Cov ceg thiab lub hypotenuse yog ob sab ntawm daim duab peb sab. Thawj yog ntu uas nyob ib sab ntawm lub kaum sab xis, thiab lub hypotenuse yog qhov ntev tshaj plaws ntawm daim duab thiab yog qhov ntxeev ntawm lub kaum sab xis ntawm 90 o. Ib daim duab peb sab Pythagorean yog ib qho uas nws sab sib npaug rau cov lej ntuj; Lawv qhov ntev hauv qhov no yog hu ua "Pythagorean triple".
daim duab peb sab Egyptian
Yuav kom cov tiam tam sim no kawm geometry hauv daim ntawv uas nws tau qhia hauv tsev kawm tam sim no, nws tau tsim los rau ntau pua xyoo. Lub ntsiab lus tseem ceeb yog Pythagorean theorem. Ob sab ntawm daim duab peb sab (daim duab paub thoob plaws ntiaj teb) yog 3, 4, 5.
Muaj tsawg tus neeg tsis paub cov kab lus "Pythagorean ris sib npaug hauv txhua qhov kev qhia." Txawm li cas los xij, lub theorem ua tau zoo li no: c2 (lub square ntawm hypotenuse)=a2+b2 (cov sum ntawm ob txhais ceg).
Ntawm cov lej, ib daim duab peb sab nrog sab 3, 4, 5 (cm, m, thiab lwm yam) hu ua "Egyptian". Nws yog qhov nthuav tias lub vojvoog ntawm lub voj voog, uas tau sau rau hauv daim duab, yog sib npaug rau ib qho. Lub npe pib nyob ib ncig ntawm lub xyoo pua 5 BC, thaum Greek philosophers mus rau tim lyiv teb chaws.
Thaum tsim lub pyramids, architects thiab cov kws tshawb fawb siv qhov piv ntawm 3: 4: 5. Cov qauv zoo li no tau muab faib ua qhov sib npaug, ua rau lub qhov muag thiab qhov dav, thiab kuj tsis tshua tawg.
Yuav ua kom lub kaum sab xis, cov neeg tsim khoom siv txoj hlua khi 12 lub pob. Hauv qhov no, qhov tshwm sim ntawm kev tsim lub kaum sab xis ntawm lub kaum sab xis nce mus rau 95%.
Cov cim ntawm cov lej sib npaug
- Ib lub kaum sab xis nyob rau hauv daim duab peb sab thiab ib sab loj, uas sib npaug rau tib lub ntsiab lus hauv daim duab peb sab thib ob, yog qhov tsis txaus ntseeg ntawm kev sib npaug ntawm cov duab. Noj rau hauv tus account lub sum ntawm cov ces kaum, nws yog ib qho yooj yim los mus ua pov thawj tias lub thib ob mob ces kaum kuj sib npaug. Yog li, daim duab peb sab yog zoo tib yam nyob rau hauv lub thib ob feature.
- Thaum ob daim duab tau muab tso rau ib leeg, tig lawv mus rau hauv txoj kev uas lawv, ua ke, ua ib daim duab peb sab isosceles. Raws li nws cov cuab yeej, ob sab, lossis theej, lub hypotenuses, sib npaug, zoo li cov ces kaum ntawm lub hauv paus, uas txhais tau hais tias cov duab no yog tib yam.
Los ntawm thawj kos npe nws yooj yim heev los ua pov thawj tias daim duab peb sab sib npaug tiag tiag, qhov tseem ceeb yog ob sab me me (piv txwv li ob txhais ceg) sib npaug.
Daim duab peb sab yuav zoo ib yam hauv II feature, qhov tseem ceeb ntawm qhov sib npaug ntawm ceg thiab lub kaum sab xis.
Txoj kev ntawm daim duab peb sab nrog lub kaum sab xis
Qhov siab qis los ntawm lub kaum sab xis faib cov duab ua ob qhov sib npaug.
