Qhov ntawd yog tangent rau lub vajvoog? Thaj chaw ntawm lub tangent rau lub voj voog. Cov hom tangent rau ob lub voj voog

Secants, tangents - tag nrho cov no pua pua ntawm lub sij hawm yuav tau hnov nyob rau hauv geometry qhia. Tab sis qhov teeb meem ntawm lub tsev kawm ntawv tom qab, dhau lub xyoo, thiab tag nrho cov no paub tsis nco qab lawm. Yuav ua li cas kuv yuav tsum tau nco ntsoov?

essence

Lub sij hawm "tangent rau lub vajvoog" kos npe rau, tej zaum, txhua yam. Tab sis nws yog tsis zoo li hais tias tag nrho cov yuav sai sai formulate ib tug txhais. Meanwhile hu ua ib tug tangent line dag nyob rau hauv tib lub dav hlau li lub vajvoog uas tshuam nws ntawm tsuas yog ib qho taw tes. Lawv myriad zaum yuav muaj nyob, tab sis tag nrho lawv muaj tib lub zog, uas yuav tsum tau los sib tham li hauv qab no. Raws li tej zaum koj yuav twv, tus taw tes ntawm kev sib cuag xa mus rau qhov chaw nyob qhov twg lub voj voog thiab cov kab sib tshuam. Nyob rau hauv txhua rooj plaub, nws yog ib tug, yog hais tias muaj ntau ntau, ces nws yuav tsum txoj kab txiav.

Lub keeb kwm ntawm lub foundations thiab kawm

Lub tswvyim ntawm ib tug tangent nyob rau hauv ancient sij hawm. Cov kev siv ntawm cov kab mus rau tus thawj lub voj voog, thiab ces mus rau lub ellipses, parabolas thiab hyperbolas nrog ib tug kav thiab ib tug compass nyob tseem nyob rau hauv thaum ntxov ua sawv ntawm txoj kev loj hlob ntawm geometry. Ntawm cov hoob kawm, keeb kwm tsis tau fwm lub npe ntawm tus discoverer, tab sis nws yog tseeb hais tias txawm nyob rau hauv hais tias lub sij hawm cov neeg twb zoo paub thaj chaw ntawm tangent rau lub voj voog.

Nyob rau hauv niaj hnub lub sij hawm cov kev txaus siab nyob rau hauv no phenomenon tsoo tawm dua - pib ib tug tshiab puag ncig ntawm txoj kev tshawb ntawm cov tswvyim no nyob rau hauv nrog cov lus qhib ntawm tshiab curves. Yog li, Galileo tswvcuab lub tswvyim ntawm cycloid thiab Fermat thiab Descartes los ua ib tug tangent rau nws. Raws li rau lub voj voog, no mas, yog rau cov ancient secrets tshuav nyob rau hauv cov cheeb tsam no.

zog

Radius twv rau cov kev tshuam taw tes yuav perpendicular mus rau lub kab. no ntsiab, tab sis tsis yog tib cov khoom teejtug uas yog tangent rau lub voj voog. Ib qho tseem ceeb feature twb muaj xws li ob ncaj. Yog li ntawd, los ntawm ib tug taw tes, uas lies sab nraum lub voj voog, nws yog tau kos ob tangents, thiab lawv lengths yog muaj sib npaug. Yog lwm theorem ntawm cov ntawv no, tab sis nws yog tsis tshua muaj nyob rau hauv lub moj khaum ntawm tus txheej txheem lub tsev kawm ntawv cov hoob kawm, tab sis nws yog tsis tshua muaj pab tau daws tej yam teeb meem. Nws mus raws li nram no. Los ntawm ib tug taw tes nyob sab nraum lub voj voog, kos ib tangent thiab secant rau nws. Tsim feem AB, AC thiab AD. A - cov kev tshuam ntawm cov kab, B tus taw tes ntawm tangency, C thiab D - hla kev. Nyob rau hauv cov ntaub ntawv no, cov nram qab no kab zauv no siv tau: qhov ntev ntawm lub tangent rau lub vajvoog, squared, sib npaug cov khoom ntawm lub feem AC thiab AD.

Los ntawm cov foregoing, muaj yog ib qho tseem ceeb corollary. Rau txhua taw tes ntawm lub vajvoog, koj muaj peev xwm tsim ib tug tangent, tab sis tsuas yog ib qho. Lub pov thawj ntawm no yog heev yooj yim: nyob rau hauv kev tshawb xav cia rau nws perpendicular los ntawm lub voos kheej-kheej, peb paub hais tias tsim tau ib tug daim duab peb sab yuav tsis muaj nyob. Thiab qhov no txhais tau tias lub tangent - tsuas yog ib.

tsev

Cov lwm yam nyob rau hauv geometry yog ib tug tshwj xeeb qeb, raws li ib tug txoj cai, ua tsis tau yog hlub los ntawm tub kawm ntawv thiab menyuam kawm ntawv. Yuav kom daws tau cov kev pab raws qib ntawm pawg no tsuas xav tau ib tug compass thiab ib tug nom. Nws yog neeg ua hauj lwm ntawm lub tsev. Muaj lawv tsim tau rau ib tug tangent.

