Kekahi mau aoao e hooiaio i ka Pythagorean Theorem: ano he kumu hoʻohālike, hōʻikeʻano a me ka hōʻike manaʻo

Kekahi mea mea no kaʻoiaʻiʻo hoʻokahi haneri pakeneka i ka nīnau, i mea like me ka hale o ke hypotenuse, kekahi makua wiwo ole mai olelo aku: ", i ka huina o na mika pāhoʻonui lua o nā wāwae" Kēia theorem ua paa apo la ma na naau o na hoʻonaʻauao kanaka, akā, oe wale noi aku kekahi, e hoao ia, a ma laila i ia pilikia. Nolaila, e hoomanao mai, a mau aoao okoa, e hooiaio i ka Pythagorean theorem noonoo.

An hōʻuluʻulu manaʻo o ke Kawaihae

Ke Pythagorean theorem Ua kama'āina i kokoke a pau, akā, no kekahi kumu, kanaka ola, a i hana ia i ka malamalama, i ole pela mahalo. He mea fixable. No laila, ma mua oe e makaikai i na aoao okoa, e hooiaio i ka Pythagorean theorem, pono iki ike mākou me kanaka.

Pythagoras - poe akeakamai, mathematician, poe akeakamai mua mai kahiko Greece. I kēia lā ia mea loa paakiki, e hoomaopopo i kona Kawaihae, mai na kaao i i ua hoʻokumu 'ia ma ka hoomanao ana i keia nui kanaka. Akā, ka mea e hahai mai i ka hana o kona mau ukali, Pifagor Samossky i hānauʻia ma luna o ka mokupuni o Samo. Kona makua kāne i kekahi stonecutter maʻamau, akā, hele mai la kona makuwahine, mai ke aliʻi ohana.

E like me ka moolelo, o ka hanau ana o Pythagoras wānana wahine o Pythia, i loko o kona hanohano a me ka inoa o ka keiki. E like me kona i ka olelo wanana o ka hanau ana o ke keiki e lawe mai i kekahi wahi lihi iki o ka pono a me ka maikaʻi i ka kanaka. I ka mea āna i hana ai.

I ka hanau ana o ka theorem

I kona wā'ōpiopio, Pythagoras neʻe mai Samo a hiki i Aigupita, e hālāwai me ka Aigupita sagesʻikeʻia. Laua e halawai me ia,ʻo ia i hoʻokomo ai i ka aʻo, a ike i kona wahi a pau i ka piʻi like nui o na kanaka o Aigupita akeakamai, makemakika a me ka lāʻau lapaʻau.

Ua ua paha i loko oʻAigupita Pythagoras hooeueuia lakou e ka mana a me ka nani o na pyramids, a hana i kona kumumanaʻo nui. Ua hiki hoohikilele heluhelu, akā, kēia moʻolelo manaʻo i Pythagoras i ole hoao i kona kumumanaʻo. A haawi wale i kona ike ana i ukali mea hope ana i ka mea e pono makemakika ho.

Ka mea ia ua, ka mea, ua manawa ike hou aku i kekahi ano o ka ike maopopo ana i keia theorem, akā, kekahi mau. I kēia lā hiki wale koho ana i ka poe Helene i ko lakou helu, no laila, ua nui na ano, e nana i ka hooiaio ana o ka Pythagorean theorem.

Pythagoras 'theorem

Ma mua e hoʻomaka ana i kekahi i ka ho omaulia, e pono e loaʻa mai i kumumanaʻo, e hooiaio. Ke Pythagorean theorem mea: "Ma ka triangle i loko i kekahi o na pana pua nei ^{ma kahi o} 90, lākou, i ka huina o na mika pāhoʻonui lua o ka wawae i ke kahua o ka hypotenuse."

