I-Polygon Geometry: ama-Pentagon, ama-Hexagon namaDodecagon

01 ka 05

Iyini iPolygon?

I-Polygons i-Two Dimensional

E-geometry, i-polygon yinoma yikuphi ukuma okungamabili amabili :

• Yakhiwa imigqa emithathu noma ngaphezulu eqondile
• Ivaliwe - ayikho ukuvuleka noma amakhefu ekujuleni
• Unamabili emigqa ehlangene emagumbini noma emaqenjini lapho enza ama-angles
• Unenani elilinganayo lamacala nezinhlangothi zangaphakathi (i-angles ngaphakathi kwe-polygon)

(Ububanzi obubili bubiza flat - njengesiqephu sephepha)

Yonke YesiGreki

Igama le- polygon livela ngamagama amabili esiGreki:

• poly - okusho "abaningi"
• gon elisho "angle"

Amafomu AyiziPolandoni

• Triangles
• Izikwele
• Ama-Pentagon
• Ama-Octagons
• Ama-Dodecagons - njengengqikithi engama-12 engama-Jamaica yase-Jamaican esithombeni ngenhla

Amafomu Okungeyona Ama-Polygone

• Isiyingi - ngoba sakhiwe ngomugqa ogobile kunemigqa eqondile
• Ibhokisi noma i-cube - ngoba i- three-dimensional shape ayifuni ezimbili-ntathu

02 ka 05

Ukubiza amaPolandoni

Amagama wePolygon

Amagama ama-polygoni ngamanye atholakala enombeni wezinhlangothi kanye / noma ngaphakathi angangele ukuma okunakho.

(Ngendlela, isibalo sezingaphakathi zangaphakathi - sihamba ngaphakathi kwesimo - kufanele ngaso sonke isikhathi silingane nenani lezinhlangothi).

Amagama avamile amapolgoni amaningi anesiqalo seGrisi ngenani lama-angles elihlanganiswe negama lesiGreki elibhekene ne-angle (gon).

Ngakho, amagama avamile ama-polygons avamile amathandathu anamahlanu ajwayelekile:

• i-penta (isiGreki elisho izinhlanu) + gon = i- pentagon
• i-hexa (isiGreki elisho ayisithupha) + gon = iheksagoni

Okungekho

Kukhona, okwamanje, okungafani kulolu hlelo lokuqamba igama. Okubaluleke kakhulu:

Triangle- isebenzisa isiGreki isiqalo Tri, kodwa esikhundleni Gon Greek , i -Latin angle isetshenziswa. (Ngokuvamile kuthiwa yizigidigidi).

I-quadrilateral - itholakala kwisiqalo se-Latin quadri - okusho ezine - kufakwe kwi- wordal lateral - enye enye igama lesiLatini elisho uhlangothi.

Ngezinye izikhathi, i-polygon yezinhlangothi ezine ibizwa ngokuthi i- quadrangle noma i- tetragon .

ama-n-gons

Ama-polygons anezinhlangothi ezingaphezu kweyishumi nama-angles akhona, kanti amanye anamazwi avamile - njenge-100 ehlangene e- ectogon .

Njengoba zihlangane njalo, zivame ukuthi zinikezwe igama elifaka inani lamacala nezinhlangothi ezibhekene nezwi elijwayelekile le-angle - gon .

Ngakho-ke, i-polygon emaceleni ayishumi ngokuvamile ibizwa ngokuthi i- 100-gon .

Amanye ama- n-gons namagama ajwayelekile amaphandloni anezinhlangothi ezingaphezu kweyishumi yilezi:

• 11-gon: i- Hendecagon
• I-12-gon: i- Dodecagon
• I-20-gon: Icosagon
• 50-gon: i- Pentecontagon
• 1000-gon: i- Chiliagon
• I-1000000-gon: i- Megagon

I-Polygon Limit

Ngokweqile, akukho mkhawulo kunani lamacala nezinhlangothi ze-polygon.

Njengoba ubukhulu bezingalo zangaphakathi ze-polygon ziba mncane futhi ubude bezinhlangothi zawo bufinyeleleka i-polygon ifinyelela umbuthano - kodwa akakaze ufike lapho.

03 ka 05

Ukuhlukanisa i-Polygons

Ngokuvamile vs. I-Polygons engavamile

Ku-polygon ejwayelekile zonke izingalo zilingana obulinganayo futhi zonke izinhlangothi zilingana nobude.

Ipoloni engavamile yinoma iyiphi i-polygon engenawo ama-angles amancane kanye namacala angalingana ubude obulinganayo.

Convex vs. Concave

Indlela yesibili yokuhlukanisa ama-polygons ubukhulu bezingalo zangaphakathi. Izinketho ezimbili ziyi- convex ne- concave:

• Ama- polygons e- convex - awekho ama-angles angaphakathi angaphezulu kwe-180 °;
• I-Concave polygons - okungenani i- angi eyodwa yangaphakathi inkulu kune-180 °.

I-Simple vs. Plexgons Complex

Kodwa enye indlela yokuhlukanisa ama-polygons yindlela indlela imigqa eyenza i-polygon ihamba ngayo.

• Imigqa yama-polygoni elula axhuma noma ahlangane kanye kuphela - emazwini;
• Imigqa ye-polygons eziyinkimbinkimbi ihlangene kaningi.