Yog li ntawd, muab ib lub voj voog thiab ib tug taw tes dag sab nraum nws qhov ciaj ciam teb. Thiab koj yuav tsum next los ntawm lawv tangent. Yuav ua li cas koj ua li cas? Ua ntej ntawm tag nrho cov, koj yuav tsum siv lub caij nyoog nruab nrab ntawm qhov chaw ntawm lub vajvoog O thiab teem taw tes. Ces, nrog rau cov kev pab los ntawm ib tug compass yuav tsum faib nws nyob rau hauv ib nrab. Ua li no, koj yuav tsum teem lub voos kheej-kheej - me ntsis ntau tshaj ib nrab ntawm cov kev ncua deb ntawm qhov chaw ntawm lub voj voog thiab lub thawj point. Ces koj yuav tsum tau tsim ob intersecting arcs. Lub voos kheej-kheej ntawm qhov kev hloov yuav tsum tsis txhob yuav cov compass, thiab qhov chaw ntawm ib sab ntawm lub vajvoog yuav yog tus thawj point, thiab O, ntsig txog. Qhov chaw Arcs tshuam yuav tsum tau txuas hais tias seem txiav hauv ib nrab. Nug nyob rau hauv cov compass voos kheej-kheej sib npaug zos rau qhov kev ncua deb. Ntxiv mus, nrog rau cov chaw ntawm cov kev tshuam los tsim kom tau lwm voj voog. Nws yuav tsum yog raws li nyob rau hauv ob lub yeej taw tes, thiab O. Nyob rau hauv cov ntaub ntawv no, yuav muaj ob tshuam nrog qhov teeb meem no nyob rau hauv ib lub voj voog. Hais tias lawv yuav cov ntsiab lus ntawm kev sib cuag rau cov chiv teev point.

nthuav

Nws yog tsim tau ib tug tangent rau lub vajvoog coj mus rau cov me nyuam yug differential calculus. Tus thawj ua hauj lwm ntawm cov ntawv no tau luam tawm los ntawm lub npe nrov German mathematician Leibniz. Nws muab rau cov tau nrhiav lub maxima, minima thiab tangents, tsis hais txog ntawm lub fractional thiab irrational ntau. Zoo, tam sim no nws yog siv rau ntau ntau lwm yam suav.

Ntxiv mus, lub tangent rau lub vajvoog uas txuam nrog rau geometric tangent kev txiav txim zoo. Nws yog los ntawm no, thiab nws lub npe los. Txhais los ntawm lub Latin tangens - "tangent". Yog li, cov tswvyim no tsis yog tsuas yog ib tug geometry thiab differential calculus, tab sis, nrog trigonometry.

ob lub voj voog

Tsis yeej ib txwm tangent zatragivet tsuas yog ib daim duab. Yog hais tias koj muaj peev xwm siv ntau yam kab mus rau ib lub vajvoog, ces yog vim li cas tsis vice versa? Tau. Nov yog qhov teeb meem nyob rau hauv cov ntaub ntawv no yog tiag nyuab, vim hais tias cov tangent rau ob lub voj voog yuav kis tsis tau los ntawm tej yam taw tes, thiab cov txheeb ze txoj hauj lwm ntawm tag nrho cov nuj nqis yuav ua tau heev sib txawv.

Hom thiab ntau yam

Thaum nws los txog rau lub ob lub voj voog thiab ib los yog ntau tshaj kab, ces txawm hais tias koj paub hais tias nws yog hais txog, yog tsis tam sim ntawd kom meej yuav ua li cas tag nrho cov ntawm cov pieces cov txheej txheem ntawm nyob rau hauv kev sib raug zoo rau txhua tus lwm yam. Nyob rau qhov no hauv paus, muaj ntau ntau ntau ntau yam. Yog li ntawd, lub voj voog yuav muaj ib tug los yog ob tug heev cov ntsiab lus, los yog tsis muaj tag nrho cov. Nyob rau hauv thawj cov ntaub ntawv, lawv yuav sib tshooj, thiab lub thib ob - mus kov. Thiab ntawm no yog ob hom. Yog hais tias ib tug vajvoog, raws li nws twb nyob ruaj nrees nyob rau hauv lub thib ob, qhov kov yog hu ua nrog yog hais tias tsis - ces tus sab nraum. Nkag siab txog cov txheeb ze txoj hauj lwm ntawm lub daim yuav tsis tsuas tau raws li nyob rau hauv daim duab, tab sis muaj cov lus qhia txog lub sum ntawm lawv radii thiab qhov kev ncua deb ntawm lawv cov chaw zov me nyuam. Yog hais tias cov ob qhov tseem ceeb yog muaj sib npaug, ces cov voj voog kov. Yog hais tias tus thawj ntxiv - tshuam thiab lwm yam - tsis muaj ntau cov ntsiab lus.

Yog li ntawd nws yog nrog cov kab ncaj nraim. Rau tej ob lub voj voog muaj tsis muaj ntau cov ntsiab lus yuav ua tau
tsim plaub tangents. Ob tug ntawm lawv yuav tshaj ntawm cov nuj nqis, lawv hu ua hauv. Ib ob peb ntawm lwm yam - lwm.

