Mosiyanasiyana kutsimikizira Lingaliro Lovomerezeka Pythagorean: Zitsanzo, kufotokoza ndi ndemanga

Chinthu chimodzi motsimikiza kwathunthu kuti funso, ndilo wofanana ndi m'bwalo la hypotenuse ndi wamkulu aliyense molimba mtima akuyankha kuti: ". Uwerenge mabwalo miyendo" Lingaliro Lovomerezeka ili nalonso munakhala mu malingaliro a munthu aliyense ophunzira, koma inu basi kufunsa munthu kuti kutsimikizira izo, ndipo pangakhale mavuto. Choncho, tiyeni tikumbukire ndi kuganizira njira zosiyanasiyana kuti atsimikizire Lingaliro Lovomerezeka Pythagorean.

Kufotokozera mwachidule mbiri ya

The Lingaliro Lovomerezeka Pythagorean ndi bwino kuti pafupifupi aliyense, koma pazifukwa zina, moyo wa munthu, amene wakonza kuwala, si wotchuka. Izi fixable. Choncho, musanayambe kufufuza njira zosiyanasiyana kuti atsimikizire Lingaliro Lovomerezeka Pythagorean, tiyenera mwachidule bwino kwambiri makhalidwe ake.

Pythagoras - nzeru zapamwamba, masamu, nzeru zapamwamba anachokera ku Greece wakale. Lero ndi zovuta kusiyanitsa yonena wake ku nthano zimene zakhazikitsidwa pokumbukira munthu wamkulu uyu. Koma nkoyenera kwa ntchito za otsatira ake, Pifagor Samossky anabadwa pa chisumbu cha ku Samo. bambo ake ndi miyala wabwinobwino, koma mayi ake anachokera ku banja mfulu.

Malinga ndi nthano, kubadwa kwa Pythagoras ananeneratu mkazi wotchedwa Pythia, amene ulemu ndi anatcha mwanayo. Malinga ndi kulosera kwake za kubadwa kwa mnyamata idzabweretsa kwambiri phindu ndi ubwino kwa anthu. Kuti kwenikweni anachita.

Kubadwa kwa Lingaliro Lovomerezeka ndi

Mu unyamata wake, Pythagoras anasamuka ku Samo ku Iguputo kukumana ndi anamatetule Aigupto kudziwika. Atakumana nawo, iye anavomereza kuti maphunziro, ndipo ankadziwa pamene zofunika yaikuru yonse ya Igupto anthu, masamu ndi mankhwala.

Mwina linali mu Egypt Pythagoras anauziridwa ndi ukulu ndi kukongola mapiramidi ndipo analenga chiphunzitso chake chachikulu. Mwina kudabwitsa owerenga, koma olemba mbiri amakono amakhulupirira kuti Pythagoras Sanatumikire chiphunzitso chake. Ndipo kokha poona chidziwitso chake otsatira amene pambuyo pake anamaliza zofunika kuwerengetsera onse masamu.

Chirichonse chimene icho chinali, icho tsopano kudziwika njira zingapo za umboni wa Lingaliro Lovomerezeka izi, koma zingapo. Lero likhoza ndikuganiza mmene Agiriki anapanga kuwerengetsera awo, choncho pali njira zosiyanasiyana kuyang'ana umboni wa Lingaliro Lovomerezeka Pythagorean.

Pythagoras 'Lingaliro Lovomerezeka

Asanayambe mawerengedwe iliyonse, muyenera kupeza zomwe chiphunzitso kutsimikizira. The Lingaliro Lovomerezeka Pythagorean ndi: "Mu kansalu mu amene kumathandiza kupeza ngodya zabwino ndi ^90, Uwerenge mabwalo miyendo liri lalikulu la hypotenuse lapansi."

Okwana pali njira 15 osiyana kutsimikizira Lingaliro Lovomerezeka Pythagorean. Ichi ndi m'malo okwezeka chithunzi, kotero kulabadira wotchuka kwambiri a iwo.

njira imodzi

Choyamba, ife kutanthauza kuti tinapatsidwa. deta zimenezi anawonjezera kuti njira zina umboni wa Lingaliro Lovomerezeka Pythagorean, choncho ndi bwino kukumbukira mayina onse alipo.

Kuganiza kupatsidwa ufulu-angled makona ndi miyendo, ndi hypotenuse wofanana c. Yoyamba njira zachokera umboni kuti, chifukwa cha kansalu bwino kwambiri kumaliza lalikulu.

Kuti tichite zimenezi, muyenera kutalika mwendo wa gawo wofanana kumaliza mwendo, ndi mosemphanitsa. Choncho ayenera awiri mbali wofanana lalikulu. Tikhonza kujambula mizere iwiri yomweyi, ndi lalikulu ndi wokonzeka.

