Muaj ntau yam kev ua pov thawj rau Pythagorean Theorem: Piv txwv, kev piav qhia thiab kev txheeb xyuas

Ib yam yog tseeb ib puas feem pua uas rau lo lus nug, uas yog sib npaug zos rau cov square ntawm lub hypotenuse, ib tug neeg laus ua siab loj teb: "lub sum ntawm cov plaub fab ntawm ob txhais ceg." Qhov no theorem yog nrees daig nyob rau hauv lub minds ntawm txhua txhua kawm ntawv tus neeg, tab sis koj cia li hais kom ib tug neeg los ua pov thawj nws, thiab tej zaum yuav muaj teeb meem. Yog li ntawd, cia peb nco ntsoov thiab xav txog ntau txoj kev los ua pov thawj rau Pythagorean theorem.

Ib tug txheej txheem cej luam ntawm lub biography

Lub Pythagorean theorem yog paub yuav luag txhua leej txhua tus, tab sis rau ib txhia yog vim li cas, tib neeg lub neej, uas tau ua nws mus rau lub teeb, tsis yog li ntawd nrov. Qhov no yog fixable. Yog li ntawd, ua ntej koj tshawb txog ntau txoj kev los ua pov thawj rau hauv lub Pythagorean theorem, peb yuav tsum luv luv ntsib nrog nws cwm pwm.

Pythagoras - philosopher, mathematician, philosopher Ameslikas los ntawm ancient Greece. Niaj hnub no nws yog heev yooj yim kom paub qhov txawv nws biography los ntawm cov legends uas tau raug tsim nyob rau hauv lub cim xeeb ntawm no kuj zoo kawg txiv neej. Tab sis nws li nram no los ntawm tej hauj lwm ntawm nws cov thwjtim, Pifagor Samossky yug nyob rau cov kob ntawm Samos. Nws txiv yog ib tug stonecutter li qub, tab sis nws niam tuaj los ntawm ib tug noble tsev neeg.

Raws li cov lus dab neeg, cov me nyuam yug ntawm Pythagoras kwv yees poj niam hu ua Pythia, nyob rau hauv uas nws yawm thiab npe hu ua cov me nyuam tub. Raws li nws twv ua ntej ntawm yug me nyuam ntawm ib tug me nyuam tub yuav coj ib tug ntau ntawm cov kev pab thiab ua siab zoo rau noob neej. Tias nyob rau hauv qhov tseeb nws puas tau.

Cov me nyuam yug ntawm tus theorem

Nyob rau hauv nws cov hluas, Pythagoras tsiv los ntawm Samos rau tim lyiv teb chaws kom tau raws li nrog Iyiv sages paub. Tom qab lub rooj sib tham nrog lawv, nws twb mus nyob hauv lub kawm, thiab paub qhov twg tag nrho cov poj achievements ntawm tus Iyiv philosophy, lej thiab cov tshuaj.

Nws yog tej zaum nyob rau hauv Egypt Pythagoras tshwm sim los ntawm lub hwj chim thiab kev zoo nkauj ntawm cov pyramids thiab tsim nws kuj zoo kawg kev tshawb xav. Nws yuav shock txawj nyeem ntawv, tab sis niaj hnub historians ntseeg tau hais tias Pythagoras tsis ua pov thawj nws kev tshawb xav. Thiab tsuas imparted nws paub ntawm cov thwjtim uas tom qab ua tiav tag nrho cov tsim nyog zauv.

Txawm nws yog, nws yog tam sim no lub npe hu ntau tshaj ib txoj kev ntawm cov ntawv pov thawj ntawm no theorem, tab sis ob peb. Niaj hnub no muaj peev xwm tsuas yog twv yuav ua li cas lub Greeks ua lawv suav, li ntawd, muaj ntau txoj kev mus saib cov ntawv pov thawj ntawm cov Pythagorean theorem.

