Nws tsis tuaj yeem lees paub tias koj paub lej yog tias koj tsis paub yuav ua li cas kos duab kos duab, kos qhov tsis sib xws ntawm kab sib koom ua ke, thiab ua haujlwm nrog kev sib koom tes. Cov khoom pom pom hauv kev tshawb fawb yog qhov tseem ceeb, vim tias tsis muaj cov qauv pom hauv cov qauv thiab kev suav, qee zaum koj tuaj yeem tsis meej pem. Hauv tsab xov xwm no, peb yuav pom yuav ua li cas ua haujlwm nrog kev sib koom tes axes thiab kawm yuav ua li cas los tsim cov duab ua haujlwm yooj yim.
Daim ntawv thov
Cov kab sib koom ua ke yog lub hauv paus ntawm hom kab kos yooj yim tshaj plaws uas tus tub ntxhais kawm ntsib ntawm nws txoj kev kawm. Nws yog siv nyob rau hauv yuav luag txhua lub ntsiab lus lej: thaum xam qhov nrawm thiab sijhawm, ntsuas qhov loj ntawm cov khoom thiab suav lawv thaj chaw, hauv trigonometry thaum ua haujlwm nrog sines thiab cosines.
Tus nqi tseem ceeb ntawm txoj kab ncaj nraim yog kev pom. Vim hais tias kev ua lej yog ib qho kev tshawb fawb uas yuav tsum tau muaj kev xav paub daws teeb meem, cov duab kos pab sawv cev rau ib yam khoom hauv lub ntiaj teb tiag. Nws coj li cas? Lub sijhawm twg hauv qhov chaw yuavob peb vib nas this, feeb, teev? Yuav hais li cas txog nws piv nrog rau lwm yam khoom? Nws ceev yog dab tsi ntawm lub sij hawm xaiv random? Yuav ua li cas qhia nws lub zog?
Thiab peb tab tom tham txog kev nrawm rau qhov laj thawj - nws feem ntau tshwm sim los ntawm cov duab ua haujlwm. Thiab lawv tuaj yeem tso saib cov kev hloov pauv ntawm qhov kub thiab txias hauv qhov khoom, nws qhov loj me, kev taw qhia txog lub qab ntug. Yog li, tsim txoj kab sib koom ua ke feem ntau xav tau hauv physics ib yam nkaus.
Ib-dimensional graph
Muaj ib lub tswv yim ntawm multidimensionality. Hauv ib qhov chaw, tsuas yog ib tus lej txaus los txiav txim qhov chaw ntawm qhov taw tes. Qhov no yog qhov tseeb nrog kev siv cov kab sib txuas. Yog hais tias qhov chaw yog ob-seem, ces ob tug lej yuav tsum tau. Cov kab kos ntawm hom no tau siv ntau zaus, thiab peb yuav xav txog lawv me ntsis tom qab hauv kab lus.
Dab tsi tuaj yeem pom nrog kev pab ntawm cov ntsiab lus ntawm lub axis, yog tias tsuas muaj ib qho axis? Koj tuaj yeem pom qhov loj ntawm cov khoom, nws txoj hauj lwm hauv qhov chaw txheeb ze rau qee qhov "zero", piv txwv li cov ntsiab lus xaiv raws li qhov taw qhia siv.
Hloov pauv ntawm lub sijhawm yuav tsis pom, vim tias txhua qhov kev nyeem yuav tshwm sim rau ib lub sijhawm tshwj xeeb. Txawm li cas los xij, koj yuav tsum pib qhov twg! Yog li cia peb pib.
Yuav ua li cas los tsim ib qho kev sib koom tes
Ua ntej, koj yuav tsum kos kab kab rov tav - qhov no yuav yog peb axis. Nyob rau sab xis, "ntse" nws kom nws zoo li tus xub. Yog li, peb yuav qhia qhov kev taw qhia uas cov lej yuav yognce. Nyob rau hauv lub downward kev taw qhia, lub xub yog feem ntau tsis muab tso rau. Kev lig kev cai, axis taw qhia rau sab xis, yog li peb tsuas yog ua raws li txoj cai no.