Mkati, ziwerengero chifukwa muyenera kudziikira lalikulu wina ndi mbali wofanana ndi hypotenuse wa makona pachiyambi. Kuti izi kuthetsa mfundo za Mac ndi kulankhulana n'kofunika jambulani zigawo ziwiri wofanana ndi kufanana. Choncho kupeza mbali zitatu mbali zinayi zofanana, mmodzi amene ndi amakona anayi choyambirira Triangles ndi hypotenuse. Docherty amakhalabe yekha gawo lachinayi.

Potengera chitsanzo chifukwa Ndizachidziwikire kuti malo akunja a lalikulu ndi wofanana (a + b) ^2. Ngati muyang'ana kanjedza, mukhoza kuona kuti kuwonjezera lalikulu lamkati lili anayi bwino-angled Triangles. Dera lililonse ndi 0,5av.

Choncho, dera ndi wofanana: 4 * 0,5av + m'ma ² = ² + 2av

Choncho, (a + b) ² = m'ma ² + 2av

Ndipo chotero, ndi ² = ² + ²

Izi zikutsimikizira pa Lingaliro Lovomerezeka.

Njira ziwiri: Triangles ofanana

chilinganizo Ichi ndi chitsimikizo cha Lingaliro Lovomerezeka Pythagorean anali linachokera pa maziko a movomerezedwa ndi gawo Masamu Triangles izi. Lembali limati miyendo kansalu bwino - ndi njila pafupifupi kwa hypotenuse ake ndi kutalika kwa hypotenuse ndi, wochokera vertex ^90.

Deta koyamba ndinu yemweyo, kotero tiyeni tiyambe pomwepo ndi umboni. Jambulani perpendicular kwa mbali ya gawo AB CD. Kuchokera pa chovomerezedwa pamwamba miyendo ya Triangles ofanana:

AC = √AV * AD, CB = √AV * nkhanza za m'banja.

Kuti tiyankhe funso mmene kutsimikizira Lingaliro Lovomerezeka Pythagorean chitsimikizo ayenera anagonjetsa mwa squaring kusiyana onse.

AC ² = AB * BP ndi CB ² = AB * nkhanza za m'banja

Tsopano muyenera kuwonjezera pa lochitira chifukwa.

Au ^{2 2} + CB = AB * (BP * opuma) komwe BP = AB + opuma

Iwo likukhalira kuti:

AC ² + ² = CB AB * AB

Ndipo chotero:

Au ^{2 2} + CB = AB ²

Chitsimikizo cha Lingaliro Lovomerezeka Pythagorean ndi njira zosiyanasiyana za njira zake ayenera kukhala Mipikisano faceted njira yothetsera vuto limeneli. Komabe, njirayi ndi imodzi mwa losavuta.

njira ina mawerengedwe

Kufotokozera za m'njira zosiyanasiyana kuti atsimikizire Pythagorean Lingaliro Lovomerezeka kungakhale kanthu kunena, bola ngati anthu ambiri sadziwa okha ayamba kuchita. Ambiri mwa njira amakhudza osati kokha masamu, komanso kumanga choyambirira makona kanjedza latsopano.

Pankhaniyi m'pofunika kuti atsirizitse BC mwendo wa kudzanja angled wina makona ya IRR. Kotero tsopano pali Triangles awiri ndi mwendo wamba Sun.

Podziwa kuti madera a kanjedza zofanana ndi chiŵerengero monga mabwalo miyeso yawo inali yofanana liniya, ndiye:

S _ABC * ² - S ² * _HPA = S * ndi _AVD ² - S ² * ndi _VSD

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

-kuti ^{2 2} = ²

² = ² + ²

Chifukwa cha njira zosiyanasiyana za umboni wa Lingaliro Lovomerezeka Pythagorean sitandade 8, njirayi si abwino, mungathe kugwiritsa ntchito ndondomeko izi.

Chophweka njira kutsimikizira Lingaliro Lovomerezeka Pythagorean. Reviews

Akukhulupirira ndi azambiriyakale, njira ichi poyamba ntchito umboni wa Lingaliro Lovomerezeka ku Greece. Iye ndi zovuta monga sikutanthauza alibiretu malipiro. Ngati inu kujambula chithunzi molondola chitsimikizo cha mfundo yakuti ² + ² = m'ma ^2, adzakhululukidwa taonanso bwino.

Terms ndi zinthu mnjira adzakhala wosiyana pang'ono kwa wina m'mbuyomu. Kutsimikizira Lingaliro Lovomerezeka, amaganiza kuti kumanja angled makona ABC - isosceles.