Pythagoras 'theorem

Ua ntej yuav pib ib yam muab xam, koj yuav tsum paub uas tshawb xav los ua pov thawj. Lub Pythagorean theorem yog: "Nyob rau hauv ib daim duab peb sab nyob rau hauv uas yog ib tug ntawm cov ces kaum yog ^{hais txog} 90, lub sum ntawm cov plaub fab ntawm ob txhais ceg sib npaug rau hauv lub square ntawm lub hypotenuse."

Nyob rau hauv tag nrho muaj yog 15 ntau txoj kev los ua pov thawj rau hauv lub Pythagorean theorem. Qhov no yog ib tug theej siab daim duab, thiaj li them cov xim lub nrov tshaj plaws ntawm lawv.

txoj kev ib tug

Ua ntej, peb txhais hais tias peb yuav muab. Cov ntaub ntawv no yuav muab ncua rau lwm txoj kev ntawm cov ntawv pov thawj ntawm cov Pythagorean theorem, li ntawd, nws yog txoj cai yuav tsum nco ntsoov tag nrho cov uas twb muaj lawm designations.

Xav hais tias muab txoj cai-angled daim duab peb sab nrog ob txhais ceg ib tug, thiab ib tug hypotenuse sib npaug zos rau c. Tus thawj txoj kev yog raws li pov thawj hais tias, vim hais tias ntawm ib txoj cai daim duab peb sab uas yuav tsum tau kom tiav qhov square.

Ua li no, koj yuav tsum mus rau ib tug ceg ntev ntawm ib ya sib npaug zos rau tag ib ceg nyob rau hauv, thiab vice versa. Yog li ntawd nws yuav tsum tau muaj ob sib npaug zos sab ntawm lub square. Peb yuav tsuas kos ob thaum uas tig mus kab, thiab cov square yog npaj txhij.

Sab hauv, lub resulting nuj nqis yuav tsum kos lwm square nrog ib tug sab sib npaug zos rau cov hypotenuse ntawm tus thawj daim duab peb sab. Yuav kom qhov no kawg lub vertices ntawm ac thiab kev sib txuas lus yog tsim nyog los kos ob sib npaug zos feem nrog mus tib seem. Yog li muab cov peb sab ntawm ib tug square, yog ib tus uas yog tus thawj lub duab peb ceg lub hypotenuse. Docherty tseem tsuas cov plaub ya.

Raws li cov ua qauv nws yuav xaus lus tias tus txheej thaj tsam ntawm lub square yog sib npaug zos rau (a + b) ^2. Yog hais tias koj saib mus rau hauv cov nuj nqis, koj yuav pom tias nyob rau hauv tas li ntawd mus rau lub puab square nws muaj plaub txoj cai-angled cov vajvoos peb sab. Lub cheeb tsam ntawm txhua yog 0,5av.

Yog li ntawd, lub cheeb tsam yog sib npaug zos rau: 4 * 0,5av + c ² = ² + 2av

Li no, (a + b) ² = c ² + 2av

Thiab yog li ntawd, nrog ² = ² + ²

Qhov no qhia tau cov theorem.

Txoj kev ob: zoo xws li cov duab peb ceg

Qhov no mis yog qhov pov thawj ntawm tus Pythagorean theorem twb muab tau rau lub hauv paus ntawm kev pom zoo los ntawm lub seem geometry ntawm cov duab peb ceg. Nws hais tias ob txhais ceg ntawm ib txoj cai daim duab peb sab - qhov nruab nrab proportional rau nws hypotenuse thiab qhov ntev ntawm lub hypotenuse, emanating los ntawm lub kab los sib ntsib ^90.

Tus ntaub ntawv no yog tib yam, thiaj li cia tus pib tam sim ntawd nrog cov pov thawj. Kos perpendicular mus rau sab ntawm lub ya AB CD. Raws li cov saum toj no tso cai ob txhais ceg ntawm cov vajvoos peb sab yog muaj sib npaug:

AC = √AV * AD, CB = √AV * DV.

