Nzira dzakasiyana kuratidza theorem no kuna Achibvuma pfungwa yaPythagoras: mienzaniso, tsananguro uye wongororo

Chimwe chinhu ndechokuti chokwadi zana muzana kuti mubvunzo, izvo zvakaenzana yaiungana ari hypotenuse, chero mukuru kupindura noushingi: ". Vakaverenga dzinoungana vanhu makumbo" theorem no iyi zvakasimba rakabayirwa mupfungwa ose munhu akadzidza, asi iwe chete kubvunza mumwe munhu kuzviratidza, uye pangava nematambudziko. Saka, ngatirangarirei uye funga dzakasiyana kuratidza Pythagorean theorem no.

Zvakaita Biography

The Pythagorean theorem no inozivikanwa anenge munhu wose, asi vamwe chikonzero, upenyu hwevanhu, rakamwisa kuti chiedza, hazvina kukurumbira kudaro. Izvi fixable. Saka, usati mundotarisisa dzakasiyana kuratidza Pythagorean theorem no, tinofanira muchidimbu kuzivana unhu hwake.

Achibvuma pfungwa yaPythagoras - muzivi, yemasvomhu, muzivi anobva Greece yekare. Nhasi zvakaoma chaizvo kusiyanisa Biography yake kubva ngano kuti zvakatangwa pakuyeuka murume uyu mukuru. Asi anotevera mabasa vateveri vake, Pifagor Samossky akaberekwa pachitsuwa Samosi. baba vake aiva matombo kuipa, asi mai vake aibva mumhuri chakanaka.

Maererano nengano, kuzvarwa Achibvuma pfungwa yaPythagoras rakafanotaura mukadzi anonzi Pythia, uyo nokukudzwa uye akatumidza mukomana. Maererano wokufembera yake yokuberekwa mukomana aizounza yakawanda kubatsirwa uye kunaka kuvanhu. Kuti chokwadi zvaakaita.

Kuzvarwa theorem no

In hwake, Achibvuma pfungwa yaPythagoras akatama kubva Samosi kuIjipiti kusangana muEgipita vakachenjera anozivikanwa. Asangana navo, akanga akabvuma kudzidziswa, uye aiziva apo zvose nokubudirira zvikuru muEgipita uzivi, masvomhu uye mishonga.

Zvinoita sokuti muIjipiti Achibvuma pfungwa yaPythagoras rakafuridzirwa noumambo uye runako mapiramidhi uye akasika ake zvikuru dzidziso. Zvingaita ungazoshamisa vaverengi, asi kare ano vanodavira kuti Achibvuma pfungwa yaPythagoras haana kuratidza dzidziso yake. Uye chete akapa ruzivo rwake vateveri uyo gare gare apedza zvose zvakafanira masvomhu.

Chero kwakanga, zvino inozivikanwa vanopfuura mumwe nzira uchapupu theorem no ichi, asi akawanda. Nhasi anogona chete zvokufungidzira kuti vaGiriki vakaita Masvomhu dzavo, saka pane dzakasiyana kutarira uchapupu Pythagorean theorem no.

Achibvuma pfungwa yaPythagoras theorem no

Usati kutanga chero kukarukureta, unofanira kutsvaka kuti dzidziso kuratidza. The Pythagorean theorem no iri: "Mune netriangle umo mumwe pamakona ^anenge 90, vakaverenga dzinoungana vanhu makumbo vakaenzana muchivara yacho hypotenuse."

In zvachose pane 15 dzakasiyana kuratidza Pythagorean theorem no. Iri panzvimbo yakakwirira mufananidzo, saka kuteerera kupfuura nevanhu vavo.

nzira imwe

Chokutanga, tinofanira kuratidza kuti tiri kupiwa. Data Vachapiwa kuratidzirwa dzimwe nzira uchapupu Pythagorean theorem no, saka zvakanaka kuyeuka zvose zviripo mazita.

Tambira kupiwa kodzero-angled netriangle makumbo a, uye hypotenuse akaenzana c. nzira yokutanga pauchapupu kuti, pamusana netriangle kodzero vaifanira kupedza pachivara.

Kuti aite izvi, unofanira kuva gumbo Kureba chidimbu wakaenzana kupedza imwe gumbo mukati, uye vakutarisire. Saka tinofanira kutendeuka kubva vaviri vakaenzana kumativi pachivara. Tinogona chete kuswedera dzakafanana mitsetse miviri, uye mativi zvagadzirirwa.

