qhov chaw ntawm ib tug rhombus, ib tug rhombus paub lub kaum sab xis thiab cov kev taw qhia. Nws yog tsuas tsim nyog los paub dab tsi yog qhov sine ntawm lub kaum sab xis, thiab muab nws los ntawm ob zaug sab. Nrhiav cov sine yuav siv lub tswvyim los yog Bradis rooj.

Tej zaum, mention ntawm yuav ua li cas nrhiav tau qhov chaw ntawm lub rhombus, siv sine ntawm lub kaum sab xis thiab lub voos kheej-kheej ntawm ib lub voj voog inscribed nyob rau hauv nws, uas tas yog siab tshaj plaws.

Txawm li cas los, feem ntau cov feem ntau xam lub cheeb tsam ntawm ib tug rhombus los ntawm diagonally. Los ntawm cov mis no nws hais ntxiv hais tias lub cheeb tsam yog poluproizvedeniyu diagonals.

Ua pov thawj tias nws yog yooj yim zoo nkauj, xav tias ob cov vajvoos peb sab QWE thiab ERQ, uas tau txais thaum lub sij hawm cov pob zeb diamond nyob rau hauv ib tug kab pheeb ces kaum. Cov duab peb ceg yog muaj sib npaug rau peb sab los yog hauv qab thiab ib tug nyob ib sab ob ces kaum.

Tom qab koj siv ib tug thib ob lub pob zeb diamond kab pheeb ces kaum, peb tau lub qhov siab ntawm cov duab peb ceg, vim hais tias cov diagonals tshuam ntawm taw tes X ntawm ib kaum ntawm 90 degrees. Lub cheeb tsam ntawm daim duab peb sab QWE yog qhov khoom ntawm QE, uas yog ib tug nti nyob rau hauv WX - ib nrab ntawm lub thib ob diagonally muab faib los ntawm ob.

Tam sim no rau lo lus nug ntawm yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib tug rhombus, cov lus teb yog tseeb: qhov no qhia yuav tsum tau ob npaug. Rau qhov yooj yim ntawm nqa algebraic qhia yuav ua tau ib tug kab pheeb ces kaum denoted los ntawm tsab ntawv z, thaum lub sij hawm thib ob - nrog tsab ntawv u. peb tau txais:

2 (z X 1 / 2u: 2) = z X 1 / 2u, uas cia li tawm - poluproizvedenie diagonals.