Hypotenuse AC kulanda malangizo a lalikulu ndi docherchivaem mbali zonse zitatu. Kuwonjezera m'pofunika yocheza mizere iwiri opendekera kupanga lalikulu. Motero, kuti anayi Triangles equilateral mkati.

Ndi Catete AB ndi CD akamavutika Docherty pa lalikulu ndi kuumirirabe mzere umodzi opendekera mu aliyense wa iwo. Lembani mzere kuchokera woyamba vertex A, wachiwiri - kuchokera C.

Tsopano tiyenera kuonanso pa chithunzi chifukwa. Monga hypotenuse ndi AC ndi anayi Triangles wofanana wapachiyambi, koma Catete ziwiri, amalankhula za zoti Yesu Lingaliro Lovomerezeka izi.

Mwa njira, chifukwa njira imeneyi, umboni wa Lingaliro Lovomerezeka Pythagorean, ndipo anabadwira wotchuka akuti: ". Mathalauza Pythagorean malangizo onse ndi ofanana"

J. Umboni. Garfield

Dzheyms Garfild - makumi awiri Purezidenti wa United States of America. Komanso wasiya chilemba chake mu mbiri monga mkulu wa United States, komanso anali mphatso kudziona anaphunzitsa.

Pa chiyambi cha ntchito yake, iye anali mphunzitsi zonse kusukulu Folk, koma posakhalitsa anakhala mkulu wa mmodzi wa mabungwe a maphunziro apamwamba. Chilakolako chofuna kudzilemeretsa chitukuko ndi zinamuthandiza akamufunsirire chiphunzitso chatsopano cha umboni wa Lingaliro Lovomerezeka la Pythagoras. Lingaliro Lovomerezeka ndi chitsanzo cha njira yake ndi iyi.

Choyamba m'pofunika kuti ajambule pa pepala awiri amakona anayi makona mwendo moti umodzi umene unali kupitiriza otsiriza. The mfundo za Triangles awa ayenera olumikizidwa kwa kukathera kupeza oimba ng'oma pamodzi.

Monga amadziwika, dera trapezoid ndi wofanana ndi mankhwala a hafu ya ndalama maziko ake ndi kutalika.

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

Ngati tikulingalira trapezoid chifukwa, monga chithunzi ndi lopangidwa Triangles atatu, malo ake tingawapeze motere:

S = AW / 2 * 2 + ^2/2

Tsopano m'pofunika mwakufuna awiri akuti original

2av / 2 + m'ma / 2 = (a + b) ^2/2

² = ² + ²

Za Pythagoras ndi mmene kutsimikizira mukhoza kulemba limodzi buku buku. Koma chiyani tinganene pamene zinthu zimene sangathe ntchito mchitidwe?

Othandiza ntchito ya Lingaliro Lovomerezeka Pythagorean

Mwatsoka, mu maphunziro kusukulu zamakono amapereka ntchito Lingaliro Lovomerezeka uno wokha mavuto zojambula. Omaliza posachedwapa kusiya makoma sukulu, ndi wosadziwa, ndi momwe angatsatire chidziwitso ndi luso lawo ntchito.

Ndipotu, ntchito Lingaliro Lovomerezeka Pythagorean mu moyo wawo mungathe lililonse. Ndipo osati ntchito akatswiri komanso mu ntchito wamba banja. Taonani zina pamene Lingaliro Lovomerezeka Pythagorean ndi momwe kutsimikizira izo zingakhale zofunikira kwambiri.

theorems kulankhulana ndi zakuthambo

Zingatanthauze kuti iwo akhoza zogwirizana ndi nyenyezi Triangles pa pepala. Ndipotu zakuthambo - dera sayansi imene ankagwiritsa ntchito pa Lingaliro Lovomerezeka Pythagorean.

Mwachitsanzo, taganizirani za kayendedwe ka mtengo kuwala malo. Amadziwika kuti kuŵala kumayenda malangizo onse pa liwiro. AB njira yodutsamo, chimene chimatichititsa mtanda wa kuwala amatchedwa L. Ndi hafu ya nthawi chofunika kuwala kuti mfundo kufika B, ife timachitcha T. Ndi liwiro la mtengo wa - c. Iwo likukhalira kuti: c * T = L

Ngati inu muyang'ana pa mtengo imeneyi ya ndege ina mwachitsanzo, danga chombo, umene umayenda ndi liwiro ndime, ndiye pansi pa matupi kuyang'aniridwa idzasintha liwiro awo. Komabe, ngakhale zinthu atathana kudzalimbikitsa ndi mathamangidwe ndi ndime zosiyana.

