Trigonometric Ratios hauv Pyramids: Kev Tshuaj Xyuas Txog Kev Ua lej thiab Architecture Thaum Ub
Cov pyramids hauv tebchaws Iziv, tshwj xeeb yog lub Pyramid Loj ntawm Giza, tau ntev los ua lub cim ntawm tib neeg lub peev xwm tsim vaj tsev thiab yog qhov paub tsis meej uas tsis tau daws. Cov qauv no tsis yog tsuas yog qhov zoo kawg nkaus hauv lawv qhov loj me thiab qhov tseeb, tab sis kuj muab ntau cov ntaub ntawv rau cov kws lej, tshwj xeeb tshaj yog hauv kev siv trigonometry. Tsab xov xwm no tshuaj xyuas seb cov txheej txheem thiab cov tswv yim trigonometric tau siv li cas hauv kev tsim cov pyramids hauv tebchaws Iziv thiab vim li cas cov piv trigonometric tseem ceeb hauv kev nkag siab txog cov thev naus laus zis qub no.
1. Keeb Kwm Luv Luv ntawm Cov Pyramids Iyiv
Cov pyramids hauv tebchaws Iziv yog cov qauv loj uas tau tsim los ua lub ntxa rau cov vaj ntxwv thiab poj huab tais hauv kev ntseeg ntawm cov neeg Iziv thaum ub hauv lub neej tom qab. Lub pyramid qub tshaj plaws uas paub yog Pyramid ntawm Djoser ntawm Saqqara, uas tau tsim thaum lub sijhawm thib peb Dynasty los ntawm Imhotep, tus kws kes duab vajtse nto moo tshaj plaws hauv keeb kwm Iziv thaum ub. Lub ncov ntawm kev tsim pyramid tau tshwm sim thaum lub sijhawm thib plaub Dynasty, nrog rau Pyramid Loj ntawm Giza, uas tau tsim rau Pharaoh Khufu nyob ib puag ncig 2580–2560 BC.
2. Trigonometry: Cov Ntsiab Lus Tseem Ceeb thiab Cov Kev Siv
Trigonometry yog ib ceg ntawm kev suav lej uas kawm txog kev sib raug zoo ntawm cov ces kaum thiab qhov ntev ntawm sab hauv cov duab peb ceg. Cov ntsiab lus tseem ceeb ntawm trigonometry cuam tshuam nrog cov sine (sin), cosine (cos), thiab tangent (tan) functions ntawm cov ces kaum ntawm ib daim duab peb ceg. Peb lub functions no cuam tshuam txog qhov ntev ntawm cov sab ntawm daim duab peb ceg thiab pab hauv kev xam cov ces kaum thiab sab uas tsis paub.
Hauv cov ntsiab lus ntawm kev tsim lub pyramid, trigonometry siv los txiav txim siab qhov ntxhab ntawm cov sab thiab qhov siab tshaj plaws ntawm lub pyramid. Ob lub tswv yim tseem ceeb trigonometric uas siv ntau yog "inclination," uas feem ntau ntsuas ua degrees lossis radiants, thiab "slope," uas cuam tshuam txog qhov sib piv ntawm sab nraud thiab ceg ntawm lub duab peb ceg hauv cov ntsiab lus ntawm qhov ntxhab ntawm lub pyramid.
3. Kev Siv Trigonometry Hauv Kev Tsim Pyramid
Rov qab mus rau lub sijhawm ua ntej muaj cov tshuab xam zauv thiab khoos phis tawj, trigonometry thaum ub yuav zoo li xav tsis thoob. Txawm li cas los xij, cov kws kes duab vajtse Iyiv thaum ub tau siv cov tswv yim trigonometric yooj yim rau hauv kev tsim cov pyramids, xws li Great Pyramid.
a. Lub kaum sab xis ntawm lub pyramid
Lub Pyramid Loj ntawm Giza muaj qhov nqes hav meej heev ntawm kwv yees li 51,5 degrees. Lawv ua tiav qhov no li cas? Cia peb tshuaj xyuas nws siv trigonometry. Yog tias peb xav txog lub duab peb sab uas tsim los ntawm ib nrab ntawm lub hauv paus ntawm lub pyramid, qhov siab ntawm lub pyramid, thiab hypotenuse ntawm lub hauv paus mus rau apex, peb tuaj yeem siv lub luag haujlwm tangent.
Tus tangent ntawm lub kaum sab xis (θ) yog qhov piv ntawm qhov siab ntawm lub pyramid (h) rau ib nrab ntawm qhov ntev ntawm lub hauv paus ntawm lub pyramid (b/2).