Ob sab ntawm lub kaum sab xis ntawm daim duab peb sab thiab nws qhov nruab nrab yog qhov yooj yim rau kev paub los ntawm txoj cai: qhov nruab nrab, uas yog qis rau lub hypotenuse, yog sib npaug rau ib nrab ntawm nws. Lub cheeb tsam ntawm ib daim duab tuaj yeem pom ob qho tib si los ntawm Heron cov qauv thiab los ntawm cov lus hais tias nws yog ib nrab ntawm cov khoom ntawm ob txhais ceg.
Nyob hauv ib daim duab peb sab, cov khoom ntawm cov kaum ntawm 30o, 45o thiab 60o.
- Nrog lub kaum sab xis yog 30o, nco ntsoov tias txhais ceg rov qab yuav sib npaug li 1/2 ntawm sab loj.
- Yog lub kaum sab xis yog 45o, ces lub kaum sab xis thib ob kuj yog 45o. Qhov no qhia tias daim duab peb sab yog isosceles, thiab nws ob txhais ceg yog tib yam.
- Txoj khoom ntawm kaum ntawm 60 o yog tias lub kaum peb muaj qhov ntsuas ntawm 30o.
Thaj chaw yooj yim nrhiav tau los ntawm ib qho ntawm peb tus qauv:
- dhau qhov siab thiab sab uas nws ntog;
- raws li Heron's formula;
- ntawm ob sab thiab lub kaum sab xis ntawm lawv.
Ob sab ntawm daim duab peb sab sab xis, lossis ob txhais ceg, sib sau ua ke nrog ob qhov siab. Yuav kom nrhiav tau qhov thib peb, nws yog ib qho tsim nyog yuav tsum xav txog qhov tshwm sim daim duab peb sab, thiab tom qab ntawd, siv Pythagorean theorem, xam qhov ntev yuav tsum tau ua. Ntxiv rau cov qauv no, kuj tseem muaj qhov sib piv ntawm ob zaug ntawm thaj chaw thiab qhov ntev ntawm hypotenuse. Cov lus qhia feem ntau ntawm cov tub ntxhais kawm yog thawj zaug, vim nws yuav tsum tau suav tsawg dua.
Theorems siv rau lub duab plaubdaim duab peb sab
Lub geometry ntawm daim duab peb sab txoj cai suav nrog kev siv theorems xws li:
- Pythagorean theorem. Nws lub ntsiab lus nyob rau hauv qhov tseeb hais tias lub square ntawm lub hypotenuse yog sib npaug zos rau cov sum ntawm cov squares ntawm ob txhais ceg. Hauv Euclidean geometry, qhov kev sib raug zoo no yog qhov tseem ceeb. Koj tuaj yeem siv cov mis yog tias muab ib daim duab peb sab, piv txwv li SNH. SN yog lub hypotenuse thiab yuav tsum tau pom. Then SN2=NH2+HS2.
- Cosine theorem. Generalizes Pythagorean theorem: g2=f2+s2-2fscos ntawm lub kaum sab xis ntawm lawv. Piv txwv li, muab ib daim duab peb sab DOB. Cov ceg DB thiab lub hypotenuse DO yog paub, nws yog tsim nyog los nrhiav OB. Ces tus qauv siv daim ntawv no: OB2=DB2+DO2-2DBDO cos lub kaum sab xis D. Muaj peb qhov tshwm sim: lub kaum sab xis ntawm daim duab peb sab yuav raug mob, yog tias lub square ntawm qhov ntev ntawm qhov thib peb raug rho tawm los ntawm cov lej ntawm cov squares ntawm ob sab, qhov tshwm sim yuav tsum tsawg dua xoom. Lub kaum sab xis yog obtuse yog tias qhov kev qhia no ntau dua xoom. Lub kaum sab xis yog kaum sab xis thaum sib npaug rau xoom.
- Sine theorem. Nws qhia tau hais tias kev sib raug zoo ntawm sab mus rau opposite lub kaum sab xis. Hauv lwm lo lus, qhov no yog qhov piv ntawm qhov ntev ntawm ob sab mus rau qhov sib txawv ntawm cov kaum sab xis. Hauv daim duab peb sab HFB, qhov twg hypotenuse yog HF, nws yuav muaj tseeb: HF / kev txhaum ntawm lub kaum B=FB / kev txhaum ntawm lub kaum H=HB / kev txhaum ntawm lub kaum F.
