Bisector kaum sab xis ntawm daim duab peb sab

Yuav ua li cas yog lub bisector ntawm lub kaum sab xis ntawm daim duab peb sab? Nyob rau lo lus nug no nyob rau hauv ib co neeg nrog cov lus lov hais tsis zoo hais tias: "Qhov no yog ib tug nas khiav ib ncig ntawm nyob rau hauv lub ces kaum thiab faib lub kaum sab xis nyob rau hauv ib nrab." Yog hais tias cov lus teb yuav tsum tau "humorous", ces tej zaum nws yog muaj tseeb. Tab sis los ntawm ib tug scientific point of view, cov lus teb rau lo lus nug no yuav tau tsis nyuaj ib yam dab tsi zoo li no: "Qhov no yog ib tug ray pib ntawm lub sab saum toj kaum thiab faib rau tom kawg rau hauv ob sib npaug zos qhov chaw." Lub geometry ntawm no xam yog tseem ntaus nqi raws li lub bisector ntawm lub ya mus rau nws lub tshuam nrog cov opposite sab ntawm lub duab peb sab. Qhov no yog tsis yog ib tug yuam kev. Yuav ua li cas lwm tus paub txog tus bisector ntawm lub kaum sab xis, tab sis nws txiav txim?

Raws li cov kev locus ntawm cov ntsiab lus, nws muaj nws tus yam ntxwv. Tus thawj ntawm cov - es, tsis txawm tias ib tug kos npe rau, thiab lub theorem, uas yuav tsum tau luv luv qhia raws li nram no: "Yog hais tias lub bisector ntawm ib tug opposite sab muab faib ua ob qhov chaw, lawv tus yam ntxwv yuav haum tiv thaiv cov sab ntawm lub loj daim duab peb sab."

Qhov thib ob cuab yeej yog hais tias nws muaj: tus taw tes ntawm kev tshuam ntawm lub bisectors ntawm cov ces kaum tag nrho cov hu ua intsentrom.

Qhov thib peb kos npe rau: lub bisector ntawm ib puab thiab ob txheej ntawm cov ces kaum ntawm daim duab peb sab tshuam ntawm qhov chaw ntawm ib qho ntawm peb cov nws inscribed lub voj voog.

Plaub bisector kaum sab xis ntawm daim duab peb sab cuab yeej yog hais tias yog txhua tus ntawm lawv yog sib npaug zos, ces tus tom kawg yog ceskaum.

Lub tsib feature ntawm tib kev txhawj xeeb ntawm ib tug ceskaum daim duab peb sab thiab yog lub ntsiab taw tes ntawm reference rau nws paub nyob rau hauv lub bisectors ntawm daim duab, namely, nyob rau hauv ib tug equilateral daim duab peb sab, nws kuj ua hauj lwm pab raws li ib tug nruab nrab thiab qhov siab.

Lub bisector ntawm lub kaum sab xis yuav raug ua lub tsev los ntawm kev siv ib tug pas ntsuas thiab compass:

Qhov thib rau txoj cai yog hais tias nws yog tsis yooj yim sua los mus tsim ib tug daim duab peb sab siv qhov tseeb muaj tsuas yog hais tias tus bisectors li tsis yooj yim sua kom lawv muaj xws li ib tug txoj kev doubling lub voos xwmfab, lub squaring ntawm lub voj voog thiab lub trisection ntawm lub kaum sab xis. Nyob rau hauv qhov tseeb, nws muaj tag nrho lub zog ntawm cov bisector ntawm lub kaum sab xis ntawm daim duab peb sab.

Yog hais tias koj tau nyeem yav dhau los cov pawg lus, nws yog tau hais tias koj yog txaus siab nyob rau hauv ib tug kab lus. "Yuav ua li cas yog lub trisection ntawm lub kaum sab xis?" - paub tseeb tias koj nug. Trisectors ib tug me ntsis zoo xws li cov bisector, tab sis yog hais tias tus kawg kos, lub kaum sab xis yog muab faib ua ob sib npaug zos qhov chaw, thiab nyob rau hauv kev tsim kho ntawm lub trisection - peb. Lawm, lub bisector yog muab tau yooj yim dua, vim hais tias trisection tom tsev kawm ntawv lawv tsis qhia. Tab sis mus ua kom tiav daim duab thiab tham txog nws.

Trisectors, raws li kuv hais, koj yuav tsis tsim kom muaj ib tug cia li kav thiab compass, tab sis nws yog tau los mus tsim nrog kev pab los ntawm cov kev cai Fujita thiab ib co curves: Pascal qwj, quadratrix, conchoid Nicomedes, conic khej, lub Archimedes kauv.

Paub tab ntawm trisection ntawm lub kaum sab xis tsuas daws tau los ntawm neusis siv.

Nyob rau hauv geometry, muaj yog ib tug theorem txog trisectors kaum sab xis. Nws yog hu ua ib tug theorem Morley (Morley). Nws cav hais tias tus taw tes ntawm kev tshuam yog nyob rau hauv nruab nrab ntawm txhua lub ces kaum yuav trisectors vertices ntawm ib tug equilateral daim duab peb sab.

Ib tug me me dub daim duab peb sab hauv ib tug loj yeej ib txwm yuav equilateral. Qhov no theorem twb nrhiav tau los ntawm ib tug British tus paub txog Frenkom Morli nyob rau hauv 1904.

Qhov ntawd yog ntau npaum li cas koj yuav paub txog lub division ntawm lub ces kaum bisector trisectors thiab yeej ib txwm yuav tsum tau ib tug ncauj lus kom ntxaws piav. Tiam sis ntawm no peb twb muab ib tug ntau tau tsis qhia tawm kuv txhais cov ntsiab lus: Qwj Pascal conchoid Nicomedes, etc. Tsis txhob txhawj, koj yuav tau sau ntawv hais txog lawv txawm ntau.