Cia peb teeb lub cim xoom, uas yuav qhia txog keeb kwm ntawm kev tswj hwm. Qhov no yog qhov chaw uas lub countdown raug coj mus, txawm nws loj, qhov hnyav, ceev, lossis lwm yam. Ntxiv rau qhov xoom, peb yuav tsum tau tsim lub npe hu ua tus nqi faib, piv txwv li, qhia tus qauv chav tsev, raws li peb yuav npaj qee qhov ntau ntawm cov axis. Qhov no yuav tsum tau ua kom thiaj li nrhiav tau qhov ntev ntawm ntu ntawm txoj kab sib koom ua ke.
Los ntawm qhov sib npaug ntawm qhov sib npaug, muab cov dots lossis "notches" rau ntawm kab, thiab hauv qab lawv sau 1, 2, 3, raws, thiab lwm yam. Thiab tam sim no, txhua yam yog npaj txhij. Tab sis nrog rau lub sijhawm tshwm sim, koj tseem yuav tau kawm paub ua haujlwm li cas.
Hom ntsiab lus ntawm txoj kab sib koom ua ke
Los ntawm thawj ib saib ntawm cov duab kos uas tau hais hauv cov ntawv nyeem, nws pom tseeb: cov ntsiab lus ntawm cov axis tuaj yeem sau lossis tsis sau. Koj puas xav tias nws yog ib qho coincidence? Tsis yog kiag li! Ib qho "khoom" dot yog siv rau qhov tsis sib xws tsis nruj - ib qho uas nyeem ua "ntau dua lossis sib npaug". Yog tias peb yuav tsum nruj me ntsis txwv lub sijhawm (piv txwv li, "x" tuaj yeem coj qhov tseem ceeb ntawm xoom mus rau ib qho, tab sis tsis suav nrog), peb yuav siv lub ntsiab lus "hollow", uas yog, qhov tseeb, lub voj voog me me. ntawm axis. Nws yuav tsum raug sau tseg tias cov tub ntxhais kawm tsis nyiam qhov tsis sib xws nruj, vim tias lawv nyuaj ua haujlwm nrog.
Nyob ntawm cov ntsiab lus twg kojsiv nyob rau hauv daim ntawv qhia, lub sij hawm tsim los kuj yuav raug hu. Yog tias qhov tsis sib xws ntawm ob tog tsis nruj, ces peb tau txais ib ntu. Yog hais tias ntawm ib sab nws hloov mus ua "qhib", ces nws yuav raug hu ua ib nrab-lub caij nyoog. Thaum kawg, yog tias ib feem ntawm txoj kab raug khi rau ob sab los ntawm cov ntsiab lus hollow, nws yuav raug hu ua ntu ntu.
dav hlau
Thaum tsim ob txoj kab ncaj nraim ntawm lub dav hlau sib koom ua ke, peb tuaj yeem xav txog cov duab ntawm cov haujlwm. Cia peb hais tias kab kab rov tav yog lub sijhawm axis, thiab kab ntsug yog qhov nrug. Thiab tam sim no peb muaj peev xwm txiav txim siab seb qhov deb ntawm qhov khoom yuav kov yeej hauv ib feeb lossis ib teev ntawm kev mus ncig. Yog li, kev ua haujlwm nrog lub dav hlau ua rau nws tuaj yeem saib xyuas qhov kev hloov pauv hauv lub xeev ntawm ib qho khoom. Qhov no yog qhov nthuav ntau dua li kev tshawb nrhiav lub xeev zoo li qub.
Daim duab yooj yim tshaj plaws ntawm lub dav hlau no yog kab ncaj nraim, nws qhia txog kev ua haujlwm Y(X)=aX + b. Txoj kab puas khoov? Qhov no txhais tau hais tias tus kwv hloov nws cov yam ntxwv thaum kawm.
Xav txog tias koj tab tom sawv ntawm lub ru tsev ntawm lub tsev tuav lub pob zeb hauv koj txhais tes tawm. Thaum koj tso nws, nws yuav ya mus, pib nws txav los ntawm xoom ceev. Tab sis nyob rau hauv ib tug thib ob nws yuav kov yeej 36 kilometers ib teev. Lub pob zeb tseem yuav ua kom nrawm ntxiv, thiab txhawm rau txhawm rau kos nws lub zog ntawm daim duab, koj yuav tsum ntsuas nws qhov nrawm ntawm ob peb lub sijhawm los ntawm kev teeb tsa cov ntsiab lus ntawm cov axis hauv qhov chaw tsim nyog.