Inside, kwaizoita nhamba vanofanira kuswedera mumwe padare aine divi akaenzana hypotenuse yacho Triangle yepakutanga. Kwaizvozvi vertices ose, ac uye kutaurirana zvinokosha kuwana mbiri dzakaenzana zvikamu chete yakafanana. Saka kuwana mativi matatu sikweya, rimwe riri yepakutanga rectangular Triangles ari hypotenuse. Docherty anoramba chete chidimbu wechina.

Zvichienderana kunoguma muenzaniso zvinganzi vakagumisa kuti rokunze nzvimbo yaiungana akaenzana (a + b) ^2. Kana iwe tarisa mifananidzo, unogona kuona kuti kunze rwomukati yazvinofanira zvina zvakanaka-angled zvokuridza. Nzvimbo imwe neimwe ndizvo 0,5av.

Naizvozvo, nharaunda akaenzana: 4 * 0,5av + c ² = ² + 2av

Nokudaro, (a + b) ² = c ² + 2av

Naizvozvo zvino, pamwe ² = ² + ²

Izvi zvinoratidza kuti theorem no.

Nzira mbiri: zvakafanana zvokuridza

mutoo uyu ndiwo uchapupu Pythagorean theorem no yakanga hwokurara pachishandiswa kufarirwa chikamu geometry pakati zvokuridza izvi. Rinotaura kuti makumbo netriangle rworudyi - avhareji Proportional wayo hypotenuse uye kureba hypotenuse, zvinobva kuna vertex ^90.

The kutanga Data ndiwo chete, saka ngatigarei kutanga pakarepo chete uchapupu. Swedera perpendicular kusvikira kurutivi chidimbu AB CD. Zvichienderana tendero apa makumbo zvokuridza vakaenzana:

AC = √AV * AD, CB = √AV * DV.

Kuti tipindure mubvunzo kuratidza kuti Pythagorean theorem no, uchapupu anofanira vakakundwa squaring vose Misiyano.

AC ² = AB * BP uye CB ² = AB * DV

Zvino unofanira kuwedzera kukwira kunoguma kusaruramisira.

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

Zvakaratidza kuti:

AC ² + ² = CB AB * AB

Naizvozvo:

AU ^{2 2} + CB = AB ²

The uchapupu Pythagorean theorem no uye dzakasiyana nzira kwayo yokugadzirisa vanofanira kuva multi-faceted ainoita dambudziko iri. Zvisinei, pfungwa iyi imwe nyore.

Chimwe nzira kukarukureta

Tsananguro dzakasiyana kuratidza Pythagorean Theorem kungava pasina, chero vakawanda regai pachavo makatanga kuita. Vakawanda nzira inosanganisira kwete chete masvomhu, asiwo kuvakwa yepakutanga Triangle nenhamba itsva.

Muchiitiko ichi zvinokosha kupedza BC gumbo rimwe, triangle rworudyi-angled ari IRR. Saka zvino pane zvokuridza vaviri vane gumbo nevakawanda Svondo

Kuziva kuti dzine nhamba yakafanana vane reshiyo sezvo dzinoungana dzavo Linear kukura zvakafanana, ipapo:

S _ABC * ² - S ² * _hPa = S * uye _AVD ² - S ² * mumwe _VSD

_ABC * S ⁽² -c ²⁾ = ² * (S _AVD -S _VVD)

yekuva ^{2 2} = ²

² = ² + ²

Nokuda akasiyana nzira uchapupu Pythagorean theorem no kuti giredhi 8, pfungwa iyi haisi rakakodzera, tinogona kushandisa zvinotevera nzira.

Nyore nzira kuratidza Pythagorean theorem no. Reviews

Zvinonzi vakatenda dzakaitika, nzira iyi yakatanga kushandiswa nokuda uchapupu theorem no muGirisi yekare. Ndiye nyore sezvo haatarisiri zvachose pasina muripo. Kana ukaswedera mufananidzo nemazvo, uchapupu kutaura kuti ² + ² = c ^2, zvichava kuonekwa zvakajeka.

Terms uye mamiriro ezvinhu izvi zvichava siyanei kubva yaimbovapo. Kuti aratidze kuti theorem no, vanofunga kuti akarurama-angled netriangle ABC - isosceles.

Hypotenuse AC tora pamusoro kutungamirirwa pachivara uye docherchivaem mativi acho matatu. Kunze zvakafanira kupedza diagonal mitsetse miviri kuti vaumbe sikweya. Saka, kuti vana equilateral zvokuridza mukati maro.

