I-Polygon Geometry: ii-Pentagon, iiHexagon kunye neeDodecagon

01 ngo 05

Yintoni iPolygon?

Iipolgoni ziLinganiso ezimbini

Kwijometri, i-polygon nayiphi na imimiselo emibili ephezulu:

• Yenziwe ngemigca emithathu okanye ngaphezulu
• Ivalwe - akukho zivulo okanye ikhefu kwindawo
• Unombini wemigca edibanisa kumacangca okanye kwii-vertic apho zakha ii-angles
• Unamaqela alinganayo namacala angaphakathi (ii-angles ngaphakathi kwipolygoni)

(Ezimbini-dimensional zithetha i-flat-like piece of paper)

Yonke YesiGrike

Igama le- polygon livela kumagama amabini aseGrike:

• i-poly - ithetha "ezininzi"
• gon lithetha "i-angle"

Iimilo ZiyiPolgoni

• Triangles
• Izikwere
• Pentagon
• Octagons
• Iidodecagons - njengengqekembe ye-Jamaican engama-12 kumfanekiso ongentla

Iimilo Azinjalo Iipolgoni

• Isangqa - kuba sakhiwe ngomgca onqamkileyo kunokuba imigca eqondekileyo
• Ibhokisi okanye ikerubhi - kuba i- three-dimensional in shape ayiyiyo mibini

02 we 05

Ukubiza iipolgoni

Amagama ePolygon

Amagama ama-polygoni ngamnye athatyathwa kwinani lamacandelo kunye / okanye ingangaphakathi yangaphakathi .

(Ngendlela, inani leengalo zangaphakathi - iingongoma ngaphakathi kwimilo - mazihlale ilingana nenani lamacala).

Amagama aqhelekileyo kwiipolgoni ezininzi anesiqalo seGrike kwinani leengxube ezixhomekeke kwigama lesiGrike kwi-angle (gon).

Ngoko, amagama aqhelekileyo kwiipolgoni eziqhelekileyo ezintlanu kunye nesithandathu zisezantsi:

• ipenta (isiGrike esithetha intsuku ezintlanu) + gon = ipentagon
• hexa (isiGrike esithetha intsandathu) + gon = ihektare

Okungekho

Kukho, ngokuqinisekileyo, ukungafani nakweli cwangciso legama. Okubalulekileyo:

I-Triangle- isebenzisa isiqendu seGrike isiGrike , kodwa endaweni yeGrike yesiGrike , i-Latin angle isetyenziswa. (Ngokuqhelekileyo zibizwa ngokuba ngama-trigons).

I-quadrilateral - itholakala kwisiqalo sesiLatini isi- quadri- esichazayo ezine-eqhotyoshelweyo kwigama elisecaleni- lelinye nelinye igama lesiLatin elisecaleni.

Ngamanye amaxesha, iipoloniki ezine-side zibizwa ngokuba yi- quadrangle okanye i- tetragon .

n-gons

Iipolgoni ezinamaqela angaphezulu kwama-10 kunye nama-angles akhona, kwaye amanye anamazwi aqhelekileyo - njengama-100 ecaleni ye-ectogon .

Ekubeni bahlanganisane nexesha eliqhelekileyo, kunjalo, baninzi banikwa igama elibandakanya inani lamacandelo kunye nama-angles kwixesha eliqhelekileyo le-angle- gon .

Ngoko, i-polygon ye-100-side ibizwa ngokuba yi- 100-gon .

Ezinye i- n-gons kunye namagama aqhelekileyo kwiipolgoni ezinamaqela angaphezu kwelishumi zi:

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

Umda wePolygon

Iingqungquthela, akukho mda kwinqanaba lamacandelo kunye nama-angles kwi-polygon.

Njengoko ubukhulu beengalo zangaphakathi ze-polygon zincinci kwaye ubude bamacala abo buba mfutshane ipolgoni isondela isangqa - kodwa ayiyi kufika khona.

03 we 05

Ukuqulunqa iipolgoni

Ngokuqhelekileyo ngokumalunga ne-Irregular Polygons

Kwiipoloni rhoqo rhoqo onke ama-angles afana nobukhulu obulinganayo kwaye onke macala alinganayo ubude.

Iipoloni engavumelekanga nayiphina iipoloni engenawo angele alinganayo nobubanzi obulinganayo.

Convex vs Concave

Indlela yesibini yokuhlenga iipolgoni yileyayizi yeengalo zangaphakathi. Ezi zimbini zikhethi ziyi- convex kunye ne- concave:

• Iipolgoni zeConvex - akukho zingalo zangaphakathi ezinkulu kune 180 °;
• Iconcave iipolgoni - ubuncinane ibanga langaphakathi likhulu kune 180 °.

Elula kunye neePolgoni eziPhezulu

Kanti enye indlela yokuhlukanisa iipolgoni yindlela indlela yokwenza ipoloni idibene ngayo.

• Imigca ye-polygon elula idibanisa okanye idibanise kanye kuphela - kwii-vertices;
• Imizila yeepolgoni eziyinkimbinkimbi idibanisa ngaphezu kweyodwa.