I huina, he 15 naʻano likeʻole, e hooiaio i ka Pythagorean theorem. He Heʻano kiʻekiʻe huahelu, no laila, e lohe i ka loa hanohano o ia.

hana kekahi

Mua, ke Kû ke ana mākou i haawiia mai. Kēia mau 'ikepili e e waiho loihi ana i nā ano o ka hooiaio ana o ka Pythagorean theorem, no laila ia mea pono ke hoomanao i na designations.

Lawe haawi pono-huina triangle me nā wāwae i ka, a me ka hypotenuse like i ka c. Ka papa hana mua ua nānā 'ana i hoike ia, no ka mea, o ka pono triangle pono ai no ka hoʻopauʻana i ka hale ma.

E hana i kēia, e pono ai i ka uha lōʻihi o ka Hoʻohana like, e hoʻopau i ka uha mua i loko, a me ka hope versa. A ka mea, e loaʻa nā likeʻaoʻaoʻelua o ka hale. Mākou hiki wale unuhi ia laua laina elua, a me ka huinahalike mea makaukau.

Loko, ka mea kūpono kii Pono, e kikoo aku i kekahiʻahā like me kaʻaoʻao like me ka hypotenuse o ka palapala triangle. A hiki i keia pau na vertices o AC a me ka launa pu, Ua pono, e huki mau like Hoʻohana me laua. Pela ka loaa ana o ka ekoluʻaoʻao o ka huinahalike, kekahi o i o ka palapala huinahń triangle mauna i ka hypotenuse. Docherty koe wale nō ka ha o Hoʻohana.

Ma muli o ka kūpono kumu ka mea, hiki e manao ia ka pā wahi o ka hale, ua like ia (i + b) ^2. Inā 'oe e nānā i loko o nā kiʻi, e hiki ike ia ma ka hou ana i ka pā hale i loko ka mea, he eha pono-huina triangle mauna. I ka wahi o kela a me keia mea 0,5av.

No laila, i ka wahi ua like ia: 4 * 0,5av + c. ² = a ² + 2av

Nolaila, (he + b) ² = c. ² + 2av

A nolaila, me ² = a ² + ²

Kēia proves ka theorem.

Na Huaolelo elua: like triangle mauna

Kēia haʻilula o ka hooiaio ana o ka Pythagorean theorem i loko ma ke kumu o ka apono ia ana o ka pauku anahonua o kēia mau triangle mauna. Ua hākālia nō i nā wāwae o ka triangle akau - ka awelika hapaʻauhau i kona hypotenuse a me ka lōʻihi o ka hypotenuse, emanating mai ka vertex ^90.

Ka loiloi mua 'ikepili i ka ia, no laila, e ka hoʻomaka koke i ka maopopo. E unuhi oe i ÷ haku i kaʻaoʻao o ka Hoʻohana AB CD. Ma muli o ka luna apono wāwae o nā triangle mauna e like:

AC = √AV * AD, CB = √AV * DV.

E pane mai i ka ninau o ke ana, e hooiaio i ka Pythagorean theorem, me ka maopopo e eʻulupāʻia squaring nā inequalities.

AC ² = AB * BP a me CB ² = AB * DV

Ano, e pono e hoonui i ka kūpono like ole.

AU ^{2 2} + CB = AB * (BP * listen) kahi BP = AB + listen

Ua huli mai ia:

AC ² + ² = CB AB * AB

A nolaila:

AU ^{2 2} + CB = AB ²

Ka hooiaio ana o ka Pythagorean theorem, a me nāʻano likeʻole o kona kākoʻo pāʻoihana Pono e e nunui-faceted kokoke i kēia pilikia. Naʻe, ua koho o kekahi o ka simplest.

Kekahi hana o i ka ho omaulia

Description o kekahi aoao, e hooiaio i ka Pythagorean Theorem e kekahi mea e olelo aku i, like loa me ka hapanui e ole ia lakou iho i hoomaka i ka hana. He nui o nā 'ana i kūpono Komo ole wale makemakika, akā, i ka hana o ka palapala triangle hou huahelu.

