Iindlela ezahlukeneyo ukungqina theorem kaPythagoras: Imizekelo, inkcazelo kunye nohlolo

Enye into ngekhulu Qiniseka ekhulwini ukuba mbuzo, nto leyo ilingana isikweri hypotenuse, nawuphi na umntu omdala phendula ngesibindi: ". Udibaniso lwezikweri imilenze" Le theorem ngokuqinileyo wanamathela ezingqondweni wonke umntu abafundileyo, kodwa nje cela umntu bokubonisa oko, yaye kusenokubakho iingxaki. Ngoko ke, masikhumbule Ndibheke kumendo ezahlukeneyo ukungqina theorem kaPythagoras.

Wayo biography

Le theorem kaPythagoras liqhelekile phantse wonke umntu, kodwa ngenxa yesizathu esithile, ubomi bomntu, nto leyo iye yenza ukuba ukhanyiso, asinto ithandwayo kangaka. Oku fixable. Ngoko ke, ngaphambi kokuba ukuhlola iindlela ezahlukeneyo ukungqina theorem kaPythagoras, simele ngokufutshane ebazi ubuntu bakhe.

Pythagoras - sobulumko, ingcali yezibalo, sobulumko ekuqaleni ukusuka Greece yamandulo. Namhlanje kunzima kakhulu ukwahlula ngobomi bakhe amavo eziye zaqulunqwa kwinkumbulo yale ndoda omkhulu. Kodwa lulandelayo imisebenzi abalandeli bakhe, Pifagor Samossky wazalwa ngomhla kwisiqithi Samos. Uyise amatshe eqhelekileyo, kodwa unina kwintsapho unguwo.

Ngokutsho ilivo, ukuzalwa kaPythagoras kwangaphambili nomfazi ogama Pythia, athanda ukuyibeka embekweni yaye igama lo mfana. Ngokutsho ukuqikelela yakhe yokuzalwa inkwenkwe babeza eninzi inzuzo nokulunga eluntwini. Oko enyanisweni ayenzayo.

Ukuzalwa le theorem

Xa kwasebuncinaneni bakhe, kaPythagoras bafuduka Samos eYiputa ukudibana zo baseYiputa ezaziwayo. Emva kokudibana kunye nabo, yena usiwe uqeqesho, yaye wazi apho yonke imisebenzi emikhulu ye-bulumko baseYiputa, izibalo kunye namayeza.

Mhlawumbi eYiputa Pythagoras waphefumlela yi bobukhulu ubuhle iiphiramidi wadala ingcamango yakhe enkulu. Kusenokuba yothuse abafundi, kodwa mbali mihla bakholelwa ukuba kaPythagoras ayizange imfundiso yakhe. Kwaye kuphela udlulisele ulwazi lwakhe ngayo abalandeli abathi kamva zonke izibalo eziyimfuneko zemathematika.

Enoba lwalunjani, ngoku eyaziwa ngaphezu kwesinye indlela ubungqina le theorem, kodwa eziliqela. Namhlanje uyakwazi ukuthelekelela kuphela indlela amaGrike wenza izibalo zabo, ngoko kukho iindlela ezahlukileyo ukujonga ubungqina theorem kaPythagoras.

KaPythagoras theorem

Phambi kokuqala Nakuphi na ukubala oku, kufuneka ufumanise ukuba yeyiphi theory ukubonisa. Le theorem kaPythagoras kukuba: "Xa unxantathu apho omnye engile ^umalunga 90, udibaniso lwezikweri imilenze ilingana isikweri hypotenuse."

Xa iyonke kukho iindlela-15 ezahlukeneyo ukungqina theorem kaPythagoras. Oku oyintsobi kunokuba ukuphakama, ukuze sinikele ingqalelo kakhulu ethandwa ngabo.

indlela enye

Okokuqala, ukubonisa ukuba banikwe. Ezi data iza kwandiselwa kwezinye iindlela ubungqina theorem kaPythagoras, ngoko ke kulungile ukuba ukukhumbula yonke abizwa ezikhoyo.

Thelekelela ukuba banikwe unxantathu lasekunene-engile egqithe imilenze a, kunye hypotenuse ngokulinganayo c. Indlela lokuqala esekelwe kubungqina ukuba, ngenxa unxantathu ilungelo ukuze agqibe isikwere.

Ukuze wenze oku, kufuneka ube nobude umlenze we icandelo elingana ukugqiba umlenze, kunye vice versa. Ngoko ke kufuneka ukuba amacala amabini alinganayo ze kwisikwere. Hi nga tshinela kuphela imigca emibini parallel, isikwere sekulungile.

