Polygoner
en polygon er en plan form med lige sider.
er det en Polygon?
polygoner er 2-dimensionelle former. De er lavet af lige linjer, og formen er “lukket” (alle linjer forbinder op).
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| Polygon (lige sider) |
Ikke en Polygon (har en kurve) |
Ikke en Polygon (åbne, ikke lukkede) |
Polygon kommer fra græsk., Poly- means “many” and -gon means “angle”.
Types of Polygons
Regular or Irregular
A regular polygon has all angles equal and all sides equal, otherwise it is irregular
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| Regular | Irregular |
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.,
Hvis en intern vinkel er større end 180., er polygonen konkav. (Tænk: konkav har en “hule” i det)
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| Konveks | Konkave |
Enkle eller Komplekse
En simpel polygon har kun en grænse, og det gør ikke”t-kors over sig selv. En kompleks polygon skærer sig selv! Mange regler om polygoner don ” t arbejde, når det er komplekst.,entagon)
(also a Pentagon)
More Examples
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| Irregular Hexagon | Concave Octagon | Complex Polygon (a “star polygon”, in this case a pentagram) |
Play With Them!,
Try Interactive Polygons … make them regular, concave or complex.
Names of Polygons
| If it is a Regular Polygon…, | |||
| Name | Sides | Shape | Interior Angle |
|---|---|---|---|
| Triangle (or Trigon) | 3 |  |
60° |
| Quadrilateral (or Tetragon) | 4 |  |
90° |
| Pentagon | 5 | |
108° |
| Hexagon | 6 |  |
120° |
| Heptagon (or Septagon) | 7 |  |
128.,571° |
| Octagon | 8 |  |
135° |
| Nonagon (or Enneagon) | 9 |  |
140° |
| Decagon | 10 |  |
144° |
| Hendecagon (or Undecagon) | 11 |  |
147.273° |
| Dodecagon | 12 |  |
150° |
| Triskaidecagon | 13 | 152.,308° | |
| Tetrakaidecagon | 14 | 154.286° | |
| Pentadecagon | 15 | 156° | |
| Hexakaidecagon | 16 | 157.5° | |
| Heptadecagon | 17 | 158.824° | |
| Octakaidecagon | 18 | 160° | |
| Enneadecagon | 19 | 161.,053° | |
| Icosagon | 20 | 162° | |
| Triacontagon | 30 | 168° | |
| Tetracontagon | 40 | 171° | |
| Pentacontagon | 50 | 172.8° | |
| Hexacontagon | 60 | 174° | |
| Heptacontagon | 70 | 174.,857° | |
| Octacontagon | 80 | 175.5° | |
| Enneacontagon | 90 | 176° | |
| Hectagon | 100 | 176.4° | |
| Chiliagon | 1,000 | 179.64° | |
| Myriagon | 10,000 | 179.,964° | |
| Megagon | 1,000,000 | ~180° | |
| Googolgon | 10100 | ~180° | |
| n-gon | n |  |
(n−2) × 180° / n |
You can make names using this method:
BUT, for polygons with 13 or more sides, it is OK (and easier) to write “13-gon”, “14-gon” … “100-gon”, etc.,
En Quad Bike har 4 hjul
Pentagon (5 Sider)
“Pentagon” i Washington DC har 5 sider
Sekskant (6 Sider)
Honeycomb har Sekskanter
Septagon (7 Sider)
Tror Septagon er en “Syv-agon”
Octagon (8 Sider)
En Blæksprutte har 8 fangarme
Nonagon (9 Sider)
Tror Nonagon er en “Ni-agon”
Decagon (10 Sider)
Tror Decagon har 10 sider,
ligesom vores Decimal systemet har 10 cifre