Ib tug duab geometric muaj ntau yam li polygons. Lawv suav nrog daim duab peb sab uas paub, square, thiab pentagon, tab sis qhov ntawd tsuas yog qhov pib xwb.
Nyob rau hauv geometry, ib tug polygon yog ib qho duab ob sab uas ua tau raws li cov hauv qab no:
- Yog ua los ntawm peb lossis ntau kab ncaj
- Tau kaw tsis muaj qhov qhib lossis tawg hauv cov duab
- Muaj cov kab uas txuas ntawm cov ces kaum lossis ntsug uas lawv tsim cov kaum
- Muaj tus lej sib npaug ntawm sab thiab sab hauv
Ob sab txhais tau tias tiaj tus zoo li daim ntawv. Cubes tsis yog polygons vim lawv yog peb-dimensional. Cov voj voog tsis yog polygons vim lawv tsis muaj kab ncaj.
Ib yam tshwj xeeb ntawm polygon tuaj yeem muaj cov ces kaum uas tsis sib npaug. Hauv qhov no, nws yog hu ua tus irregular polygon.
About Polygons
Lub npe polygon los ntawm ob lo lus Greek:
- Poly, uas txhais tau tias ntaus
- Gon, txhais tau tias angle
Shapes That Are Polygons
- Trigon (daim duab peb sab): 3 sab
- Tetragon (square): 4 sab
- Pentagons: 5 sab
- Hexagon: 6 sab
- Heptagon: 7 sab
- octagons: 8 sab
- Nonagon: 9 sab
- Decagon: 10 sab
- Undecagon: 11 sab
- Dodecagons: 12 sab
How Polygons Npe
Cov npe ntawm tus kheej polygons yog muab los ntawm cov lej ntawm sab lossis cov ces kaum uas cov duab muaj. Polygons muaj tib tus lej ntawm sab thiab cov ces kaum.
Lub npe nrov rau feem ntau cov polygons yog Greek prefix rau "sab" txuas rau Greek lo lus rau kaum (gon).
Piv txwv ntawm qhov no rau tsib thiab rau-sided ib txwm polygons yog:
- Penta (Greek lub ntsiab lus tsib) + gon= pentagon
- Hexa (Greek lub ntsiab lus rau) + gon= hexagon
Tseem muaj kev zam rau lub npe no. Qhov tshwj xeeb tshaj plaws nrog cov lus siv ntau dua rau qee qhov polygons:
- Daim duab peb sab: Siv cov lus Greek ua ntej Tri, tab sis tsis yog Greek gon, Latin angleyog siv. Trigon yog lub npe geometrical tseeb tab sis tsis tshua siv.
- Quadrilateral: Muab los ntawm Latin prefix quadri, lub ntsiab lus plaub, txuas rau lo lus lateral, uas yog lwm lo lus Latin lub ntsiab lus side.
- Square: Qee zaum, plaub-sided polygon (ib square) raug xa mus ua ib qho quadrangle lossis tetragon.
N-Gons
Polygons nrog ntau dua 10 sab tau ntsib ntau zaus tab sis ua raws tib lub npe Greek lub rooj sib tham. Yog li, 100-sided polygon raug xa mus rau hectogon.
Txawm li cas los xij, hauv lej, pentagons qee zaum yooj yim dua hu ua n-gons:
- 11-gon: Hendecagon
- 12-gon: Dodecagon
- 20-gon: Icosagon
- 50-gon: Pentecontagon
- 1000-gon: Chiliagon
- 1000000-gon: Megagon
Hauv kev ua lej, n-gons thiab lawv cov npe greek-npe yog siv sib hloov.
Polygon txwv
Txoj kev xav, tsis muaj kev txwv rau tus naj npawb ntawm sab ib tus polygon tuaj yeem muaj.
Raws li qhov loj ntawm cov kaum sab hauv ntawm lub polygon loj dua, thiab qhov ntev ntawm nws sab tau luv dua, lub polygon mus txog lub voj voog, tab sis nws yeej tsis tau mus txog qhov ntawd.
Kev faib cov Polygons
Regular vs. Irregular Polygons
Polygons raug cais raws li seb puas yog lossis tsis tag nrho cov ces kaum lossis ob sab sib npaug.
- Regular polygon: Txhua lub ces kaum yog qhov sib npaug, thiab txhua sab yog sib npaug ntawm qhov ntev.
- Irregular polygon: Tsis muaj cov kaum sib npaug lossis ob sab ntawm qhov sib npaug.
Convex vs. Concave Polygons
Ib txoj hauv kev thib ob los faib cov polygons yog qhov loj ntawm lawv cov kaum sab hauv.
- Convex polygons: Tsis muaj cov kaum sab hauv siab dua 180 °.
- Concave polygons: Muaj tsawg kawg ib lub kaum sab hauv uas siab dua 180 °.
Yooj yim vs. Cov Polygons complex
Lwm txoj hauv kev los faib cov polygons yog txoj hauv kev uas cov kab ua cov kab sib tshuam.
- Yam yooj yim polygons: Cov kab txuas lossis sib tshuam tsuas yog ib zaug - ntawm qhov vertices.
- Complex polygons: Cov kab sib tshuam ntau dua ib zaug.
