Pythagoras neTheorem yake [ZVINONAKA]
Iyo Pythagorean Theorem ndiyo imwe yedzidziso dzinonyanya kukosha. Base mune masvomhu, geometry, trigonometry, algebra uye zvinonyanya kushandiswa muhupenyu hwezuva nezuva sekuvaka, kufamba, topography, pakati pevamwe.
Iyo Pythagorean Theorem inokutendera iwe kuti uwane hurefu hwemativi etriangle yekurudyi, uye kunyangwe akawanda mativi matatu asiri echokwadi, iwo ese anogona kuve akapatsanurwa kuita mativi matatu akarurama, uko iyo Pythagorean Theorem inogona kuiswa.
BASIC CONCEPTS "Kuti unzwisise Pythagorean theorem"
Triangle:
Geometric nhamba, mundege, yakaumbwa nemativi matatu anosangana kuma vertices. MaVertices anonyorwa nemavara makuru uye kudivi rakatarisana nerevheti ine mavara ezasi akafanana. Ona mufananidzo 1. Mumatatu:
- Huwandu hwemaviri emativi ayo hwakakura kudarika rimwe divi.
- Huwandu hwemakona etriangle anoyera 180º.
Kupatsanurwa kwematatu
Zvichienderana nehurefu hwemativi, katatu inogona kuenzana kana iine mativi matatu akaenzana, isosceles kana iine mativi maviri akaenzana, kana scalene kana pasina mativi ayo akaenzana. Ona mufananidzo 2.
Kona yekurudyi ndiyo inoyera 90 °. Kana kona yacho iri pasi pe90 ° inonzi "acute angle". Kana kona yacho iri pamusoro pe90 ° zvino inonzi "obtuse angle". Zvinoenderana nemakona, iwo mativi matatu akaiswa mu:
- Makona akadzika: kana vaine iwo matatu akona makona.
- Rectangles: kana vaine kona yakatwasuka uye mamwe mairi angli akaomarara.
- Angle makona: kana vane kona yekufungidzira uye imwe yacho yakaoma. Ona mufananidzo 3.
Triangle kurudyi:
Triangle kurudyi imwe nekona yekona (90 °). Pamativi matatu etriangle yekurudyi, kureba kunonzi "hypotenuse", mamwe acho anonzi "makumbo" [1]:
- Hypotenuse: divi rakatarisana nekona yekurudyi mune kurudyi katatu. Rutivi rurefu rwunonzi hypotenuse irwo rwakatarisana nekona yekurudyi.
- Makumbo: iyo ndeimwe yemativi madiki maviri etriangle yekurudyi inogadzira kona chaiyo. Ona mufananidzo 4.
Pythagoras theorem
Chirevo chePythagorean Theorem:
Iyo Pythagorean Theorem inotaura kuti, nekatatu nekona, iyo hypotenuse yakapetwa yakaenzana neuwandu hwemakwere emakumbo maviri. [piri]. Ona mufananidzo 2.
Iyo Pythagorean dzidziso Inogona zvakare kutaurwa seinotevera: Iyo square yakavakirwa pane fungidziro yetriangle kurudyi ine nzvimbo imwechete sehuwandu hwenzvimbo dzemakwere akavakwa pamakumbo. Ona mufananidzo 6.
With the Pythagoras theorem Iwe unogona kuona kureba kwerimwe divi rekatatu kurudyi. Mumufananidzo 7 ndiwo mafomula ekuti uwane hypotenuse kana mamwe emakumbo eatatu.
Zvishandiso zvePythagora's theorem
Kuvakwa:
Iyo Pythagorean dzidziso Izvo zvinobatsira mukugadzirwa uye kuvaka kwenzira, masitepisi, diagonal zvivakwa, pakati pevamwe, semuenzaniso, pakuverenga kureba kwedenga rakatsvedza. Mufananidzo 8 unoratidza kuti pakuvakwa kwemakoramu ekuvaka, trestles netambo zvinoshandiswa izvo zvinofanirwa kutevedzera Pythagorean Theorem.
Topography:
Mune topography, pamusoro kana kuzorodza kwenzvimbo inomiririrwa graphic pane ndege. Semuenzaniso, iko kuda kwenzvimbo kunogona kuverengerwa uchishandisa tambo yekuyera yekukwirira kunozivikanwa uye teresikopu. Kona yekurudyi inoumbwa pakati pemutsara wekuona kweteresikopu uye tsvimbo, uye kana kukwirira kwetsvimbo kwazivikanwa, Pythagorean theorem inoshandiswa kuona kutsvedza kwenzvimbo. Ona mufananidzo 8.