Ngaphakathi, amanani nto kufuneka ukuba bafunxe esinye isikwere kunye kwicala elingana hypotenuse lo nxantathu yokuqala. Ukuzokuthi ga ngoku eziphezulu uku kunye nonxibelelwano kuyimfuneko ukuzoba ziqwempu ezimbini ngokulinganayo kunye ngaxeshanye. Ngaloo ekufumaneni amacala ezintathu wesikwere, enye yazo na okoxande original kanxantathu le hypotenuse. Docherty ihlala kuphela ingxenye yesine.

Ngokusekelwe ipateni ngenxa kunokwenziwa isigqibo sokuba le ndawo olungaphandle isikwere silingana (a + b) ^2. Ukuba ujonga kwi amanani, ungabona ukuba ukongeza isikwere ngaphakathi eye oonxantathu ezine lasekunene-engile egqithe. Ummandla ngasinye 0,5av.

Ngoko ke, le ndawo ilingana: 4 * 0,5av + c ² = ² + 2av

Ngenxa yoko, (a + b) ² = c ² + 2av

Kwaye ngoko, ^nge-2 = ² + ²

Oku kubonisa theorem.

Indlela ezimbini: oonxantathu ezifanayo

Le fomyula ke ubungqina theorem kaPythagoras kususelwe ngokusekelwe kwemvume kwicandelo geometry ezi oonxantathu. Uyatsho ukuba imilenze unxantathu ekunene - i-kisekiyo avareji ukuya hypotenuse yayo kwaye ubude hypotenuse, ukusuka enekona ^{90 avela.}

Idatha okuqala ayafana, ngoko ke ukuqala kwangoko kunye nobungqina. Zoba aa Incopho ecaleni kwicandelo AB CD. Ngokusekelwe imvume ngasentla imilenze oonxantathu bayalingana:

AC = √AV * AD, CB = √AV * ivuma.

Ukuze uphendule umbuzo ukungqina indlela theorem kaPythagoras, ubungqina kufuneka kukhawuleze ngokuthi squaring zombini nokungalingani.

AC ² = AB * BP kunye CB ² = AB * ivuma

Ngoku ke kufuneka ukuba dibanisa gqo ukungalingani ngenxa.

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

Kubonakala ukuba:

AC ² + ² = CB AB * AB

Ke ngoko:

AU ^{2 2} + CB = AB ²

Le ubungqina theorem kaPythagoras kunye neendlela ezahlukeneyo isisombululo sayo kufuneka ukuba indlela multi-amaninzi kule ngxaki. Nangona kunjalo, olu khetho yenye yezona zilula.

Enye indlela yokubala

Inkcazelo ngeendlela ezahlukeneyo ukungqina kaPythagoras theorem abe nto athi, elide kakhulu abawuthobeli siqalisile ukwenza. Uninzi ndlela ziquka izibalo nje kuphela, kodwa ke ulwakhiwo nxantathu original amanani ezintsha.

Kule meko kuyimfuneko ukuba agqibe BC umlenze omnye unxantathu lasekunene-engile egqithe le IRR. Ngoko ke kukho oonxantathu ezimbini ngomlenze eqhelekileyo Sun

Ukwazi ukuba iindawo amanani afanayo kufuneka nje ubenesahlulo njengoko zembutho zobukhulu zabo efanayo yomgama, ngoko:

S _ABC * ² - S ² * _HPA = S * kunye _AVD ² - S ² * a _VSD

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

-ukuze ^{2 2} = ²

² = ² + ²

Ngenxa iindlela ezahlukeneyo ubungqina theorem kaPythagoras ukuya kwibakala 8, olu khetho nzima ezifanelekileyo, ungasebenzisa le nkqubo ilandelayo.

Indlela elula ukungqina theorem kaPythagoras. reviews

Kukholelwa yi mbali, le ndlela yasetyenziswa kuqala bubungqina theorem eGrisi yamandulo. Nguye lo elula njengoko ingakufuni ngokupheleleyo akukho ntlawulo. Ukuba uzobe umfanekiso ngokuchanekileyo, ubungqina ngoluvo lokuba ² + ² = c ^2, oko kuya kubonakala ngokucacileyo.

Imigaqo nemiqathango yale nkqubo iya kwahluka kancinci kowangaphambili. Ukungqina ukuba theorem cingela ukuba lo nxantathu ekunene-engile egqithe ABC - isosceles.

Hypotenuse AC ukuthatha phezu ulwalathiso isikwere kunye docherchivaem namacala aso ezintathu. Ngaphandle kuyimfuneko tirhisa imigca emibini oxwesileyo ukwenza isikwere. Ngenxa yoko, ukuba oonxantathu amane alinganayo ngaphakathi kuyo.

