Pythagoras thiab nws Theorem [YOOJ YIM]
Pythagorean Theorem nws yog ib qho ntawm cov tseem ceeb theorems. Hauv paus hauv kev ua lej, geometry, trigonometry, algebra thiab siv dav hauv lub neej txhua hnub xws li kev tsim kho, kev tshawb fawb, lub ntsiab lus saum toj, thiab lwm yam.
Pythagorean Theorem tso cai rau koj kom pom qhov ntev ntawm ob sab ntawm ib daim duab peb sab xis, thiab txawm hais tias ntau daim duab peb sab tsis raug, lawv txhua tus muaj peev xwm muab faib ua ob txoj hauv daim duab peb sab, qhov twg Pythagorean Theorem tuaj yeem siv tau.
COV LUS TSEEM CEEB "Kom nkag siab txog Pythagorean theorem"
Daim duab peb sab:
Cov duab geometric, hauv lub dav hlau, tsim los ntawm peb sab uas sib ntsib ntawm cov chaw loj. Cov ntawv sau siab yog sau ua cov tsiaj ntawv loj thiab sab rau sab sau txog qhov sib txawv ntawm cov tsiaj ntawv me. Saib daim duab 1. Hauv daim duab peb ceg:
- Qhov sib xyaw ntawm ob ntawm nws sab yog ntau dua li ntawm lwm sab.
- Qhov suav ntawm cov ces kaum ntawm ib daim duab peb sab ntsuas 180º.
Kev faib tawm ntawm cov duab peb ceg
Ua raws li qhov ntev ntawm ob sab, ib daim duab peb sab tuaj yeem yog sib npaug yog tias nws muaj peb lub vaj huam sib luag, isosceles yog tias nws muaj ob sab sib npaug, lossis scalene yog tias tsis muaj ib sab nws sib npaug. Saib daim duab 2.
Txoj cai kaum sab xis yog ib qho uas ntsuas 90 °. Yog hais tias lub kaum sab xis tsawg dua 90 ° nws hu ua "lub kaum ntse ntse". Yog hais tias lub kaum sab xis siab dua 90 ° ces nws hu ua "obtuse angle". Raws li cov ces kaum, daim duab peb ceg tau muab faib ua:
- Cov ces kaum: yog tias lawv muaj 3 lub kaum ntse ntse.
- Duab plaub: yog tias lawv muaj txoj cai kaum sab xis thiab ob lub kaum sab xis muaj qhov sib txawv.
- Cov ces kaum ruam: yog tias lawv muaj obtuse kaum sab xis thiab lwm yam mob. Saib daim duab 3.
Txoj cai daim duab peb sab:
Daim duab peb sab xis yog ib qho uas muaj lub kaum sab xis (90 °). Ntawm peb sab ntawm cov duab peb sab xis, ntev tshaj plaws yog hu ua "hypotenuse", lwm qhov hu ua "ceg" [1]:
- Kev Ua Phem: sab sib xws Lub kaum sab xis ntawm ib lub duab peb ceg kaum. Sab ntev dua yog hu ua hypotenuse uas yog qhov fab ntxeev ntawm lub kaum sab xis.
- Ob txhais ceg: nws yog ib qho ntawm ob qho me me ntawm ib sab xis uas ua muaj lub kaum sab xis. Saib daim duab 4.
Pythagoras theorem
Nqe lus ntawm Pythagorean Theorem:
Pythagorean Theorem hais tias, rau ib daim duab peb sab zoo, hypotenuse plaub fab sib npaug yog sib npaug ntawm cov lej sib npaug ntawm ob ceg. [ob]. Saib daim duab 2.
Pythagorean theorem Nws tseem tuaj yeem hais raws li hauv qab no: Lub xwmfab ua rau lub hypotenuse ntawm ib txoj cai peb ceg kaum muaj qhov chaw tib yam ntawm cov lej ntawm thaj chaw ntawm plaub fab ua rau ntawm txhais ceg. Saib duab 6.
Nrog rau Pythagoras theorem Koj tuaj yeem txiav qhov ntev ntawm ib qho ntawm ib sab ntawm daim duab peb sab xis. Hauv daim duab 7 yog cov qauv qauv los nrhiav cov hypotenuse lossis qee cov ceg ntawm lub duab peb ceg.
Kev Siv Cov Pythagora theorem
Kev Tsim Kho:
Pythagorean theorem Nws muaj txiaj ntsig hauv kev tsim qauv thiab kev tsim kho ntawm kev nce ntaiv, ntaiv, kab pheeb ces kaum, ntawm lwm tus, piv txwv li, rau kev suav qhov ntev ntawm lub vov tsev ntu. Daim duab 8 qhia tau hais tias rau kev tsim kho ntawm cov tsev sib txuas, trestles thiab hlua yog siv cov khoom uas yuav tsum ua raws li Pythagorean Theorem.
Xov Xwm:
Hauv topography, qhov saum npoo los yog nyem ntawm qhov av ib qho yog sawv cev ntawm ntawm qhov dav hlau. Piv txwv li, qhov tsis yooj yim ntawm cov thooj av tuaj yeem suav nrog siv ntsuas pas ntsuas ntawm qhov siab paub thiab lub tsom iav. Txoj cai kaum sab xis yog tsim los ntawm txoj kab ntawm qhov pom ntawm lub tsom iav thiab pas nrig, thiab ib zaug qhov siab ntawm tus pas nrig paub, Pythagorean theorem siv los txiav txim siab qhov nqes hav ntawm qhov av. Saib duab 8.