Cov npe ntawm cov polygons nyuaj qee zaum txawv ntawm cov yooj yim polygons nrog tib tus lej ntawm sab.
Piv txwv:
- Ib yam tsis tu ncua hexagon yog rau-sab, yooj yim polygon.
- Ib lub hnub qub zoo li hexagram yog 6-sided, complex polygon tsim los ntawm kev sib tshooj ob daim duab peb sab sib npaug.
Sum of Interior Angles Rule
Raws li txoj cai, txhua lub sij hawm ib sab ntxiv rau ib tug polygon, xws li:
- Los ntawm daim duab peb sab mus rau plaub fab (peb mus rau plaub sab)
- Los ntawm lub pentagon mus rau hexagon (tsib rau rau sab)
lwm 180 ° ntxiv rau tag nrho cov kaum sab hauv.
txoj cai no tuaj yeem sau ua qauv:
(n - 2) × 180°
qhov twg n sib npaug ntawm cov sab ntawm lub polygon.
Yog li cov lej ntawm cov kaum sab hauv rau lub hexagon tuaj yeem pom los ntawm kev siv cov mis:
(6 - 2) × 180 °=720 °
Puas muaj pes tsawg daim duab peb sab hauv lub Polygon?
Cov qauv saum toj no sab hauv lub kaum sab xis yog muab los ntawm kev faib ib lub polygon rau hauv daim duab peb sab, thiab tus lej no tuaj yeem pom nrog kev suav:
n - 2
Nyob hauv cov qauv no, n yog sib npaug rau tus naj npawb ntawm sab ntawm lub polygon.
Ib hexagon (rau sab) tuaj yeem muab faib ua plaub daim duab peb sab (6 - 2) thiab dodecagon ua 10 daim duab peb sab (12 - 2).
Lub kaum ntse ntse rau cov polygons tsis tu ncua
Rau cov polygon tsis tu ncua, nyob rau hauv cov ces kaum yog tag nrho cov loj tib yam thiab ob sab yog tib qhov ntev, qhov loj ntawm txhua lub kaum sab xis nyob rau hauv ib lub polygon tuaj yeem xam los ntawm kev faib tag nrho qhov loj ntawm cov ces kaum (hauv degrees) los ntawm tag nrho cov lej ntawm sab.
Rau ib txwm muaj rau-sided hexagon, txhua lub kaum yog:
720° ÷ 6=120°
Qee lub npe hu ua Polygons
Zoo-paub polygons suav nrog:
Tsev
ru tsev trusses feem ntau yog daim duab peb sab. Nyob ntawm qhov dav thiab lub suab ntawm lub ru tsev, lub truss yuav suav nrog cov duab sib npaug lossis cov duab peb sab isosceles. Vim lawv lub zog loj, daim duab peb sab yog siv rau hauv kev tsim cov choj thiab cov tsheb kauj vab thav duab. Lawv yog cov tseem ceeb hauv Eiffel Ntauwd.
Pentagon
Lub Pentagon - lub hauv paus chaw haujlwm rau US Department of Defense - siv nws lub npe los ntawm nws cov duab. Lub tsev yog tsib sab, ib txwm pentagon.
Hmoob Phaj
Lwm tus paub zoo tsib-sab ib txwm pentagon yog lub tsev phaj ntawm pob zeb diamond baseball.
Tus Fake Pentagon
Lub khw loj loj nyob ze Shanghai, Tuam Tshoj, tau tsim ua cov duab ntawm lub pentagon tsis tu ncua thiab qee zaum hu ua Fake Pentagon.
Snowflakes
Txhua lub paj daus pib tawm ua lub hexagon, tab sis qhov kub thiab txias thiab noo noo ntxiv cov ceg thiab cov leeg kom txhua tus xaus saib txawv.
Nyob zoo ib tsoom niam txiv kwv tij neej tsas sawv daws.
Natural hexagons kuj suav nrog beehives, qhov twg txhua lub xovtooj ntawm lub honeycomb uas muv tsim los tuav zib ntab yog hexagonal. Lub zes ntawm daim ntawv wasps kuj muaj cov hlwb hexagonal uas lawv tsa lawv cov hluas.
Tus Giant's Causeway
Hexagons kuj pom nyob rau hauv Giant's Causeway nyob rau sab qaum teb sab hnub tuaj Ireland. Nws yog ib lub pob zeb ntuj tsim muaj li ntawm 40,000 interlocking bas alt kab uas tau tsim raws li lub lava los ntawm ib tug ancient volcanic eruption maj mam txias.
Lub octagon
Lub Octagon - lub npe muab rau lub nplhaib lossis lub tawb siv nyob rau hauv Qhov Kawg Sib Ntaus Championship (UFC) bouts - siv nws lub npe los ntawm nws cov duab. Nws yog yim-sided tsis tu ncua octagon.
Stop Signs
Daim paib nres - ib qho ntawm cov cim kev tsheb uas paub zoo tshaj plaws - yog lwm yim sab octagon. Txawm hais tias xim, lo lus, lossis cov cim ntawm lub cim yuav txawv, cov duab octagonal rau lub cim nres yog siv ntau lub tebchaws thoob ntiaj teb.
