Nyob hauv tsev kawm ntawv chav kawm geometry, lub sij hawm loj heev tau mob siab rau txoj kev kawm ntawm peb tog. Cov tub ntxhais kawm suav cov kaum, tsim bisectors thiab qhov siab, nrhiav seb cov duab sib txawv li cas, thiab qhov yooj yim tshaj plaws los nrhiav lawv thaj chaw thiab ib puag ncig. Nws zoo li qhov no tsis muaj txiaj ntsig zoo hauv txhua txoj hauv kev hauv lub neej, tab sis qee zaum nws tseem muaj txiaj ntsig kom paub, piv txwv li, yuav ua li cas txiav txim siab tias daim duab peb sab yog qhov sib npaug lossis obtuse. Yuav ua li cas?
Timpeb daim duab peb sab
Peb lub ntsiab lus uas tsis dag ntawm tib txoj kab ncaj nraim, thiab ntu uas txuas rau lawv. Nws zoo nkaus li tias daim duab no yog qhov yooj yim tshaj plaws. Daim duab peb sab yuav zoo li cas yog tias lawv tsuas muaj peb sab? Qhov tseeb, muaj ntau txoj kev xaiv, thiab qee qhov ntawm lawv tau txais kev saib xyuas tshwj xeeb raws li ib feem ntawm chav kawm geometry hauv tsev kawm. Ib daim duab peb sab sib npaug yog ib qho sib npaug, uas yog, tag nrho nws cov kaum sab xis thiab sab sib npaug. Nws muaj ntau yam khoom zoo kawg li, uas yuav tau tham tom qab.
Lub isosceles tsuas muaj ob sab sib npaug, thiab nws kuj yog qhov nthuav heev. Nyob rau hauv txoj cai-angled thiab obtuse-angled daim duab peb sab, raws li koj yuav twv, feem, ib tug ntawm cov ces kaum yog txoj cai los yog obtuse. Ntawmqhov no lawv kuj tuaj yeem yog isosceles.
Tseem muaj ib qho tshwj xeeb ntawm daim duab peb sab hu ua Egyptian. Nws sab yog 3, 4 thiab 5 units. Txawm li cas los xij, nws yog duab plaub. Nws ntseeg tau hais tias xws li daim duab peb sab tau nquag siv los ntawm Egyptian cov kws tshawb fawb thiab cov kws tsim vaj tsev tsim cov kaum sab xis. Nws ntseeg tau tias cov pyramids nto moo tau tsim nrog nws txoj kev pab.
Thiab tseem, tag nrho cov vertices ntawm daim duab peb sab tuaj yeem pw ntawm ib txoj kab ncaj nraim. Hauv qhov no, nws yuav raug hu ua degenerate, thaum tag nrho lwm tus hu ua non-degenerate. Lawv yog ib qho ntawm cov kev kawm ntawm geometry.
Daim duab peb sab sib npaug
Tau kawg, cov duab raug yog ib txwm nyiam tshaj plaws. Lawv zoo li zoo tag nrho, ntau graceful. Cov qauv rau kev suav lawv cov yam ntxwv feem ntau yooj yim thiab luv dua li cov duab zoo tib yam. Qhov no kuj siv tau rau daim duab peb sab. Nws tsis yog qhov xav tsis thoob tias lawv tau them nyiaj ntau rau lawv thaum kawm geometry: cov menyuam kawm ntawv tau qhia kom paub qhov txawv ntawm cov lej ntawm tus so, thiab kuj tham txog qee yam ntawm lawv cov yam ntxwv nthuav.
Cov cim thiab cov khoom
Raws li koj tuaj yeem twv los ntawm lub npe, txhua sab ntawm daim duab peb sab sib npaug yog sib npaug rau lwm qhov. Tsis tas li ntawd, nws muaj ntau tus yam ntxwv, ua tsaug uas nws tuaj yeem txiav txim siab seb daim duab puas yog lossis tsis yog.
- tag nrho nws cov kaum sib npaug, lawv tus nqi yog 60 degrees;
- bisectors, qhov siab thiab nruab nrab kos los ntawm txhua qhov vertex yog tib yam;
- daim duab peb sab tsis tu ncua muaj 3 axes ntawm symmetry, nwstsis hloov thaum tig 120 degrees.
- qhov nruab nrab ntawm lub voj voog tseem yog qhov nruab nrab ntawm lub voj voog ncig thiab lub ntsiab lus ntawm kev sib tshuam ntawm cov nruab nrab, cov bisectors, qhov siab thiab perpendicular bisectors.
Yog tias tsawg kawg ib qho ntawm cov cim saum toj no tau pom, ces daim duab peb sab yog sib npaug. Rau ib daim duab tsis tu ncua, tag nrho cov nqe lus saum toj no muaj tseeb.