Yuav kom teb tau lo lus nug ntawm yuav ua li cas los ua pov thawj rau hauv lub Pythagorean theorem, lub pov thawj yuav tsum tau routed los ntawm squaring ob tsis sib npaug.

AC ² = AB * BP thiab CB ² = AB * DV

Tam sim no koj yuav tsum ntxiv txog lub resulting inequality.

AU ^{2 2} + CB = AB * (BP * ET) qhov twg BP = AB + ET

Nws hloov tawm hais tias:

AC ² + ² = CB AB * AB

Thiab yog li ntawd:

AU ^{2 2} + CB = AB ²

Lub pov thawj ntawm cov Pythagorean theorem thiab qhov sib txawv txoj kev uas nws tshuaj yuav tsum tau multi-ncau mus kom ze rau qhov teeb meem no. Txawm li cas los, qhov kev xaiv no yog ib tug ntawm cov nyuaj.

Lwm txoj kev xam

Hauj lwm ntawm txoj kev sib txawv los ua pov thawj rau hauv lub Pythagorean Theorem tej zaum yuav tsis muaj dab tsi hais, raws li ntev raws li feem ntau tsis tau lawv tus kheej tau pib xyaum. Muaj ntau ntawm cov hom kev kawm koom nrog tsis tau tsuas yog lej, tab sis kuj tsim kho ntawm lub thawj daim duab peb sab tshiab nuj nqis.

Nyob rau hauv cov ntaub ntawv no nws yog tsim nyog los suaj kaum qhov BC ceg ntawm lwm txoj cai-angled daim duab peb sab hauv lub IRR. Yog li ntawd tam sim no muaj ob tug duab peb ceg nrog tus ceg ntau tiv tshav ntuj kub

Paub txog hais tias lub chaw uas zoo xws li cov nuj nqis muaj ib tug piv raws li lub plaub fab ntawm lawv zoo xws li cov linear qhov ntev, ces:

S _ABC * ² - S ² * _HPA = S * thiab _AVD ² - S ² * ib _VSD

_Abc * S ⁽² C ²⁾ = ² * (S _AVD -S _VVD)

-to ^{2 2} = ²

² = ² + ²

Vim hais tias ntawm qhov sib txawv txoj kev pov thawj ntawm cov Pythagorean theorem rau qib 8, qhov kev xaiv no yog tsis yog tsim, koj muaj peev xwm siv cov nram qab txoj kev.

Qhov yooj yim txoj kev uas yuav ua pov thawj rau Pythagorean theorem. Xyuas

Nws yog ntseeg hais los ntawm historians, qhov no txoj kev twb xub siv rau cov ntawv pov thawj ntawm cov theorem nyob rau hauv ancient Greece. Nws yog ib qho yooj yim raws li nws tsis yuav tsum tau kiag li tsis muaj nyiaj them. Yog hais tias koj kos ib daim duab kom raug, qhov pov thawj ntawm tus assertion hais tias ib tug ² + ² = c ^2, nws yuav tau pom kom meej meej.

Cov ntsiab lus uas thiab tej yam kev mob rau txoj kev no yuav yuav ib nyuag txawv los ntawm lub yav dhau los yog ib tug. Ua pov thawj rau theorem, xav hais tias cov cai-angled daim duab peb sab ABC - ceskaum.

Hypotenuse AC noj cov kev taw qhia ntawm cov square thiab docherchivaem nws peb sab. Dhau li nws yog tsim nyog los siv ob kab pheeb ces kaum kab mus ua ib lub square. Yog li, yuav tau plaub equilateral cov vajvoos peb sab hauv nws.

Los ntawm Catete AB thiab CD raws li xav tau Docherty rau hauv lub square thiab tuav rau ntawm ib kab pheeb ces kaum kab nyob rau hauv txhua ntawm lawv. Kos ib kab los ntawm tus thawj kab los sib ntsib A, ib tug thib ob - los ntawm C.

