Yuav ua kom yooj yim rau cov neeg nyeem kom xav txog qhov hyperboloid yog dab tsi - cov khoom peb sab - koj thawj zaug yuav tsum xav txog qhov nkhaus nkhaus ntawm tib lub npe, uas haum rau qhov chaw ob sab.
Ib lub hyperbola muaj ob lub axes: qhov tiag, uas nyob rau hauv daim duab no coincides nrog lub abscissa axis, thiab lub tswv yim ib tug, nrog lub y-axis. Yog tias koj lub hlwb pib tig qhov sib npaug ntawm ib qho hyperbola nyob ib ncig ntawm nws txoj kev xav, ces qhov chaw "pom" los ntawm qhov nkhaus yuav yog ib daim ntawv hyperboloid.
Yog tias, txawm li cas los xij, peb pib tig lub hyperbola nyob ib ncig ntawm nws qhov axis tiag tiag hauv txoj kev no, ces txhua tus ntawm ob "halves" ntawm qhov nkhaus yuav tsim nws tus kheej qhov chaw sib cais, thiab ua ke nws yuav hu ua ob- sheeted hyperboloid.
Tau txais los ntawm kev tig lub dav hlau sib thooj, lawv raug hu ua hyperboloids ntawm kev sib hloov. Lawv muaj parameters nyob rau hauv tag nrho cov kev taw qhia perpendicular mus rau lub axis ntawm kev sib hloov,belongs rau lub rotated nkhaus. Feem ntau, qhov no tsis yog qhov teeb meem.
Hyperboloid equation
Feem ntau, qhov chaw tuaj yeem txhais tau los ntawm qhov sib npaug hauv qab no hauv Cartesian kev tswj hwm (x, y, z):
Nyob rau hauv cov ntaub ntawv ntawm ib tug hyperboloid ntawm kiv puag ncig, nws symmetry txog lub axis nyob ib ncig ntawm nws rotated yog qhia nyob rau hauv qhov sib npaug ntawm cov coefficients a=b.
tus yam ntxwv hyperboloid
Nws muaj kev dag. Peb paub tias curves ntawm lub dav hlau muaj foci - nyob rau hauv cov ntaub ntawv ntawm ib tug hyperbola, piv txwv li, lub module ntawm qhov sib txawv nyob rau hauv qhov kev ncua deb ntawm ib tug arbitrary point ntawm ib tug hyperbola mus rau ib tug tsom xam thiab qhov thib ob yog tas li los ntawm txhais, qhov tseeb, ntawm kev tsom xam. cov ntsiab lus.
Thaum tsiv mus rau qhov chaw peb sab, lub ntsiab lus tsis hloov pauv: foci yog dua ob lub ntsiab lus, thiab qhov sib txawv ntawm qhov kev ncua deb ntawm lawv mus rau qhov chaw tsis txaus ntseeg ntawm qhov chaw hyperboloid yog tas li. Raws li koj tuaj yeem pom, tsuas yog qhov thib peb kev tswj hwm tau tshwm sim los ntawm kev hloov pauv rau txhua qhov ua tau, vim tias tam sim no lawv tau teeb tsa hauv qhov chaw. Feem ntau hais lus, txhais lub hom phiaj yog sib npaug los txheeb xyuas hom nkhaus lossis qhov chaw: los ntawm kev sib tham txog yuav ua li cas cov ntsiab lus ntawm qhov chaw nyob txheeb ze rau foci, peb tau teb cov lus nug ntawm seb lub hyperboloid yog dab tsi thiab nws zoo li cas.
Nws tsim nyog nco ntsoov tias ib qho hyperbola muaj asymptotes - cov kab ncaj, uas nws cov ceg zoo li infinity. Yog hais tias, thaum tsim lub hyperboloid ntawm kiv puag ncig, ib lub hlwb tig cov asymptotes ua ke nrog hyperbola, ces ntxiv rau cov hyperboloid, ib tug kuj yuav tau txais ib lub khob hu ua asymptotic. Lub asymptotic cone yograu ib daim ntawv thiab ob daim ntawv hyperboloids.
Lwm tus yam ntxwv tseem ceeb uas tsuas yog ib daim ntawv hyperboloid muaj yog lub tshuab hluav taws xob rectilinear. Raws li lub npe implies, cov no yog kab, thiab lawv pw tag nrho ntawm ib tug muab nto. Ob lub tshuab hluav taws xob rectilinear dhau los ntawm txhua qhov chaw ntawm ib daim ntawv hyperboloid. Lawv suav nrog ob tsev neeg ntawm kab, uas tau piav qhia los ntawm cov kab ke hauv qab no ntawm kev sib npaug:
Yog li, ib daim ntawv hyperboloid tuaj yeem ua tiav ntawm cov kab ncaj nraim ntawm ob tsev neeg, thiab txhua kab ntawm ib qho ntawm lawv yuav cuam tshuam nrog tag nrho cov kab ntawm lwm tus. Qhov chaw sib thooj rau cov khoom zoo li no yog hu ua txiav; lawv tuaj yeem tsim tau los ntawm kev sib hloov ntawm ib txoj kab ncaj nraim. Kev txhais los ntawm kev sib koom ua ke ntawm cov kab (rectilinear generators) nyob rau hauv qhov chaw kuj ua hauj lwm raws li ib tug unambiguous designation ntawm dab tsi ib tug hyperboloid yog.
Ntawm yam khoom ntawm ib qho hyperboloid
Qhov kev txiav txim thib ob thiab lawv qhov chaw sib thooj ntawm kev hloov pauv txhua tus muaj cov khoom siv kho qhov muag nthuav dav cuam tshuam nrog foci. Nyob rau hauv cov ntaub ntawv ntawm ib tug hyperboloid, qhov no yog formulated raws li nram no: yog hais tias ib tug hluav taws xob raug rho tawm haujlwm los ntawm ib tug ua kom pom tseeb, ces, muaj reflected los ntawm lub ze tshaj plaws "phab ntsa", nws yuav coj xws li ib tug kev taw qhia raws li yog hais tias nws yog los ntawm lub thib ob tsom xam.
Hyperboloids hauv lub neej
Feem ntau, cov neeg nyeem feem ntau pib lawv cov kev paub nrog kev txheeb xyuas geometry thiab qhov chaw thib ob los ntawm cov ntawv tseeb tshiab los ntawm Alexei Tolstoy"Hyperboloid engineer Garin". Txawm li cas los xij, tus kws sau ntawv nws tus kheej tsis paub zoo tias qhov hyperboloid yog dab tsi, lossis kev txi qhov tseeb rau kev ua yeeb yam: cov lus piav qhia, ntawm cov yam ntxwv ntawm lub cev, yog ib qho paraboloid uas sau tag nrho cov duab tshav hauv ib qho kev tsom xam (thaum lub optical zog ntawm lub hyperboloid yog txuam nrog cov tawg ntawm rays).
Cov qauv hu ua hyperboloid yog nrov heev hauv architecture: cov no yog cov qauv uas zoo li ib daim ntawv hyperboloid lossis hyperbolic paraboloid. Qhov tseeb yog tias tsuas yog cov chaw ntawm kev hloov pauv ntawm qhov kev txiav txim thib ob muaj cov tshuab hluav taws xob rectilinear: yog li, cov qauv nkhaus tuaj yeem tsim los ntawm cov kab ncaj nraim. Qhov zoo ntawm cov qauv zoo li no muaj peev xwm tiv taus cov khoom hnyav, piv txwv li, los ntawm cov cua: cov duab hyperboloid yog siv rau hauv kev tsim cov qauv siab, piv txwv li, TV yees.