Ngezinye izikhathi amagama ama-polygon eziyinkimbinkimbi ahlukile kulawo ma polygoni alula anezinhlangothi ezifanayo.

Ngokwesibonelo,

• I- hexagon enemihla ngemihla iyinhlangano ye-polygon elula ehlangene
• I-hex agram enemisebe yenkanyezi i-polygon eyinkimbinkimbi eyinkimbinkimbi enesithupha eyenziwe ngokuqothula izintathu ezimbili ezilinganayo ze-equilateral njengoba kuboniswe esithombeni esingenhla

04 ka 05

Isimiso seMingcele yezingelosi zangaphakathi

Njengomthetho, isikhathi ngasinye uhlangothi lufakwe kwi-polygon, njenge:

• Kusukela kunxantathu kuya ku-quadrilateral (izinhlangothi ezintathu kuya ezine)
• Kusukela ku-pentagon kuya ku-hegagon (izinhlangothi ezinhlanu kuya kweziyisithupha)

enye ingu-180 ° yengezwe inani eliphelele lama-angles angaphakathi.

Lo mthetho ungabhalwa njengefomula:

(n - 2) × 180 °

lapho n = inani lezinhlangothi ze-polygon.

Ngakho isibalo sezingaphakathi zangaphakathi ze-hexagon singatholakala ngokusebenzisa ifomula:

(6 - 2) × 180 ° = 720 °

Zingaki Izixathulo KuloPolygon?

I-formula yangaphakathi ye-angle yangaphakathi itholakala ngokuhlukanisa i-polygon ibe yi-triangles, futhi le nombolo ingatholakala ngokubala:

n - 2

lapho n futhi lilingana nenani lezinhlangothi ze-polygon.

Ngakho-ke i-hexagon (izinhlangothi eziyisithupha) ingahlukaniswa yaba ama-triangles amane (6 - 2) kanye ne-dodecagon ibe ngama-triangles ayishumi (12 - 2).

Ubukhulu be-Angle yamaPolandoni ajwayelekile

Ama-polygoni avamile (angena wonke ubukhulu obufanayo futhi ahlangane nobude obufanayo), ubukhulu bama-angle ngayinye ku-polygon kungabalwa ngokuhlukanisa inani eliphelele lamadijithi ngenani lezinhlangothi eziphelele.

I-hexagon engamasonto ayisithupha avamile, i-angle ngayinye yiyona:

720 ° ÷ 6 = 120 °

05 ka 05

Amanye amaPolgoni awaziwayo

IziNxushunxushu ezintathu

Izigxobo zomgodi - zivame ukuma kwezingunxantathu. Kuye ngobubanzi nobubanzi bophahla, umgoqo ungase ufake ama-trilly equilateral kanye ne-isosceles.

Ngenxa yamandla abo amakhulu, ama-triangles asetshenziswa ekwakhiweni kwamabhuloho, ama-bicycle ozimele, ne-Eiffel Tower.

I-Pentagon

I-Pentagon - indlunkulu yoMnyango wezokuVikela wase-US - ithatha igama layo ngokuma kwayo. I-pentagon ejwayelekile emihlanu ehlangene.

I-Home Plate

Enye i-pentagon ejwayelekile emihlanu eyaziwa ngamagundane i-home plate yidayimane ye-baseball.

I-Pentagon yama-Fake

I-giant shopping mall eduze ne-Shanghai, i-China yakhiwe ngendlela ejwayelekile ye-pentagon, futhi ngezinye izikhathi ibizwa ngokuthi i -Pentagon yama -Fake ngoba ifana neyokuqala.

Ama-snowflakes

Zonke izinqamu zeqhwa ziqala njengeqhekeza elilodwa, kodwa amazinga okushisa namazinga okumswakama afaka amagatsha namathenda ukuze ngamunye aqede ukubuka okuhlukile.

Izinyosi nama-Wasps

Amakhemikhali angokwemvelo ahlanganisa izinyosi lapho iseli ngalinye elithandwa khona izinyosi lapho izinyosi ezakha khona ukugcina uju liyi-hexagonal shape.

Izidleke zephepha zephepha ziqukethe namaseli angama-hexagonal lapho ekhulisa khona amancane.

I-Giant's Causeway

Ama-hexagon atholakala ku-Giant's Causeway esenyakatho-mpumalanga ye-Ireland.

Kuyinto yokwakhiwa kwedwala langokwemvelo elinamakholomu angaba ngu-40 000 angenelela e-basalt okwakhiwa njengoba i-lava evela ekuqhumeni kwe-volcanic yasendulo ipholile kancane.

I-Octagon

I-Octagon ekhonjisiwe ngenhla - igama elinikezwe indandatho noma ikamelo elisetshenziswa ku-UFC (Ultimate Fighting Championship). I-octagon ejwayelekile engamasonto ayisishiyagalolunye.

Misa izimpawu

Uphawu lokumisa - esinye sezibonakaliso zemigwaqo eyaziwa kakhulu - enye i-octagon ejwayelekile engamasonto ayisishiyagalolunye.

Nakuba umbala kanye namagama noma izimpawu ezisayinwe kuzohlukahluka, isimo se-octagonal sokumisa uphawu sisetshenziswa emazweni amaningi emhlabeni jikelele.