Tam sim no peb yuav tsum tau coj ib tug nyob ze saib lub resulting duab. Raws li cov hypotenuse AC yog plaub cov vajvoos peb sab sib npaug zos rau cov thawj, tab sis nyob rau hauv Catete ob, nws hais txog lub veracity ntawm no theorem.

Los ntawm txoj kev, ua tsaug rau cov txheej txheem no, tus pov thawj ntawm cov Pythagorean theorem, thiab yug tus naas ej kab lus: "Pythagorean ris nyob rau hauv tag nrho cov lus qhia yog muaj sib npaug."

J. pov thawj. Garfield

Dzheyms Garfild - lub thib nees nkaum Thawj Tswj Hwm ntawm lub tebchaws United States of America. Nyob rau hauv tas li ntawd, nws tau tso nws lub cim nyob rau hauv keeb kwm raws li tus uas kav lub tebchaws United States, nws kuj yog ib tug gifted nws tus kheej-qhia.

Thaum pib ntawm nws cov hauj lwm, nws yog ib tug tsis tu ncua xib fwb ntawm lub pej xeem lub tsev kawm ntawv, tab sis tsis ntev los ua tus thawj coj ntawm ib qho ntawm lub tsev kawm ntawv qib siab. Cov muaj siab rau nws tus kheej-kev loj hlob thiab ua rau nws rau qhia ib tug tshiab kev tshawb xav ntawm lub pov thawj ntawm cov theorem ntawm Pythagoras. Theorem thiab ib qho piv txwv ntawm nws daws yog raws li nram no.

Thawj zaug nws yog tsim nyog los kos rau ntawm daim ntawv ob lub daim duab peb sab li hais tias ib tug ceg ntawm uas yog ib tug continuation ntawm lub yav tas. Lub vertices ntawm cov duab peb ceg yuav tsum tau kev cob cog rua rau mus tau ib trapeze.

Raws li yog lub npe hu, lub cheeb tsam ntawm ib tug Trapezoid yog sib npaug zos rau cov khoom ntawm ib nrab-sum ntawm nws puag thiab lub qhov siab.

S = ib + b / 2 * (a + b)

Yog hais tias peb xav txog qhov uas ua Trapezoid, raws li ib daim duab li ntawm peb cov duab peb ceg, nws cheeb tsam yuav tsum pom raws li nram no:

S = aw / 2 * 2 + ^2/2

Tam sim no nws yog tsim nyog los equalize lub ob thawj qhia

2av / 2 + c / 2 = (ib tug + b) ^2/2

² = ² + ²

Hais txog Pythagoras thiab yuav ua li cas los ua pov thawj rau koj tsis tau sau ib zaug xwb volume phau ntawv nyeem. Tab sis yog nws ua kev zoo siab thaum lawv paub tias yuav tsis muaj ntaub ntawv nyob rau hauv kev xyaum?

Tswv yim rau daim ntawv thov ntawm cov Pythagorean theorem

Tu siab, nyob rau hauv lub niaj hnub tsev kawm ntawv cov ntaub ntawv kawm qhia rau kev siv ntawm no theorem xwb nyob rau hauv geometric teeb meem. Kawm Ntawv Tiav yuav sai sai no tawm hauv lub tsev kawm ntawv phab ntsa, thiab tsis paub txog, thiab yuav ua li cas lawv yuav thov lawv cov kev paub thiab kev txawj ntse nyob rau hauv xyaum.

Nyob rau hauv qhov tseeb, siv cov Pythagorean theorem nyob rau hauv lawv lub neej txhua hnub txhua. Thiab tsis tsuas nyob rau hauv kev ua si, tab sis kuj nyob rau hauv zoo tib yam tsev neeg nyias muaj nyias haujlwm. Xav txog ob peb tus neeg mob qhov twg lub Pythagorean theorem thiab yuav ua li cas los ua pov thawj nws yuav tsis tshua muaj tsim nyog.