Ma keia hihia ia mea e pono e hoʻopau i ka BC wāwae o kekahi akau-huina triangle ka IRR. No laila, e loaʻa nō nā triangle mauna a me ka uha, he pono ole (Kaonohiokala)

Ike ana i ka mau o ka like huahelu i ka lākiō like me ka mika pāhoʻonui lua o ko lākou 'ano like laina Ana, laila:

S _ABC * ² - S ² * _HPA = S * a me _AVD ² - S ² * he _VSD

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

-to ^{2 2} = a ²

² = a ² + ²

No ka mea, o ka mea okoa ano o ka hooiaio ana o ka Pythagorean theorem i ka papa 8, ua koho ka apuepue pono, e hiki ke hoʻohana i ke kēia mau kaʻina hana.

Ke easiest ala, e hooiaio i ka Pythagorean theorem. Reviews

Ua Ua manaoio ma ka moʻolelo, ua iaoia Ua hoʻohana mua no ka maopopo ana o ka theorem i kahiko Greece. He mea ka easiest me ka mea 'aʻole i koi loa i uku. Inā 'oe i hele aku i ke kiʻi pono, i ka hooiaio ana o ka assertion ana he ² + ² = c. ^2, ka mea e e ike maopopo.

Terms a me nā kumu no kēia kaʻina hana, e e iki okoa mai ka mua kekahi. E hoao i ka theorem, kuhi i ka akau-huina triangle ABC - isosceles.

Hypotenuse AC lawe maluna iho o ka olelo ana o ka kuea, a docherchivaem kona ekolu aoao. Ma waho ka mea i pono, e pana aku au i diagonal laina elua, e hana i ka huinahalike. Pela, e kiʻi eha equilateral triangle mauna ma loko ia.

By Catete AB a me CD i pono Docherty ma ke kuea, a paʻa ma luna o kekahi laina diagonal i loko o kela a me keia o ia mau mea. E kaha i kekahi laina, mai ka mua vertex A, he lua - mai C.

Ano, ua pono, e lawe i ka pili nana ma ka kūpono kiʻi. E like me ka hypotenuse AC mea eha triangle mauna like i ka palapala, akā, i loko o Catete elua, ia olelo e pili ana i ka veracity o keia theorem.

Ma ke ala, i ke aloha a hiki i kēiaʻano hana, i ka hooiaio ana o ka Pythagorean theorem, a i hanau ke kaulana hopuna'ōlelo: ". Pythagorean lole wāwae i loko o nāʻaoʻao i like"

J. maopopo. Garfield

Dzheyms Garfild - ka iwakālua Peresidena o ka Amerika Huipuia. Eia hou,ʻo ia i haʻalele i kona hoailona ma ka moolelo me ka luna o ka Amerika Huipuia, oia ua no hoi he haawina mai ka hoʻoponopono-ao mai la.

I ka hoʻomaka o kona 'oihana, oia ua he mau kumu ma ke kula poʻe, akā, koke ia i ka luna hoʻokele o kekahi o nā kulanui o ka hoʻonaʻauao kiʻekiʻe. Ka makemake no ka pakiko-ulu, a hoʻohana 'ia e hāpai i kekahi hou pähola' ana o ka hooiaio ana o ka theorem o Pythagoras. Theorem a me ke kumu hoohalike o kona kākoʻo pāʻoihana mea like penei.

Mua ia mea e pono ke kikoo ma ka pepa elua mau huinahń triangle no laila i kekahi wāwae o ka a i ka hoomau ana o ka hope. Nā vertices o kēia mau triangle mauna E e pili, e hoʻopau i ka noho i ka trapeze.

E like me ua ikeia, o ka wahi o ka trapezoid Ua like no ka huina hoonui o ka hapa-huina o kona kumu, a me ka kiekie.