Ngu Catete AB kunye CD njengoko kuyimfuneko Docherty kwi isikwere kwaye ubambe enye umgca oxwesileyo ngamnye kubo. Krwela umgca ukusuka yokuqala enekona A, owesibini - evela C.

Ngoku kufuneka ukuba sithathe jonga kwi umfanekiso ngenxa. Njengoko hypotenuse AC yi oonxantathu amane alinganayo neloqobo, kodwa Catete ezimbini, uthetha malunga ukuchana kwale theorem.

Hi ndlela leyi, enkosi le ndlela, le ubungqina theorem kaPythagoras, kwaye wazalwa ibinzana odumileyo: ". Ibhulukhwe kaPythagoras kuzo zonke iindlela bayalingana"

J. Ubungqina. Garfield

Dzheyms Garfild - uMongameli wamashumi amabini ka-United States of America. Ngaphezu koko, uye wazibalula embalini njengomlawuli eUnited States, waba naye self-wafundisa onesiphiwo.

Ekuqaleni umsebenzi wakhe, waba ngumfundisi rhoqo esikolweni iintsomi, kodwa kungekudala waba ngumlawuli we kwelinye lamaziko emfundo ephakamileyo. Umnqweno for self-uphuhliso kwamenza lokuphakamisa ingcamango elitsha ubungqina theorem bakaPythagoras. Theorem kunye umzekelo isisombululo wayo ngolu hlobo lulandelayo.

Okokuqala kuyimfuneko ukuba ephepheni ezimbini unxantathu uxande kangangokuba omnye umlenze baso nokuqhubekeka yokugqibela. Le eziphezulu zezi oonxantathu kufuneka adityaniswe iphele ukufumana neemvumi.

Njengoko yaziwa, kummandla trapezoid ilingana imveliso wesiqingatha-mali esiyi-noseko lwalo kunye nokuphakama.

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

Ukuba sicinga trapezoid onesiphumo, njengoko isafobe eyakhiwa zoonxantathu ezintathu, indawo yayo zingafumaneka ngolu hlobo lulandelayo:

S = Aw / 2 * 2 + ^2/2

Ngoku kuyimfuneko ukuba nokulinganisa ibinzana emibini yokuqala

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

² = ² + ²

Malunga kaPythagoras nendlela ukungqina awukwazi ukubhala incwadi umqulu omnye. Kodwa ngaba isengqiqweni xa olo lwazi ayikwazi enokusetyenziswa practice?

Practical isicelo theorem kaPythagoras

Ngelishwa, kwikharityhulam yesikolo mihla ubonelela ekusetyenzisweni kwale theorem kuphela iingxaki yemigca. kungekudala banezidanga bayemka iindonga zesikolo, kwaye engazi, nendlela ukusebenzisa ulwazi lwabo nezakhono practice.

Enyanisweni, ukuba ukusebenzisa theorem kaPythagoras kubomi babo bemihla ngemihla singaba. Kwaye hayi kuphela kumsebenzi oqeqeshelweyo, kodwa imisebenzi eqhelekileyo yasekhaya. Cinga nje iimeko ezimbalwa apho theorem kaPythagoras nendlela ukubonisa kunokuba yimfuneko kakhulu.

theorems Unxibelelwano nesayensi

Ibiya kuthetha ukuba zibe kunxulunyaniswa iinkwenkwezi kunye noonxantathu ephepheni. Enyanisweni, ngeenkwenkwezi - ummandla yenzululwazi apho ngokubanzi wasebenzisa theorem kaPythagoras.

Ngokomzekelo, cinga intshukumo umqadi ukukhanya emajukujukwini. Yinto eyaziwayo ukuba ukukhanya ehamba kumacala omabini ngesantya esifanayo. AB indlela leyo ihambisa msebe wokukhanya, kuthiwa l. Nesiqingatha ixesha elifunekayo ukukhanya ukusuka kwindawo A noqondo B, simbiza t. Kwaye ke isantya umqadi - c. Kubonakala ukuba: c * t = l

Ukuba ukhangela le umqadi omnye komnye moya, umzekelo, inqanawa isithuba, nto leyo ihamba ngesantya v, ngoko ngaphantsi imizimba kweliso kuya kuyitshintsha yamendu azo. Noko ke, nkqu izinto ezisisigxina kuya kuhamba kunye Velocity v hi ndlela leyi hambaneke.