By Catete AB uye CD sezvinodiwa Docherty pamusoro pachivara uye akabata imwe Mutsetse mumwe nomumwe wavo. Tara mutsetse kubva pakutanga vertex A, wechipiri - kubva C.

Zvino tinofanira tarisisa panguva zvichiguma mufananidzo. Sezvo hypotenuse AC ndiye zvokuridza mana akaenzana pakutanga, asi muna Catete maviri, rinotaura pamusoro veracity pamusoro theorem no ichi.

Panzira, akavonga unyanzvi ichi, umbowo Pythagorean theorem no, uye akaberekwa akakurumbira okuti: ". Pythagorean inotakwairira kwose vakaenzana"

J. Zvinoratidza. Garfield

Dzheyms Garfild - ramakumi maviri President of United States of America. Uyezve, iye akasiya mucherechedzo wake munhau sezvo mutongi United States, aivawo nyanzvi pakuridza kuzvidzora akadzidzisa.

Kumavambo ake basa, aiva mudzidzisi dzose pachikoro chevarwere, asi nokukurumidza akava mutungamiriri mumwe kumayunivhesiti. Kuda nokuzvidzora kukura uye akwanise Chitaura itsva dzidziso umbowo theorem no pakati Achibvuma pfungwa yaPythagoras. Theorem uye muenzaniso ayo anogadzirisa sezvinotevera.

Chokutanga zvakafanira vaswedere pamusoro bepa maviri rectangular netriangle kuitira kuti rimwe gumbo kuti raiva kuenderera yokupedzisira. The vertices pamusoro zvokuridza izvi anofanira kwakabatana kupedzisira kuwana trapeze.

Sezvo chikazozikamwa, nzvimbo ine trapezoid akaenzana chigadzirwa wokuhafu Verengai chawo kukwirira.

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

Kana tikafunga kunoguma trapezoid, sezvo munhu rinoumbwa zvokuridza matatu, nharaunda yayo anogona kuwanikwa sezvinotevera:

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

Zvino zvakafanira kuti equalize maviri yepakutanga okuti

2av / 2 + c / 2 = (a + b) ^2/2

² = ² + ²

About Achibvuma pfungwa yaPythagoras uye sei kuratidza haugoni kunyora bhuku rimwe chete bhuku. Asi zvine musoro kana kuti ruzivo haagoni kushandiswa tsika?

Practical pokushandisa Pythagorean theorem no

Zvinosuruvarisa kuti mazuva ano chikoro zvidzidzo anopa kushandiswa theorem no ichi chete matambudziko geometric. Vakapedza kudzidza nokukurumidza kusiya masvingo kuchikoro, uye asingazivi, uye sei vanogona kushandisa ruzivo rwavo uye nounyanzvi uchidzidzira.

Kutaura zvazviri, kushandisa Pythagorean theorem no zvavo zuva nezuva muupenyu anogona nomumwe. Uye kwete chete nenyanzvi basa, asiwo vanhuwo epamba. Chimboona nyaya shoma apo Pythagorean theorem no uye sei kuratidza zvingava zvakakodzera zvikuru.

Communication theorems uye asitironomi

Zvaizoratidza sokuti vanogona chokuita nyeredzi uye nezvimwe zvokuridza papepa. Kutaura zvazviri, zvenyeredzi - masayendisiti nharaunda umo zvikuru kushandisa Pythagorean theorem no.

Somuenzaniso, funga kufamba muchiedza danda riri muchadenga. Zvinozivikanwa kuti chiedza kufambisa mbiri mirayiridzo nenguva nokukurumidza. AB trajectory, izvo chinoita danda chiedza inonzi l. Uye hafu nguva inodiwa yokuti chiedza kuti semaonero A kukuratidza B, yatinoti t. Uye kumhanya danda - c. Zvakaratidza kuti: c * t = L

Kana iwe tarisa ichi chete danda rimwe ndege Somuenzaniso, imwe nzvimbo chikepe, izvo chinoita ane nokukurumidza V, ipapo pasi pokudzora miviri yakadaro richachinja dzichimhanya. Zvisinei, kunyange yakatarwa zvirimo kuchaita aine velocity V negwara risiri.

Ngatitii enyambo liner kuyangarara zvakanaka. Ipapo pfungwa A uye B, chakaurawa pakati danda kuchaita kuruboshwe. Uyezve, kana danda inofamba semaonero A kukuratidza B, taura A nguva kutama, uye, naizvozvovo, chiedza chakauya itsva pfungwa C. Kuti tiwane hafu daro panguva iyo nguva A kwakaita, unofanira anotakura kuti velocity kane hafu nguva danda kufamba (T ').