Ngamanye amaxesha ama-polygoni eziyinkimbinkimbi ahluke kwii-polygoni ezilula kunye nenani elifanayo.

Umzekelo,

• I- hexagon enemihla ngemihla i-polygon egciniweyo elula
• I-hex agram eneenkwenkwezi i-polygon yinkalo yesithandathu yecala edibeneyo eyenziwa ngokugqithisa ezimbini ze-trilateral equilateral njengokuba kuboniswe kumfanekiso ongentla

04 we 05

I-Sum ye-Angles Rule Rule

Njengomthetho, ixesha ngalinye icala longezwe kwipolygoni, njengale:

• Ukusuka kunxantathu ukuya kwi-quadrilateral (amacala amathathu ukuya kwamane)
• Ukusuka kwi-pagonagon kwi-hexagon (ngamacala amahlanu ukuya ezintandathu)

enye i-180 ° yongezwa kwisixa-mali seengalo zangaphakathi.

Lo mgaqo ungabhalwa njengendlela:

(n-2) × 180 °

apho n = inani lamacandelo e-polygon.

Ngoko ukubalwa kweengalo zangaphakathi ze-hektare kungatholakala ngokusebenzisa ifomu:

(6 - 2) × 180 ° = 720 °

Zingaphi Iingxowankulu kwiPolygon?

I-formula yangasentla ye-angle yangomlambo ivela ngokuhlula i-polygon ibe ngama-triangles, kwaye le nombolo inokufumaneka ngokubala:

n - 2

apho kwakhona kulingana nenani lamacandelo e-polygon.

Ngoko, i-hexagon (macala amathandathu) anokuhlulwa zibe zi-triangles ezine (6 - 2) kunye ne-dodecagon zibe zi-triangles ezi-10 (12 - 2).

Ubungakanani beeNgqungquthela zamaPolgon rhoqo

Iipolgoni eziqhelekileyo (idibanisa ubungakanani obufanayo kunye namacala onke ubude obufanayo), ubungakanani bekota ngalinye kwi-polygon bunokubalwa ngokuhlula inani elipheleleyo lamadigri ngamanani amaninzi.

Kwi-hexagon ye-six-side ye-six-side, nganye ngecala:

720 ° ÷ 6 = 120 °

05 we 05

Ezinye iipolgoni eziyaziwayo

Iintlanganiso zeThathu

Iintonga zengxube - zihlala zisesigxina. Ngokuxhomekeka kububanzi nobubanzi bephahla, i-truss ingafaka i-equilateral kunye ne-isosceles triangles.

Ngenxa yamandla abo amakhulu, ama-triangles asetyenziswe ekwakhiweni kweebhuloji, ama-bicycle frames, kunye ne-Eiffel Tower.

Pentagon

I-Pentagon - ikomkhulu leSebe lezoKhuseleko lase-United States-ithatha igama layo kwimo yayo. I-pentagon ephindwe ezintlanu.

I-Plate yasekhaya

Elinye iqela eliqhelekileyo elisezantsi le-Pentagon liyi-plate plate ekhaya.

I Pentagon yenkohlakalo

Indawo enkulu yokuthenga i-Shanghai kufuphi ne-Shanghai, i-China yakhiwe ngendlela ye-pentagon rhoqo, kwaye ngamanye amaxesha ibizwa ngokuba yi -Fake Pentagon ngenxa yokufana kwayo neyokuqala.

Snowflakes

Yonke inqabana yeqhwa iqala njengeqhekeza elincinane, kodwa izinga lokushisa kunye namanqanaba omnyuli longeza amagatsha kunye nama-tendrils ukuze nganye iphele ekhangelekile.

Inyosi kunye neeVilisi

Iimpawu zezilwanyana zendalo ziquka iinyosi apho inqwelyana nganye kwi-honeycomb leyo inyosi eyakhayo ukuze ibambe ubusi i-hexagonal in shape.

Izilwanyana zamaphepha ephepha ziqulethe iiseli ezingamagxobhozo apho ziphakamisa zabo iintsana.

I-Giant Causeway

Iikhoxagoni zifumaneka kwiCyant's Causeway e-North-east Ireland.

Ingqungquthela yendalo eyakhiwa ngamakholomu angama-40,000 angenelela e-basalt ayenziwe njengoko i-lava evela kwintyatyambo ye-volcanic yasendulo yacima.

I-Octagon

I-Octagon eboniswe ngasentla - igama elinikwe kwindandatho okanye igumbi elisetyenziswe kwi-UFC (Ultimate Fighting Championship) - ithatha igama layo kwimo yayo. I-octagon egciniweyo yecala.

Yeka Iimpawu

Uphawu lokuma - enye yeempawu zendlela zezona ndawo ziyaziwayo - enye enye i-octagon rhoqo.

Nangona umbala kunye negama okanye iimpawu ezibonakalisiweyo zingasahluka, ukuma kwe-octagonal yesigxina sokumisa kusetyenziswa kumazwe amaninzi kwihlabathi jikelele.