Yog tias d yog qhov ntev ntawm lub hauv paus ntawm lub pyramid, ces:
tan(θ) = h / (d / 2)
Nrog lub kaum sab xis ntawm qhov inclination uas tau xam ua 51,5 degrees, peb tau txais:
xim av daj (51.5°) ≈ 1.273
Qhov no txhais tau hais tias qhov piv ntawm qhov siab ntawm lub pyramid rau ib nrab ntawm nws qhov ntev ntawm lub hauv paus yuav tsum yog kwv yees li 1.273. Qhov no tso cai rau peb kwv yees qhov siab ntawm lub pyramid yog tias paub qhov ntev ntawm nws lub hauv paus.
b. Siv Pythagorean Theorem
Ntxiv rau qhov tangent function, Pythagorean theorem kuj tseem siv los xyuas kom meej qhov tseeb ntawm cov proportions hauv kev tsim pyramid. Rau daim duab peb sab uas tau hais ua ntej, peb tuaj yeem siv Pythagorean theorem:
a² + b² = c²
Qhov twg a yog qhov siab ntawm lub pyramid, b yog ib nrab ntawm qhov ntev ntawm lub hauv paus, thiab c yog qhov siab ntawm lub pyramid.
4. Cov Pov Thawj ntawm Kev Siv Trigonometry los ntawm Cov Kws Txua Vaj Tse Thaum Ub
Txawm hais tias muaj ntau tus neeg sib cav tias cov neeg Iyiv thaum ub tej zaum yuav tsis paub txog cov tswv yim ntawm trigonometry, lawv yeej muaj kev paub txog kev ua haujlwm txaus los siv cov txheej txheem zoo sib xws. Cov pov thawj ntawm qib siab ntawm kev ua kom raug qhia tias lawv muaj cov txheej txheem ntsuas thiab npaj zoo heev.
Cov kws kes duab vajtse ntawm lub sijhawm ntawd paub tias tau siv lub kaw lus 'seked' ntawm kev ntsuas lub kaum sab xis siv caj npab thiab ntiv tes. Hauv lub kaw lus no, ib 'caj npab' yog sib npaug rau qhov ntev tshwj xeeb, thiab ib 'ntiv tes' yog ib qho ordal me dua - zoo ib yam li lub tswv yim niaj hnub ntawm trigonometry, uas faib cov ces kaum ua tej daim.
5. Kev Sib Piv Trigonometric Ntawm Cov Pyramids
Tsuas yog lub Pyramid Loj xwb, tsis yog txhua lub pyramids hauv tebchaws Iziv muaj tib lub kaum sab xis. Piv txwv li:
- Lub Pyramid Liab ntawm Dahshur muaj lub kaum sab xis ntawm kwv yees li 43 degrees, piv rau lub kaum sab xis ntawm Lub Pyramid Loj ntawm Giza.
- Lub Pyramid khoov, paub txog nws qhov kev hloov pauv ntawm lub kaum sab xis ntawm 54 degrees mus rau 43 degrees hauv nruab nrab.
Cov kev hloov pauv no qhia tau tias cov kws kes duab vajtse thaum ub kuj tau sim nrog ntau lub kaum sab xis thiab cov txheej txheem sib txawv, tsim cov pyramids nrog cov qauv sib txawv thiab cov tsos tshwj xeeb.
6. Txoj kev
Kev sib xyaw ua ke ntawm kev paub txog keeb kwm thiab lej, kev tshuaj xyuas trigonometric ntawm cov pyramids qhia txog kev txawj ntse ntawm cov txheej txheem kev tsim vaj tsev thaum ub. Lawv tsis tsuas yog xam cov ces kaum thiab qhov sib piv nrog kev txawj ntse uas zoo li qub tab sis muaj txiaj ntsig zoo. Kev siv trigonometry ua rau muaj kev tsim cov qauv uas tsis yog tsuas yog loj heev hauv qhov ntsuas tab sis kuj ruaj khov hauv qhov tseeb thiab kev sib npaug.
Los ntawm kev nkag siab txog kev siv trigonometry rau cov pyramids no, peb tsis yog tsuas yog txaus siab rau lub peev xwm engineering ntawm ancient Egypt tab sis kuj kawm ntxiv txog keeb kwm ntawm kev txhim kho lej hauv ancient architecture. Cov pyramids sawv cev rau cov pov thawj tseem ceeb ntawm kev sib xyaw ntawm kev kos duab thiab kev tshawb fawb uas tau mus txog qhov siab tshaj plaws ntau txhiab xyoo ua ntej peb cov thev naus laus zis niaj hnub no muaj.