Yog hais tias peb yuav sib tham txog lub voj voog, uas muaj ib tug taw tes nyob rau hauv ntau, qhov teeb meem tiag yooj yim zog. Qhov tseeb yog tias nyob rau hauv tej kev sib nrig sib kho, nyob rau hauv rooj plaub no tus tangent lawv yuav muaj tsuas yog ib. Thiab nws yuav kis tau los ntawm tus taw tes ntawm kev tshuam. Yog li ntawd hais tias cov tsev yuav tsis ua teeb meem.

Yog hais tias cov nuj nqis yog ob lub ntsiab lus ntawm kev tshuam, ces lawv yuav tau ua kab tangent rau lub vajvoog raws li ib tug, thiab lub thib ob, tab sis tsuas nraum zoov. Cov tshuaj rau qhov teeb meem no yog zoo li dab tsi yog los sib tham tom qab.

Lub rooj sib tham txoj kev sib tw

Ob sab hauv thiab sab nraud tangent rau ob lub voj voog nyob rau hauv lub tsev yog tsis yog li ntawd yooj yim, tab sis yog, thiab qhov teeb meem no yog solved. Lub fact tias cov koom haum pab cov qauv no yog siv rau qhov no, thiaj li xam tau tawm xws li ib txoj kev nyob ib leeg Nws yog ib heev problematic. Yog li ntawd, muab ob lub voj voog uas txawv radii thiab chaw zov me nyuam O1 thiab O2. Rau lawv, qhov yuav tsum tau los tsim kom tau ob khub ntawm tangents.

Ua ntej ntawm tag nrho cov, hais txog qhov chaw ntawm lub loj lub vajvoog kom lawv muaj kev txhawb nqa. Nyob rau tib lub sij hawm nyob rau compass yuav tsum tau muab qhov txawv nruab nrab ntawm tus radii ntawm ob thawj cov nuj nqis. Los ntawm qhov chaw ntawm lub voj voog me tangent mus rau lub koom haum pab tsev. Tom qab ntawd ntawm O1 thiab O2 yog muaj perependikulyary cov ncaj nraim rau cov kev tshuam nrog cov thawj cov nuj nqis. Raws li nram no los ntawm qhov yooj yim thaj chaw ntawm lub tangent, lub yuav tsum tau cov ntsiab lus muaj nyob rau ob qho tag nrho lub voj voog. Qhov teeb meem yog solved, yam tsawg kawg nyob rau hauv nws thawj feem.

Nyob rau hauv thiaj li yuav tsim kom muaj nrog tangents muaj los daws kom tau yuav luag ib tug teeb meem zoo li. Ib zaug ntxiv, peb yuav tsum tau ib tug pab daim duab, tab sis lub sij hawm no nws voos kheej-kheej yog sib npaug zos rau cov sum ntawm tus thawj. Yuav kom nws tsim tangent los ntawm qhov chaw ntawm ib qho ntawm cov voj voog. Lub ntxiv rau thaum kawg ntawm qhov kev txiav txim yuav tsum to taub los ntawm lub yav dhau los piv txwv.

Lub tangent rau lub vajvoog, los yog ob tug txawm los yog ntau tshaj - tsis yog xws li ib tug yooj yim ua hauj lwm. Ntawm cov hoob kawm, mathematicians tau ntev ceased mus daws tau teeb meem zoo li manually thiab tso siab rau xam tshwj xeeb cov kev pab cuam. Tab sis tsis txhob xav tias nws yog tam sim no tsis tas yuav tau ua nws tus kheej, vim hais tias ib tug muaj tseeb formulation ntawm neeg ua hauj lwm rau lub computer ua npaum li cas thiab to taub. Tu siab, muaj kev ntshai tias tom qab zaum kawg txoj kev hloov mus rau lub xeem daim ntawv ntawm kev txawj ntse tswj teeb meem rau kev tsim kho yuav ua rau cov menyuam kawm ntawv ntau thiab ntau teeb meem.

Raws li rau nrhiav cov tangents mus rau ntau lub voj voog, nws tsis yog ib txwm ua tau, txawm yog hais tias lawv pw nyob rau hauv tib lub dav hlau. Tab sis tej zaum nws yog ua tau rau nrhiav tau xws li ib tug kab.

Lub neej piv txwv

Cov hom tangent rau ob lub voj voog yog feem ntau pom nyob rau hauv kev xyaum, tab sis nws tsis yog ib txwm muaj tseeb. Conveyors, modular systems, kis tau tus mob koj cov menyuam Pulleys, nro ntawm cov xov nyob rau hauv ib tug tshuab xaws, tab sis txawm cia li ib tug lub tsheb kauj vab saw - tag nrho cov piv txwv ntawm lub neej. Yog li ntawd tsis txhob xav tias geometrical teeb meem nyob twj ywm xwb nyob rau hauv kev tshawb xav: nyob rau hauv engineering, physics, kev tsim kho thiab ntau lwm qhov chaw yog nyob rau hauv kev siv tswv yim.