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

Inā ka kūpono trapezoid, e like me ke aka haku o ekolu triangle mauna mākou noonoo, hiki ke loaʻa kona wahi like penei:

S = nā / 2 * 2 + ^2/2

Ano ka mea, Ua pono, e equalize i ka palapala hōʻike mau

2av / 2 + l / 2 = (i + b) ^2/2

² = a ² + ²

About Pythagoras, a pehea e ho'āʻo iāʻoukou hiki ole kākau i hookahi ka leo puke. Akā, 'aʻole ia e hoohalike i ka wa i ike hiki ole ke pili ma ka hoʻomaʻamaʻa?

E pili ana o ka Pythagorean theorem

Eia naʻe, i loko o ka kēia kula laulā maʻamau eaaaony no ka hana ana i keia theorem wale nō i loko o geometric pilikia. Puka e koke haʻalele i ka pā kula, a me ka ike ole, a pehea e hiki pili i ko lakou ike a me ka mākau ma ka hoʻomaʻamaʻa.

I mea, e hoʻohana i ka Pythagorean theorem i loko o kā lākou mau kela la i keia ola ke kēlā me kēia. Aʻaʻole wale nō i loko o 'oihana haʻawina, akā, i loko o maʻamau hale chores. E noonoo oe i kekahi mau hihia ma ka Pythagorean theorem, a pehea e hoao mea hiki ia'āina pono.

Palapala theorems a me kilohōkū

Ua makemake mea i ka mea, hiki e ua hoʻopili i na hoku, a triangle mauna ma luna o ka pepa. I ka mea, kilohōkū - he 'epekema' āpana ma i hoʻomano hoʻohana i ka Pythagorean theorem.

No ka laʻana, noonoo i ka holo ana o ka malamalama kaola i loko o ka lewa. Ua ua ike ia ka malamalama holo ÿana i loko o nāʻaoʻao ma ka ia māmā. AB ala, a kolo ana i ka laau o ka malamalama ua kapaia ho'āo ai. A me ka hapalua o ka manawa koi 'ia no ka malamalama, e kiʻi mai ka wahi A e kuhikuhi B, ke kapa nei kakou 'ole. A me ka mämä holo o ka mea nana i ulana - c. Ua huli mai i: c. * K = H

Inā 'oe e nana i keia mau kaola o kekahi pelane, no kekahi laʻana, he pokole moku, a kolo ana i ka mämä holo V., laila, ma lalo o ka hooponopono kino, e hoʻololi' ana i kā lākou māmā. Naʻe, i ka haka hehee wale, e neʻe me ka māmā holo V i loko o ke ku pono ana i ka ao ao.

Ina puke kātuna liner lana pono. A laila, e neʻe i ka nui A a me B, i ua haehaeʻia ma waena o ka laau a hiki i ka hema. ¶ A, i ka wa a ka laau mai ka wahi A e kuhikuhi B, kuhikuhi A manawa e neʻe, a, me, ua hiki mai ka malamalama i loko o ka hou wahi C. No ka huli hapalua ka mamao ma i ka welau A ua hoʻoneʻe, ia mea e pono ke hoonui i ka mämä holo o ka moku ma ka hapalua o ka mea ulana lole Hotele manawa (Halau ').

b =, t '* V

A e loaʻa i ka mamao i loko o ia manawa ua hiki ke hele i ka laau o ka malamalama ua pono e hoailona i ke kahi hapa wahi o ka hou beech ke a me na kēia hōʻike:

ke = c. * 'ole'

Inā mākou e manao ana o ka wahi o ka malamalama C a me B, e like me ka makahiki moku - o ka luna o ka isosceles triangle, ka Hoʻohana mai kaʻoi A i ka liner e Wāwahi ia i loko o nā pono-huina triangle mauna. No laila, mahalo i ka Pythagorean theorem ke loaʻa i ka mamao ua e hiki ke hele i ka laau o ka malamalama.

ka = k ^{2 2} + b ²

Kēia laʻana mea, o ka papa, i ka mea maikai, no ka mea, wale he mau hiki e laki lawa e ho'āʻo ia i loko o nä hana kilokilo. Nolaila, o ka oi mundane palapala noi o keia theorem mākou noonoo.