Daim duab peb sab:
Nws yog txoj kev siv los txiav txim siab qhov chaw ntawm ib qho khoom, paub ob lub ntsiab lus siv. Daim duab peb sab yog siv hauv xov tooj ntawm tes nrhiav, hauv kev qhia kev siv tshuab, hauv kev tshawb pom ntawm lub nkoj hauv qhov chaw, thiab lwm yam. Saib duab 9.
Pythagoras yog leej twg?
Pythagoras yug nyob rau tim Nkij teb chaws 570 BC, tuag xyoo 490 BC Nws yog ib tug neeg txawj ntse thiab txawj lej. Nws lub tswv yim yog tias txhua tus lej muaj lub ntsiab lus los saum ntuj, thiab kev sib txuas ntawm cov naj npawb tau nthuav tawm lwm lub ntsiab lus. Txawm hais tias nws tsis tau tshaj tawm ib qho kev sau ntawv thoob plaws nws lub neej, nws paub rau kev qhia txog theorem uas muaj nws lub npe, muaj txiaj ntsig zoo rau kev kawm ntawm cov duab peb ceg. Nws suav hais tias yog thawj thawj cov neeg ua lej zoo, uas tau tsim cov kev tshawb fawb txog lej nyob rau hauv geometry thiab astronomy. [ob]. Saib duab 2.
Xyaum ua si
Txhawm rau Siv Pythagorean Theorem, thawj qhov yuav tsum tau paub yog qhov twg txoj cai daim duab peb sab tsim, uas ntawm lub sab yog lub hypotenuse thiab ob txhais ceg.
Txoj Haujlwm 1. Txheeb xyuas tus nqi ntawm lub hypotenuse rau daim duab peb sab xis rau hauv daim duab
Tshuaj:
Daim duab 12 qhia tau qhov kev suav ntawm lub hypotenuse ntawm daim duab peb sab.
Kev Ua Rog 2. Ib tus ncej yuav tsum tau txais kev txhawb nqa los ntawm kev teeb tsa peb txoj hlua hluav taws xob, raws li qhia hauv daim duab 13. Yuav tsum tau yuav ntau txoj hlua hluav taws xob cable?
Tshuaj
Yog hais tias qhov cable tau txiav txim siab raws li qhov hypotenuse ntawm ib txoj cai daim duab peb sab tsim nruab nrab ntawm lub cable, ncej thiab hauv av, qhov ntev ntawm ib qho ntawm cov cable tau txiav txim siab siv Pythagorean theorem. Txij li thaum muaj peb kab, qhov ntev tau tau yog khoo los ntawm 3 kom tau tag nrho ntev uas xav tau. Saib duab 14.
Cov Lus Cog Tseg 3. Txhawm rau thauj qee lub thawv, los ntawm chav tsev thib ob mus rau hauv av, koj xav yuav ib txoj hlua khi conveyed zoo li qhov uas tau qhia hauv daim duab 15. Yuav tsum siv lub conveyor siv ntev npaum li cas?
Tshuaj:
Xav txog txoj kev siv conveyor raws li kev hypotenuse ntawm txoj cai daim duab peb sab tsim nruab nrab ntawm txoj siv txoj hlua, hauv av thiab phab ntsa, hauv Daim duab 16 qhov ntev ntawm txoj siv conveyor siv xam tau.
Kev Ua Si 4. Ib tug kws ntoo txua ib daim rooj tog uas cov phau ntawv yuav tsum tau mus, thiab ib qho ntawm 26 television TV. Qhov dav thiab siab npaum li cas qhov kev faib tawm yuav tsum nyob qhov twg hauv TV yuav mus? Saib duab 17.
Tshuaj:
Qhov ntsuas siv hauv cov khoom siv hluav taws xob xws li xov tooj, ntsiav tshuaj, TV, thiab lwm tus, hauv kab pheeb ces kaum ntawm lub vijtsam. Rau ib 26 "TV, lub vij vij kab pheeb ces kaum yog 66,04 cm. Xav txog ntawm daim duab peb sab zoo tsim los ntawm kab pheeb ces kaum ntawm lub vijtsam, thiab ob sab ntawm lub TV, Pythagorean theorem tuaj yeem siv los txiav txim siab qhov dav ntawm lub TV. Saib duab 18.
SIB THAM ntawm Pythagorean Theorem
Pythagorean Theorem tso cai rau koj los nrhiav qhov ntev ntawm ob sab ntawm ib daim duab peb sab xis, thiab txawm tias muaj lwm daim duab peb tog, vim cov no yuav muab faib ua cov ceg kaum hauv txoj cai.
Pythagorean Theorem qhia tau hais tias lub xwmfab ntawm hypotenuse ntawm ib daim duab peb sab yog sib npaug ntawm cov lej ntawm cov ceg ntawm ob txhais ceg, tau txais txiaj ntsig zoo hauv kev kawm txog geometry, trigonometry, thiab kev ua lej feem ntau, nrog kev siv dav hauv kev tsim kho, kev tshawb fawb, topography, ntau lwm yam kev siv.
Peb thov caw koj saib cov kab lus Newton cov cai "yooj yim to taub"
