Pythagoras ndi Theorem yake [YOSAVUTA]
Chiphunzitso cha Pythagorean ndi imodzi mwazinthu zothandiza kwambiri. Base mu masamu, geometry, trigonometry, algebra ndipo amagwiritsidwa ntchito kwambiri pamoyo watsiku ndi tsiku monga zomangamanga, kuyenda, zojambulajambula, pakati pa ena.
Chiphunzitso cha Pythagorean imakupatsani mwayi wopeza kutalika kwa mbali zamakona atatu olondola, ndipo ngakhale ma triangoko ambiri sali olondola, onse amatha kugawidwa m'makona atatu olondola, pomwe Pythagorean Theorem itha kugwiritsidwa ntchito.
ZOKHUDZA KWAMBIRI "Kuti timvetse chiphunzitso cha Pythagorean"
Chachitatu:
Chithunzi cha geometric, mundege, chopangidwa ndi mbali zitatu zomwe zimakumana mozungulira. Mavekedwewo amalembedwa m'malembo akulu ndipo mbali inayo moyang'anizana ndi vertex yokhala ndi chilembo chofanana. Onani chithunzi 1. M'makona atatu:
- Kuchuluka kwa mbali zake zonse ndikokulirapo kuposa mbali inayo.
- Chiwerengero cha ngodya za kansalu kakang'ono ndi 180º.
Gulu la makona atatu
Kutengera kutalika kwa mbalizo, kansalu kakhoza kukhala kofanana ngati ili ndi mbali zitatu zofanana, isosceles ngati ili ndi mbali ziwiri zofanana, kapena scalene ngati palibe mbali yake yofanana. Onani chithunzi 2.
Ngodya yolondola ndiyomwe imayeza 90 °. Ngati mbaliyo ndi yochepera 90 ° amatchedwa "pachimake mbali". Ngati ngodyayo imaposa 90 ° ndiye amatchedwa "angle obtuse". Malingana ndi ngodya, ma triangles amagawidwa mu:
- Kumathandiza kupeza ngodya zabwino: ngati ali ndimakona atatu ovuta.
- Amanjenje: ngati ali ndi ngodya yolondola ndipo ngodya ziwiri zija ndizovuta.
- Ma ngodya opindika: ngati ali ndi ngodya yovuta komanso ina yovuta. Onani chithunzi 3.
Triangle yolondola:
Makona atatu olondola ndi amodzi okhala ndi ngodya yolondola (90 °). Mwa mbali zitatu za kansalu kolondola, lalitali kwambiri limatchedwa "hypotenuse", enawo amatchedwa "miyendo" [1]:
- Hypotenuse: mbali yoyang'ana mbali yoyenera kumakona atatu. Mbali yayitali imatchedwa hypotenuse yomwe ili moyang'anizana ndi mbali yolondola.
- Miyendo: ndi mbali ziwiri zazing'ono zazing'ono zamakona zomwe zimakhala zolondola. Onani chithunzi 4.
Chiphunzitso cha Pythagoras
Ndemanga ya Pythagorean Theorem:
Chiphunzitso cha Pythagorean akunena kuti, pakatatu kakumanja, hypotenuse lalikulu lofanana ndikofanana ndi mabwalo amiyendo iwiri. [awiri]. Onani chithunzi 2.
Chiphunzitso cha Pythagorean Ikhozanso kufotokozedwa motere: Bwalo lomangidwa pamalingaliro amakona atatu amakona atatu ali ndi malo ofanana ndi kuchuluka kwa mabwalo omangidwa pamiyendo. Onani chithunzi 6.
Ndi Chiphunzitso cha Pythagoras Mutha kudziwa kutalika kwa mbali zonse zitatu zamanja. Pazithunzi 7 pali njira zopezera hypotenuse kapena miyendo ina ya Triangle.
Ntchito Zolingalira za Pythagora
Ntchito Yomanga:
Chiphunzitso cha Pythagorean Imathandiza pakupanga ndi kumanga makwerero, masitepe, nyumba zophatikizana, pakati pa ena, mwachitsanzo, kuwerengera kutalika kwa denga lotsetsereka. Chithunzi 8 chikuwonetsa kuti pomanga zipilala zomangira, ma trestles ndi zingwe zimagwiritsidwa ntchito zomwe ziyenera kutsatira Pythagorean Theorem.
Zojambula Pamwamba:
Pamalo, pamwamba kapena kupumula kwamtunda kumayimiriridwa mndege. Mwachitsanzo, momwe zimakhalira pamtunda zitha kuwerengedwa pogwiritsa ntchito ndodo yoyezera kutalika kwakutali ndi telescope. Mbali yolondola imapangidwa pakati pa mzere wowonera telescope ndi ndodo, ndipo kutalika kwa ndodo kutadziwika, theorem ya Pythagorean imagwiritsidwa ntchito kudziwa kutsetsereka kwa malowo. Onani chithunzi 8.