Kev sib txuas lus theorems thiab astronomy

Nws yuav zoo li uas lawv yuav tsum tau txuas mus rau lub hnub qub thiab cov vajvoos peb sab ntawm daim ntawv. Nyob rau hauv qhov tseeb, astronomy - ib tug scientific cheeb tsam nyob rau hauv uas dav siv lub Pythagorean theorem.

Piv txwv li, xav txog lub zog ntawm lub teeb beam nyob rau hauv qhov chaw. Nws yog lub npe hu hais tias lub teeb mus nyob rau hauv ob qho tib si qhia nyob rau tib lub ceev. AB trajectory, uas txav cov beam ntawm lub teeb yog hu ua l. Thiab ib nrab ntawm cov sij hawm yuav tsum tau rau lub teeb mus tau txais los ntawm point A taw tes B, peb hu t. Thiab cov kev ceev ntawm lub beam - c. Nws hloov tawm hais tias: c * t = l

Yog hais tias koj saib nyob rau ntawm no tib yam beam ntawm lwm lub dav hlau, piv txwv li, ib qhov chaw nkoj, uas tsiv rau tus ceev v, ces nyob rau hauv xws saib xyuas lub cev yuav hloov lawv ceev. Txawm li cas los, txawm lub tsau hais yuav tsiv mus nyob nrog ib tug tshaj tawm v nyob rau hauv kev coj rov qab.

Piv txwv comic liner floating txoj cai. Ces cov ntsiab lus A thiab B, uas yog torn ntawm tus nqaj yuav tsiv mus nyob rau sab laug. Ntxiv mus, thaum lub beam tsiv los ntawm point A taw tes B, taw tes Ib lub sij hawm yuav tawm mus, thiab, raws li, lub teeb tau tuaj mus rau hauv ib tug tshiab point C. Yuav kom nrhiav tau ib nrab qhov kev ncua deb ntawm uas tus taw tes A tau tsiv, nws yog tsim nyog los muab cov kev ceev ntawm lub nkoj nyob rau hauv ib nrab nqaj mus txawv tebchaws lub sij hawm (t ').

d = t '* v

Thiab mus nrhiav tau deb npaum li cas nyob rau hauv lub sij hawm yog tau dhau ib beam ntawm lub teeb uas yuav tsum tau mus kos tus cim rau tog taw tes rau ntawm lub tshiab beech s thiab cov nram qab no qhia:

s = c * t '

Yog hais tias peb xav txog tej yam uas tus taw tes ntawm lub teeb C thiab B, raws li zoo raws li lub qhov chaw nkoj - yog sab saum toj ntawm ib tug ceskaum daim duab peb sab, lub ya los ntawm tus taw tes A mus rau lub liner yuav phua nws mus rau hauv ob txoj kev-angled cov vajvoos peb sab. Yog li ntawd, ua tsaug rau Pythagorean theorem yuav nrhiav tau qhov kev ncua deb uas yog tau dhau ib beam ntawm lub teeb.

s = l ^{2 2} + d ²

Qhov no piv txwv yog, ntawm chav kawm, tsis yog tus zoo tshaj plaws, vim hais tias tsuas muaj ob peb tug yuav ua tau muaj hmoo txaus mus sim nws nyob rau hauv xyaum. Yog li ntawd, peb xav txog qhov ntau mundane daim ntaub ntawv ntawm no theorem.

Radius mobile teeb liab kis tau tus mob

Niaj hnub nimno lub neej yog tsis yooj yim sua xav txog tej yam tsis muaj lub hav zoov ntawm cov smartphone. Tab sis yuav ua li cas muaj ntau yam ntawm lawv yuav tau Proc yog hais tias lawv tsis muaj cuab kav mus cuag subscribers los ntawm mobile?!

mobile sib txuas lus zoo ncaj qha nyob rau hauv lub qhov siab ntawm uas tus kav hlau txais xov mus yuav tus mobile neeg teb xov tooj. Nyob rau hauv kev txiav txim los mus xyuas seb yuav ua li cas nyob deb deb ntawm cov xov tooj txawb yees yuav tau txais lub teeb liab, koj siv tau cov Pythagorean theorem.