Cov cim ntawm kab kab rov tav los ntawm lub neej ntawd yog lub npe X1, X2, X3, thiab ntawm txoj kab ntsug - Y1, Y2, Y3, raws li. projectinglawv mus rau lub dav hlau thiab nrhiav kev sib tshuam, peb pom cov seem ntawm cov qauv tshwm sim. Txuas lawv nrog ib kab, peb tau txais ib daim duab ntawm kev ua haujlwm. Nyob rau hauv cov ntaub ntawv ntawm ib tug ntog pob zeb, lub quadratic muaj nuj nqi yuav zoo li: Y(X)=aXX + bX + c.
Ncua
Tau kawg, nws tsis tas yuav tsum muab cov lej suav nrog ib sab ntawm kev faib los ntawm txoj kab ncaj nraim. Yog tias koj tab tom xav txog kev txav ntawm cov qwj uas nkag mus ntawm qhov nrawm ntawm 0.03 meters ib feeb, teem caij raws li qhov tseem ceeb ntawm qhov sib koom ua ke. Nyob rau hauv rooj plaub no, teem lub ncua sij hawm rau 0.01 meters.
Nws yog qhov yooj yim tshwj xeeb los ua cov duab kos hauv phau ntawv sau hauv lub tawb - ntawm no koj tuaj yeem pom tam sim ntawd yog tias muaj qhov chaw txaus ntawm daim ntawv rau koj daim ntawv, yog tias koj mus dhau ntawm cov npoo. Nws tsis yog qhov nyuaj los xam koj lub zog, vim qhov dav ntawm lub xov tooj ntawm tes hauv phau ntawv no yog 0.5 centimeters. Nws coj - txo cov duab. Kev hloov pauv hauv qhov ntsuas ntawm daim duab yuav tsis ua rau nws poob lossis hloov nws cov khoom.
Point and segment coordinates
Thaum qhov teeb meem lej tau muab rau hauv ib zaj lus qhia, nws tuaj yeem muaj qhov tsis sib xws ntawm ntau cov duab geometric, ob qho tib si nyob rau hauv daim ntawv ntawm sab ntev, ib puag ncig, cheeb tsam, thiab hauv daim ntawv ntawm kev tswj hwm. Hauv qhov no, koj yuav xav tau ob qho tib si tsim cov duab thiab tau txais qee cov ntaub ntawv cuam tshuam nrog nws. Cov lus nug tshwm sim: yuav ua li cas thiaj nrhiav tau cov ntaub ntawv xav tau ntawm txoj kab sib koom ua ke? Thiab yuav ua li cas thiaj tsim tau ib daim duab?
Piv txwv li, peb tab tom tham txog ib qho ntsiab lus. Tom qab ntawd ib tsab ntawv loj yuav tshwm sim nyob rau hauv qhov xwm txheej ntawm qhov teeb meem, thiab ob peb tus lej yuav tshwm sim hauv cov cim, feem ntau yog ob (qhov no txhais tau tias peb yuav suav hauv qhov chaw ob sab). Yog hais tias muaj peb tus lej nyob rau hauv cov cim, sib cais los ntawm ib qho semicolon los yog lub cim cim, ces qhov no yog qhov chaw peb sab. Txhua qhov ntawm qhov tseem ceeb yog kev sib koom ua ke ntawm cov axis sib xws: thawj zaug raws kab rov tav (X), tom qab ntawv ntsug (Y).
Nco ntsoov kos ib ntu? Koj dhau nws ntawm geometry. Yog tias muaj ob lub ntsiab lus, ces ib kab tuaj yeem kos ntawm lawv. Lawv cov kev tswj xyuas tau qhia hauv cov kab ke yog tias ib ntu tshwm hauv qhov teeb meem. Piv txwv li: A(15, 13) - B(1, 4). Txhawm rau tsim cov kab zoo li no, koj yuav tsum nrhiav thiab kos cov ntsiab lus ntawm lub dav hlau sib koom ua ke, thiab tom qab ntawd txuas rau lawv. Aws!