Masithi wesampula ehlekisayo zokudada ekunene. Ke amanqaku A and B, lento eqwengiweyo phakathi umqadi kuya kwenza ukuba ekhohlo. Ngaphezu koko, xa lihamba nomqadi ukusuka kwindawo A noqondo B, khomba A ixesha ukuhamba, yaye, ngokunjalo, ukuba ukhanyiso lufikile indawo C. entsha Ukuze ufumane kwisiqingatha banga apho kwindawo A iye yabangela, kuyimfuneko ukuba phinda isantya yenqanawa kwisiqingatha ixesha lokuhamba umqadi (t ').

d = t '* v

Kwaye ukufumana kude kangakanani ngelo xesha wakwazi ukuba kudlula kwavela ukukhanya efunekayo uphawu gabhu ingongoma beech entsha s kunye mazwi alandelayo:

s = c * t '

Ukuba simele sicinge ukuba kwinqanaba ukukhanya C kunye B, kwakunye inqanawa isithuba - lo phezulu unxantathu isosceles, abangakwaziyo ukusuka kwindawo A ukuya nqanawa ziya kwahluka ngayo oonxantathu ezimbini lasekunene-engile egqithe. Ngoko ke, sibonga theorem kaPythagoras Ungafumana umgama unako Kwathi kwavela ukukhanya.

s = l ^{2 2} + d ²

Lo mzekelo, Kakade ke, hayi kakhulu, ngenxa yokuba bambalwa kunokuba unethamsanqa elaneleyo ukuba zama practice. Ngoko ke, siza kuqwalasela izicelo ezingenamsebenzi ngakumbi kule theorem.

Radius transmission uphawu mobile

ubomi Modern akunakwenzeka ukuba nomfanekiso ngaphandle ubukho smart. Kodwa bangaphi kubo kuya kufuneka ukuba ngesiBheng ukuba abazange bakwazi ukudibanisa ababhalisele ngeselula?!

mobile quality lonxibelelwano ixhomekeka ngqo kwi ukuphakama apho eriyali ukuba operator mobile. Ukuze sibone indlela kude kweenqaba mobile phone uyakwazi ukufumana umqondiso, ungasebenzisa i theorem kaPythagoras.

Masithi ufuna ukufumana ubude elisondeleyo kwinqaba esisigxina, ukuze endinokumthumela umqondiso kumgama oyi-200.

AB (ukuphakama inqaba) = x;

Sun (Signal radius) = 200 km;

OC (radius yomhlaba) = 6380 km;

apha

OB = OA + AVOV = r + x

Ukusebenzisa theorem kaPythagoras, sifumanisa ukuba ukuphakama inqaba ubuncinane kufuneka 2.3 km.

theorem kaPythagoras ekhaya

Isimanga, lo theorem kaPythagoras kunokuba luncedo nkqu kwimibandela zasekhaya ezifana ukumiselwa ukuphakama gumbi kwikhabhinethi, umzekelo. Xa uqala kuqala, akukho mfuneko yokusebenzisa izibalo ezintsonkothileyo, kuba uyakwazi ukuthatha nje imilinganiselo yakho umlinganiselo tape. Kodwa abaninzi bayazibuza kutheni inkqubo yokwakha kukho iingxaki ezithile, ukuba yonke imilinganiselo zathathwa phezu kanye.

Inyaniso kukuba lo kwigunjana uhamba kwindawo oxwesileyo waza emva koko wamvusa yaye ekhwele eludongeni. Ngoko ke, udonga ecaleni kwikhabhinethi inkqubo nokuphakamisa uyilo kufuneka ukuhamba lula yaye ukuphakama, neendawo nemigca elinganayo.

Masithi unayo zabanye 800 ubunzulu mm. Umgama ukusuka emgangathweni ukuya eluphahleni - 2600 mm. Abanamava cabinet umenzi uthi ukuphakama ebiyelweyo kufuneka ibe kwi-126 mm ngaphantsi kwe ukuphakama gumbi. Kodwa kutheni ku 126mm? Khangela lo mzekelo ulandelayo.

Phantsi Ubukhulu ifanelekileyo iKhabhinethi liya kutshekisha yintshukumo theorem kaPythagoras:

√AV AC = ² + ² √VS

AU = √2474 ² 800 ² = 2600 mm - bonke livuma.

Masithi, ukuphakama yikhabhinethi akalingani 2474 mm kunye 2505 mm. ke:

AU = √2505 ² + √800 = 2629 mm ^2.

Ngenxa yoko, le cabinet ayikho ezifanelekileyo ufakelo kweli gumbi. Ekubeni xa wathatha indawo yawo tye kunokubangela umonakalo emzimbeni wakhe.

Mhlawumbi ingqalelo iindlela ezahlukeneyo ukungqina kaPythagoras theorem zizazinzulu ezahlukeneyo, sinokugqiba ukuba ngaphezu yinyaniso. Ngoku sebenzisa ulwazi kubomi babo bemihla ngemihla, uze uqiniseke ngokupheleleyo ukuba zonke izibalo azikho nje luncedo, kodwa yinyaniso.