Zamadzimadzi:
Ndi njira yogwiritsira ntchito kudziwa komwe kuli chinthu, mfundo ziwiri zodziwika. Triangulation imagwiritsidwa ntchito pakutsata foni yam'manja, pakuwunika, pakupeza chombo mlengalenga, pakati pa ena. Onani chithunzi 9.
Pythagoras anali ndani?
Pythagoras anabadwira ku Greece 570 BC, adamwalira mu 490 BC Adali wafilosofi komanso katswiri wamasamu. Malingaliro ake anali kuti nambala iliyonse inali ndi tanthauzo laumulungu, ndipo kuphatikiza manambalawo kunawululira matanthauzo ena. Ngakhale sanasindikize zolemba zilizonse pamoyo wake, amadziwika kuti adayambitsa chiphunzitso chomwe chimadziwika ndi dzina lake, chothandiza pakuphunzira ma katatu. Amawerengedwa kuti ndi woyamba masamu wangwiro, yemwe adapanga maphunziro a masamu mu geometry ndi zakuthambo. [awiri]. Onani chithunzi 2.
Zochita
Kuti mugwiritse ntchito Pythagorean Theorem, chinthu choyamba kuchita ndikuzindikira komwe kansalu kolondola kamapangidwira, mbali iti ndi hypotenuse ndi miyendo.
Kuchita masewera olimbitsa thupi 1. Tsimikizani kufunika kwa hypotenuse ya kansalu kolondola mu fanolo
Solution:
Chithunzi 12 chikuwonetsa kuwerengera kwa hypotenuse ya Triangle.
Chitani 2. Mzati umafunika kuthandizidwa ndi zingwe zitatu, monga zikuwonetsedwa pa chithunzi 13. Ndi ma mita angati omwe ayenera kugulidwa?
Solution
Ngati chingwechi chimawerengedwa kuti ndi hypotenuse ya kansalu kolondola kamene kamapangidwa pakati pa chingwe, mzati ndi nthaka, kutalika kwa chingwe chimodzi chimatsimikizika pogwiritsa ntchito Poregorean theorem. Popeza pali zingwe zitatu, kutalika komwe kumapezeka kumachulukitsidwa ndi 3 kuti mupeze kutalika kokwanira. Onani chithunzi 14.
Chitani 3. Kuti mutenge mabokosi ena, kuchokera pa nsanja yachiwiri kupita pansi, mukufuna kugula lamba wonyamula wonyamula ngati womwe ukuwonetsedwa pachithunzi cha 15. Lamba wonyamula uja ayenera kukhala wautali bwanji?
Solution:
Poganizira lamba wonyamula ngati kulingalira kwa kansalu kolondola kamene kamapangidwa pakati pa lamba, nthaka ndi khoma, mu Chithunzi 16 kutalika kwa lamba wonyamula kumawerengedwa.
Kuchita masewera olimbitsa thupi 4. Mmisiri wa matabwa amapanga mipando pomwe mabuku amayenera kupita, komanso wailesi yakanema ya 26 ”. Kodi gawolo liyenera kukhala lalitali komanso lalitali bwanji komwe TV izipita? Onani chithunzi 17.
Solution:
Muyeso womwe umagwiritsidwa ntchito pazida zamagetsi monga matelefoni, mapiritsi, ma TV, pakati pa ena, pazogwirizana pazenera. Pa TV 26 ”, zojambulazo ndi 66,04 cm. Poganizira kansalu kolondola kamene kamapangidwa ndi mawonekedwe azenera, komanso mbali zonse zawailesi yakanema, malingaliro a Pythagorean atha kugwiritsidwa ntchito kuti adziwe kutalika kwa kanema wawayilesi. Onani chithunzi 18.
pozindikira pa Pythagorean Theorem
Chiphunzitso cha Pythagorean imakupatsani mwayi wopeza kutalika kwa mbali zazing'ono zamakona atatu, komanso ngakhale makanema ena aliwonse, chifukwa awa amatha kugawidwa m'makona atatu akanja.
Chiphunzitso cha Pythagorean akuwonetsa kuti malo opendekera a triangle yolondola ndi ofanana ndi kuchuluka kwa miyendo, kukhala yothandiza kwambiri pakuphunzira za jiometri, trigonometry, ndi masamu ambiri, ogwiritsidwa ntchito kwambiri pakupanga, kuyenda, zojambula, pakati ntchito zina zambiri.
Tikukupemphani kuti muwone nkhaniyi Malamulo a Newton "osavuta kumva"