Thiab ib qho polygons, raws li koj paub, tuaj yeem kos siv ntu. Teeb meem daws tau.
Kev suav
Cia peb hais tias muaj qee yam khoom uas nws txoj hauj lwm raws X axis yog tus cwj pwm los ntawm ob tus lej: nws pib ntawm qhov taw tes nrog kev tswj hwm (-3) thiab xaus ntawm (+2). Yog tias peb xav paub qhov ntev ntawm cov khoom no, ces peb yuav tsum rho tus lej me ntawm tus lej loj. Nco ntsoov tias tus lej tsis zoo absorbs lub cim ntawm qhov kev rho tawm, vim tias "ib lub sijhawm rho tawm ib qho sib npaug ntxiv." Yog li peb ntxiv (2 + 3) thiab tau 5. Qhov no yog qhov xav tau.
Ib qho piv txwv: peb tau muab qhov kawg taw tes thiab qhov ntev ntawm cov khoom, tab sis tsis yog qhov pib taw tes (thiab peb yuav tsum nrhiav nws). Cia txoj hauj lwm ntawm qhov chaw paub yog (6), thiab qhov loj ntawm cov khoom nyob rau hauv kev kawm yog (4). Los ntawm kev rho tawm qhov ntev ntawm qhov kawg kev sib koom tes, peb tau txais cov lus teb. Total: (6 - 4)=2.
negative tooj
Nws feem ntau yuav tsum tau ua hauv kev xyaum ua haujlwm nrog qhov tsis zoo. Hauv qhov no peb yuavtxav mus rau sab laug raws qhov kev sib koom ua ke. Piv txwv li, ib yam khoom 3 centimeters siab ntab hauv dej. Ib feem peb ntawm nws yog immersed nyob rau hauv cov kua, ob feem peb yog nyob rau hauv cov huab cua. Tom qab ntawd, xaiv cov dej saum npoo raws li cov axis, peb tau txais ob tus lej siv cov lej lej yooj yim tshaj plaws: lub ntsiab lus saum toj kawg nkaus ntawm cov khoom muaj qhov sib koom tes (+2), thiab hauv qab ib qho - (-1) centimeter.
Nws yooj yim pom tias nyob rau hauv rooj plaub ntawm lub dav hlau, peb muaj plaub lub quarters ntawm txoj kab sib koom ua ke. Txhua tus ntawm lawv muaj nws tus lej. Nyob rau hauv thawj (sab sauv sab xis) ib feem yuav muaj cov ntsiab lus muaj ob tug zoo coordinates, nyob rau hauv lub thib ob - nyob rau sab saum toj sab laug - qhov tseem ceeb ntawm X axis yuav tsis zoo, thiab raws Y axis - zoo. Qhov thib peb thiab plaub yog suav ntxiv counterclockwise.
khoom tseem ceeb
Koj paub tias kab tuaj yeem sawv cev ua tus lej ntawm cov ntsiab lus tsis kawg. Peb tuaj yeem ua tib zoo saib raws li peb nyiam cov naj npawb ntawm qhov tseem ceeb hauv txhua qhov kev taw qhia ntawm axis, tab sis peb yuav tsis ua raws li qhov rov ua dua. Nws zoo nkaus li tsis paub thiab nkag siab, tab sis cov lus ntawd yog los ntawm qhov tseeb tseem ceeb: txhua tus lej sib raug rau ib qho thiab tsuas yog ib qho ntawm cov kab sib koom ua ke.
Zoo kawg
Nco ntsoov tias txhua qhov axes, cov duab thiab, yog tias ua tau, cov duab kos yuav tsum tau ua rau ntawm tus pas ntsuas. Cov chav ntsuas ntsuas tsis tau tsim los ntawm tus txiv neej los ntawm lub sijhawm - yog tias koj ua yuam kev thaum kos duab, koj khiav txoj kev pheej hmoo ntawm kev pom cov duab txawv dua li qhov nws yuav tsum tau ua.
Ceev faj thiab raug hauv kev npaj thiab suav. Zoo li txhua yam kev tshawb fawb kawm hauv tsev kawm ntawv, lej nyiam qhov tseeb. Muab tso rau hauv me ntsis kev siv zog thiab zooKev ntsuam xyuas yuav tsis ntev tom ntej.