D = t '* V

Uye kuwana sei kure munguva iyoyo akakwanisa kupfuura danda chiedza chinodiwa unotara nechepakati pfungwa itsva Beech yaJehovha uye inotevera okuti:

S = C * t '

Kana isu kufungidzira kuti pfungwa chiedza C uye B, uyewo nzvimbo chikepe - ndiro pamusoro ane isosceles Triangle, kuti chidimbu kubva pfungwa A kusvika liner achatsemuka kuva zvokuridza maviri zvakanaka-angled. Saka, nemhaka Pythagorean theorem no angawana chinhambwe kuti akakwanisa kupfuura danda wechiedza.

S = k ^{2 2} + d ²

Muenzaniso uyu Zvechokwadi, kwete zvakanaka, nekuti vashoma vanogona kuva rombo zvakakwana kuedza mune tsika. Naizvozvo, isu funga zvikuru zvisingakoshi mafomu ose theorem no ichi.

Nharaunda Mobile chiratidzo hutachiwana

upenyu Modern hazvibviri kufungidzira pasina kuvapo smartphone. Asi vangani vavo aizofanira proc kana vakanga vasingakwanisi dzaiitirwa subscribers kuburikidza Mobile?!

Mobile dzezvokukurukurirana unhu zvakananga kunoenderana mumhu uko kanyanga kuti Mobile opareta. Kuti kufunga kuti kure kure serura shongwe vanogona kugamuchira chiratidzo, unogona kushandisa Pythagorean theorem no.

Ngatitii unoda kuwana anofungidzirwa kureba munhu wakaiswa shongwe, kuitira kuti uendese chiratidzo ari nharaunda ine 200 makiromita.

AB (kukwirira shongwe) = X;

Sun (Signal nharaunda) = 200 km;

OC (nyika nharaunda) = 6380? Km;

pano

Ob = OA + AVOV = R + X

Kushandisa Pythagorean theorem no, tinoona chii shoma shongwe kukwirira kunofanira 2,3 makiromita.

Pythagorean theorem no mumba

Oddly zvakakwana, iyo Pythagorean theorem no zvinogona kubatsira kunyange mudzimba nyaya dzakadai kutsunga kukwirira cabinet mupanda, somuenzaniso. Pakutanga, hapana chikonzero kushandisa Masvomhu zvakaoma kwakadaro, nokuti unogona ingotora kuyerwa dzako tepi chiyero. Asi vakawanda vanonetseka kuti nei ari tinova muitiro pane zvimwe zvinetso, kana zvose kuyerwa vakatorwa pamusoro chaizvo.

Chokwadi ndechokuti muwadhiropu ari kuenda munyika chinjikira nechinzvimbo uye amutswa ndokubhururuka kumadziro. Naizvozvo, kurutivi rusvingo cabinet iri muitiro nokusimudza magadzirirwo anofanira kuyerera uye kureba, uye diagonal dzezvimwe.

Ngatitii une wenguvo pamusoro 800 mm udzamu. Kure kubva pasi kusvikira kumusoro - 2600 mm. Anoti ruzivo cabinet muiti kuti pakakwirira yakakomberedzwa kunofanira pa 126 mm isingasviki kureba mukamuri. Asi nei ari 126mm? Chimbofunga nezvomuenzaniso unotevera.

Under akakodzera kukura cabinet kuongorora Zvakaitwa Pythagorean Theorem:

√AV AC = ² + ² √VS

AU = √2474 ² 800 ² = 2600 mm - zvose wekuita.

Toti, kureba cabinet haana kuenzana 2474 mm uye 2505 mm. Zvadaro:

AU = √2505 ² + √800 = 2629 mm ^2.

Somugumisiro, cabinet ichi hachisi akakodzera kugadzwa muimba. Sezvo kana vakanhonga akarurama nzvimbo yacho kunogona kukuvadza muviri wake.

Zvichida akafunga dzakasiyana kuratidza Pythagorean Theorem nemasayendisiti siyana, tinogona kugumisa kuti zviri kupfuura chokwadi. Zvino unogona kushandisa ruzivo muupenyu hwavo hwezuva nezuva, uye kuva nechokwadi chokuti vose Masvomhu dzinokosha kwete chete, asiwo wechokwadi.