Ke kahahńnai o lawe lima neaiae EYI

Hoikehonua, ola mea hiki ole ke manao wale me ke ola ana o ka Phone. Akā, pehea ka nui o lakou i makemake i ke proc ina ka mea, ua hikiʻole naʻe i ka hoʻohui nā mea kūʻai mai ma lawe lima?!

Mobile palapala e like ai ma kahi e hilinaʻi nui ma luna o ke kiekie ma i ke kukuna e ia i ka lawe lima Aʻole. I mea e pohihihi mai he aha ka mamao mai ka lawe lima kelepona hale kiaʻi ke loaa i ka hōʻailona, e hiki ke hoʻohana i ka Pythagorean theorem.

Ina oe makemake e huli i ka He kokekau wale kiʻekiʻe o ka paa hale kiai, no laila, i ka mea hiki ke puunaue i ka peahi ana i loko o ke kahahńnai o ka 200 kilomika.

AB (kiʻekiʻe o ka hale kiaʻi) = m;

Sun (Neaiae kahahńnai) = 200 ei;

OC (honua ka ke kahahńnai o) = 6380 ei;

ʻaneʻi

OB = oa + AVOV = R + m

Ana i ka Pythagorean theorem, ua loaʻa mai i ka palena iki halekiai kiekie, e ia 2.3 kilomika.

Pythagorean theorem i loko o ka hale

Oddly lawa, ka Pythagorean theorem hiki e pono keia mau mea, a hiki ma ka wahi lulu mea e like me ka manao paa o ke kiʻekiʻe o ka Aha Kuhina pahu, no ka laʻana. Ma mua kilohi, aole he pono e hoʻohana i ka luna 'ho, no ka mea, e hiki e lawe i kou mau ana me ka lola ana. Akā, he nui kahaha no ke kumu o ka hana kaʻina hana, aia nō kekahi mau pilikia, ina i lawe maluna o na ana a pau ponoia mai la.

Ka mea, oia i ke keena mehameha e hele ana i loko o ka papamoe wahi, a laila, ho'āla mai, a lele akula i ka pā pōhaku. No laila, ma kaʻaoʻao paia o ka Aha Kuhina i loko o ke kaʻina hana o ka hookiekie ana i ka manao pono kahe o ka 'elele, a ma ka kiʻekiʻe, a me ka diagonal hakahaka.

Ina oe i ke keʻena lole o 800 mm o ka hohonu. Ka mamao mai ka papa a hiki i ka palena - 2600 mm o. wahi a inā pilikia ka haumāna Aha Kuhina i hana i ke kiekie o ka pa e ia i 126 mm o emi ma mua o ke kiekie o ka lumi. Akā, no ke aha la i 126mm? ke kēia kumu noonoo.

Ma lalo o maikaʻi Ana o ka Aha Kuhina, e kaha i ka hana o ka Pythagorean Theorem:

√AV AC = ² + ² √VS

AU = √2474 ² 800 ² = ²⁶⁰⁰ mm o - a pau converge.

E ka i aku nei au, ke kiekie o ka Aha Kuhina mea i like i ka 2474 mm o a me ka 2505 mm o. A laila:

AU = √2505 ² + √800 = 2629 mm o ^2.

Nolaila, keia Aha Kuhina mea i pono no ka mea hoʻonoho i loko o ka lumi. Mai ka wā hapai i kona pololei kulana hiki i poino i kona kino.

Paha noʻonoʻo i nāʻaoʻao likeʻole, e hooiaio i ka Pythagorean Theorem ma kekahi kānakaʻepekema, ua hiki ke manao nei makou ia mea oi ma mua o oiaio. Ano, e hiki ke hoʻohana i ka 'ike i loko o kā lākou kela la i keia ola ana, a e loaʻoiaʻiʻo,ʻaʻole wale nō ia o nā helu a pau e pono keia mau mea, akā, i oiaio nae.