Txhua daim duab peb sab muaj ntau yam zoo kawg nkaus. Ua ntej, txoj kab nruab nrab, uas yog, ntu faib ob sab hauv ib nrab thiab mus rau qhov thib peb, yog sib npaug rau ib nrab ntawm lub hauv paus. Qhov thib ob, cov lej ntawm tag nrho cov kaum ntawm daim duab no ib txwm sib npaug rau 180 degrees. Tsis tas li ntawd, muaj lwm qhov kev sib raug zoo hauv daim duab peb sab. Yog li ntawd, opposite sab loj yog lub kaum sab xis loj thiab vice versa. Tab sis qhov no, tau kawg, tsis muaj dab tsi ua nrog daim duab peb sab sib npaug, vim tias tag nrho nws cov ces kaum sib npaug.
Sau npe thiab hla lub voj voog
Nws tsis yog qhov txawv rau cov tub ntxhais kawm hauv chav kawm geometry los kawm seb cov duab tuaj yeem cuam tshuam nrog ib leeg. Tshwj xeeb, cov voj voog uas sau rau hauv polygons lossis piav qhia nyob ib puag ncig lawv tau kawm. Nws yog dab tsi?
Ib lub voj voog inscribed yog ib lub voj voog uas txhua sab ntawm lub polygon yog tangent. Piav - ib qho uas muaj cov ntsiab lus ntawm kev sib cuag nrog txhua lub ces kaum. Rau txhua daim duab peb sab, nws yog ib txwm ua tau los tsim ob lub voj voog thawj thiab thib ob, tab sis tsuas yog ib qho ntawm txhua hom. Cov pov thawj rau ob tus no
theorems tau muab rau hauvtsev kawm ntawv geometry chav kawm.
Ntxiv rau kev suav cov tsis txwv ntawm daim duab peb sab lawv tus kheej, qee qhov haujlwm tseem suav nrog suav cov kab hluav taws xob ntawm cov voj voog no. Thiab cov qauv rau daim duab peb sab sib npaug zoo li no:
r=a/√ ̅3;
R=a/2√ ̅3;
qhov twg r yog lub vojvoog ntawm lub voj voog sau, R yog lub vojvoog ntawm lub voj voog ncig, a yog qhov ntev ntawm sab ntawm daim duab peb sab.
xam qhov siab, ib puag ncig thiab cheeb tsam
Qhov tsis tseem ceeb, uas yog xam los ntawm cov menyuam kawm ntawv thaum kawm geometry, tseem tsis hloov pauv rau yuav luag txhua daim duab. Cov no yog cov perimeter, cheeb tsam thiab qhov siab. Kom yooj yim ntawm kev xam, muaj ntau yam qauv.
Yog li, qhov ib puag ncig, uas yog, qhov ntev ntawm txhua sab, suav nrog hauv qab no:
P=3a=3√ ̅3R=6√ ̅3r, qhov twg a yog sab ntawm daim duab peb sab, R yog lub vojvoog ntawm lub voj voog, r yog lub voj voog inscribed.
siab:
h=(√ ̅3/2)a, qhov twg yog qhov ntev ntawm sab.
Thaum kawg, cov qauv rau thaj tsam ntawm daim duab peb sab sib npaug yog muab los ntawm cov qauv qauv, uas yog, cov khoom ntawm ib nrab ntawm lub hauv paus thiab nws qhov siab.
S=(√ ̅3/4)a2, qhov twg a yog qhov ntev ntawm sab.
Tsis tas li, tus nqi no tuaj yeem suav los ntawm qhov ntsuas ntawm lub voj voog ncig lossis kos npe. Tseem muaj cov qauv tshwj xeeb rau qhov no:
S=3√ ̅3r2=(3√ ̅3/4)R2, qhov twg r thiab R yog raws qhov radii inscribed thiab circumscribed voj voog.
Kev tsim kho
Ib yam ntxivIb hom kev ua haujlwm nthuav dav, suav nrog daim duab peb sab, yog txuam nrog kev xav tau kos ib lossis lwm daim duab siv qhov tsawg kawg nkaus
tools: lub compass thiab tus kav tsis muaj kev faib.
Nws siv ob peb kauj ruam los tsim ib daim duab peb sab kom zoo nrog cov cuab yeej no xwb.
- Koj yuav tsum kos ib lub voj voog nrog ib lub vojvoog thiab nyob nruab nrab ntawm qhov chaw tsis ncaj ncees A. Nws yuav tsum raug cim.
- Tom ntej no, koj yuav tsum kos ib txoj kab ncaj nraim los ntawm qhov taw tes no.
- Kev hla ntawm lub voj voog thiab txoj kab ncaj nraim yuav tsum raug xaiv raws li B thiab C. Txhua qhov kev tsim kho yuav tsum tau ua nrog qhov tseeb tshaj plaws.
- Tom ntej no, koj yuav tsum tsim lwm lub voj voog nrog tib lub vojvoog thiab nruab nrab ntawm point C los yog ib qho arc nrog rau qhov tsim nyog. Cov kev sib tshuam yuav raug cim raws li D thiab F.
- Points B, F, D yuav tsum tau txuas los ntawm ntu. Ib daim duab peb sab sib npaug yog tsim.
Kev daws cov teeb meem no feem ntau yog teeb meem rau cov menyuam kawm ntawv, tab sis qhov txuj ci no tuaj yeem siv tau hauv lub neej txhua hnub.