Tiyerekeze azithunzithunzi zapamadzi akuyandama bwino. Ndiye mfundo A ndi B, amene chinang'ambika pakati pa mtanda ndi kudzalimbikitsa lamanzere. Komanso, mtengo chimachititsanso mfundo kufika B, sonyezani nthawi A kusuntha, ndi moyenera, kuwala kwafika latsopano mfundo C. Pofuna kupeza mtunda theka pa zimene mfundo A kwapita, m'pofunika kuchulukitsa liwiro la chombo mu theka mtengo kuyenda (T ').

D = T '* vesi

Ndipo kupeza momwe mu nthawi imeneyo anatha pochitika mtanda wa kuwala chofunika imasonyeza theka kufika latsopano mumamera s ndipo mawu otsatirawa:

m = m'ma * T '

Ngati ife kulingalira kuti mfundo za kuwala C ndi B, komanso sitima danga - ndi pamwamba pa chinthu cha makona isosceles, ndi gawo pa mfundo A kuti zapamadzi ndi Idzang'ambike mu Triangles awiri kudzanja angled. Choncho, chifukwa cha Lingaliro Lovomerezeka Pythagorean mungapeze mtunda amene anali wokhoza pochitika mtanda wa kuwala.

m = L ^{2 2} + D ²

Mwachitsanzo izi ndi, ndithudi, si zabwino, chifukwa ochepa akhoza kukhala mwayi mokwana ndi kuyensa mu ntchito. Choncho, timaona ntchito zambiri zopanda phindu Lingaliro Lovomerezeka izi.

Utali wozungulira m'manja kufala mbendera

moyo wamakono sikutheka kulingalira popanda kuli yamakono ya. Koma ndi angati a iwo anayenera Proc ngati iwo analephera kugwirizanitsa olembetsa kupyolera m'manja?

mafoni aya khalidwe mwachindunji zimadalira kutalika limene mlongoti kuti akhale woyendetsa yam'manja. Kuti muganize momwe kutali nsanja foni akhoza kulandira chizindikiro, mungathe kugwiritsa ntchito Lingaliro Lovomerezeka Pythagorean.

Yerekezerani kuti mukufuna kupeza pafupifupi kutalika kwa nsanja mapulani kotero kuti kugawira mbendera mu utali wozungulira wa makilomita 200.

AB (kutalika kwa nsanja) = ×;

Sun (Signal utali wozungulira) = 200 Km;

OC (utali wozungulira dziko lapansi) = 6380 Km;

pano

Ob = o + AVOV = r Mukhoza + ×

Kugwiritsa ntchito Lingaliro Lovomerezeka Pythagorean, ife tikupeza chimene osachepera nsanja kutalika ayenera kukhala makilomita 2.3.

Pythagorean Lingaliro Lovomerezeka panyumba

Oddly mokwanira, Lingaliro Lovomerezeka Pythagorean kungakhale kothandiza ngakhale pa nkhani za m'banja monga mtima wa kutalika kwa chipinda nduna, mwachitsanzo. Koyamba, palibe kufunika kwa ntchito kuwerengetsera osiyanasiyana, chifukwa inu mukhoza kungotenga miyezo wanu ndi muyeso tepi. Koma ambiri amadabwa chifukwa kumanga ndondomeko pali mavuto ena, ngati miyezo yonse pa chimodzimodzi.

Mfundo ndi kuti chipinda zikuchitika mu malo yopingasa ndipo anauka ndi wokwera ku khoma. Choncho, mbali linga la nduna mu ndondomeko kukweza kamangidwe ayenera amatuluka ndi kutalika, ndiponso mipata opendekera.

Tinene kuti muli ndi zovala za kuya 800 mm. Mtunda kuchokera pansi pa denga - 2600 mm. ZIMAKHALA nduna wopanga limanena kuti kutalika kwa mpanda akhale pa 126 mamilimita osachepera kutalika kwa chipindacho. Koma chifukwa pa 126mm? Taganizirani chitsanzo chotsatirachi.

Pansi miyeso yabwino nduna adzakhala onani ntchito ya Lingaliro Lovomerezeka Pythagorean:

√AV AC = ² + ² √VS

Au = √2474 ² 800 ² = 2600 mm - onse converge.

Tiyeni tinene, kutalika kwa nduna si wolingana 2474 mamilimita ndi 2505 mm. ndiye:

Au = √2505 ² + √800 = 2629 mamilimita ^2.

Choncho, nduna imeneyi si oyenera unsembe mu chipinda. Popeza pamene anatola malo ake woongoka kungawononge thupi lake.

Mwina mozama za njira zosiyanasiyana kuti atsimikizire Pythagorean Lingaliro Lovomerezeka asayansi osiyana, tinganene kuti ndi zoposa woona. Tsopano mukhoza kugwiritsa ntchito mfundo moyo wawo, ndi kukhala otsimikiza kuti kuwerengetsera onse ndi wofunika osati zowona.