Xav tias koj xav mus nrhiav cov approximate qhov siab ntawm ib tug tsau ntauwd, yog li ntawd nws muaj peev xwm faib lub teeb liab nyob rau hauv ib lub vojvoog ntawm 200 kis lus mev.

AB (qhov siab ntawm ntauwd) = x;

Sun (Teeb liab voos kheej-kheej) = 200 km;

OC (lub ntiaj teb txoj kev voos kheej-kheej) = 6380 km;

no

OB = o + AVOV = r + x

Thov lub Pythagorean theorem, peb nrhiav tau tawm yog dab tsi yam tsawg kawg nkaus ntauwd qhov siab yuav tsum 2.3 kis lus mev.

Pythagorean theorem nyob rau hauv lub tsev

Oddly txaus, lub Pythagorean theorem yuav pab tau txawm nyob rau hauv domestic teeb meem xws li qhov kev txiav txim ntawm lub qhov siab ntawm lub txee compartment, piv txwv li. Thaum xub thawj siab ib muag, yog tsis muaj yuav tsum tau siv tej complex suav, vim hais tias koj muaj peev xwm cia li coj koj ntsuam nrog ib daim kab xev ntsuas. Tab sis muaj ntau yam xav yog vim li cas qhov muaj txheej txheem muaj tej yam teeb meem, Yog hais tias tag nrho cov kev ntsuas tau noj raws nraim.

Qhov tseeb yog hais tias tus txee dai khaub ncaws yog yuav mus nyob rau hauv ib tug kab rov tav txoj hauj lwm thiab ces tsa thiab mounted phab ntsa. Yog li ntawd, lub sab phab ntsa ntawm lub txee nyob rau hauv tus txheej txheem ntawm lifting tus tsim yuav tsum ntws dawb do thiab nyob rau hauv qhov siab, thiab kab pheeb ces kaum qhov chaw.

Xav tias koj muaj ib tug wardrobe ntawm 800 hli tob. Qhov kev ncua deb ntawm lub hauv pem teb mus rau lub qab nthab - 2600 hli. Cov txee txiag hais tias lub qhov siab ntawm lub enclosure yuav tsum nyob 126 hli tsawg tshaj li qhov siab ntawm lub chav tsev. Tab sis yog vim li cas rau 126mm? Xav txog cov piv txwv nram qab.

Nyob rau hauv zoo tagnrho qhov ntev ntawm lub txee yuav xyuas qhov kev txiav txim ntawm lub Pythagorean Theorem:

√AV AC = ² + ² √VS

AU = √2474 ² 800 ² = 2600 mm - tag nrho cov sib.

Wb hais tias, lub qhov siab ntawm lub txee yog tsis sib npaug zos rau 2474 hli thiab 2505 hli. ces:

AU = √2505 ² + √800 = 2629 hli ^2.

Thiaj li, qhov no txee yog tsis haum rau installation nyob rau hauv lub chav tsev. Txij thaum khaws tau nws cov upright txoj hauj lwm yuav ua kev puas tsuaj rau nws lub cev.

Tej zaum yog qhov sib txawv txoj kev ua pov thawj rau Pythagorean Theorem los ntawm txawv zaum, peb yuav xaus uas nws yog ntau tshaj li qhov tseeb. Tam sim no koj muaj peev xwm siv cov ntaub ntawv nyob rau hauv lawv lub neej txhua hnub, thiab tau kiag li nco ntsoov hais tias tag nrho cov suav tsis tsuas pab tau, tab sis kuj muaj tseeb.