Triangulation:
Iyi inzira inoshandiswa kuona panowanikwa chinhu, inozivikanwa maviri mareferensi. Triangulation inoshandiswa mukutevera nharembozha, mumasisitimu ekufambisa, mukuonekwa kwechikepe muchadenga, pakati pevamwe. Ona mufananidzo 9.
Ndiani aive Pythagoras?
Pythagoras akaberekerwa kuGreece 570 BC, akafa muna 490 BC Aive muzivi uye nyanzvi yemasvomhu. Huzivi hwake hwaive hwekuti nhamba yega yega yaive nechirevo chaMwari, uye kusanganiswa kwenhamba kwakaratidza zvimwe zvinoreva. Kunyangwe iye asina kutsikisa chero chinyorwa muhupenyu hwake hwese, iye anozivikanwa nekuunza iyo theorem iyo ine zita rake, inobatsira mukudzidza kweatatu. Iye anonzi wekutanga akachena masvomhu, uyo akatanga masvomhu zvidzidzo muJometri uye nyeredzi. [piri]. Ona mufananidzo 2.
Kudzidzira
Kuti ushandise Pythagorean Theorem, chinhu chekutanga kuita kuziva panogadzirwa nekona katatu, ndeipi yemativi ndiyo fungidziro nemakumbo.
Exercise 1. Sarudza kukosha kweiyo hypotenuse yekona netriangle mumufananidzo
Solution:
Mufananidzo 12 unoratidza kuverenga kweye hypotenuse yetriangle.
Exercise 2. Danda rinotarisirwa kutsigirwa neseti yetambo nhatu, sezvakaratidzwa mumufananidzo 13. Mamita mangani etambo anofanira kutengwa?
Solution
Kana iyo tambo ichionekwa seyefungidziro yetriangle kurudyi yakaumbwa pakati pekambo, danda nevhu, hurefu hwetambo imwe hunotsanangurwa uchishandisa chirevo chePythagorean. Sezvo paine tambo nhatu, kureba kunowanikwa kunowedzerwa ne3 kuti uwane hurefu hwese hunodiwa. Ona mufananidzo 14.
Kudzidzira 3. Kutakura mamwe mabhokisi, kubva paburiro repiri kuenda kune yepasi, iwe unoda kutenga yakada kutakura bhandi seyakaratidzwa mumufananidzo 15. Bhandi rekutakura rinofanira kunge rakareba sei?
Solution:
Tichifunga nezve conveyor bhandi seyekufungidzira kwetatu kona yakaumbwa pakati pebhanhire, pasi uye madziro, muMufananidzo 16 kureba kwebhandi rekutakura kunoverengerwa.
Kudzidzira muviri 4. Muvezi anogadzira fenicha panofanira kuenda mabhuku, uye terevhizheni 26 ”. Yakakura sei uye yakakwirira sei chikamu chinofanira kunge chiri icho TV ichaenda? Ona mufananidzo 17.
Solution:
Chiyero chinoshandiswa mumagetsi zvigadzirwa semafoni, mapiritsi, materevhizheni, pakati pevamwe, mune iyo diagonal yechidzitiro. Kune 26 "TV, iyo skrini diagonal ndeye 66,04 cm. Tichifunga netriangle yekurudyi inoumbwa neiyo diagonal yechidzitiro, uye mativi eterevhizheni, iyo Pythagorean theorem inogona kuiswa kuona upamhi hweterevhizheni. Ona mufananidzo 18.
CONCLUSIONS pane iyo Pythagorean Theorem
Iyo Pythagorean Theorem inokutendera iwe kuti uwane kureba kwemativi etriangle kurudyi, uye kunyangwe kune chero imwe kona, nekuti izvi zvinogona kukamurwa kuita mativi matatu akakodzera.
Iyo Pythagorean Theorem inoratidza kuti iyo square of the hypotenuse yekona netriangle yakaenzana nechiyero chekwere yemakumbo, ichinyanya kubatsira mukudzidza kwejometri, trigonometry, uye masvomhu zvakawandisa, nekushandiswa kwakawanda mukuvaka, kufamba, topography, pakati mamwe akawanda mafomu.
Tinokukoka iwe kuti uone iyo chinyorwa Mitemo yaNewton "iri nyore kunzwisisa"
