Patterns in Mathematics
Regular polygons
Learn what regular polygons are, and find patterns in shapes.
Patterns are not only in numbers but also in shapes. The part of mathematics that studies patterns in shapes is called geometry. Your book's Table 3 shows famous shape sequences. The first is the regular polygons.
A polygon is a flat shape made only of straight sides. The shapes are named by their number of sides, and the numbers of sides are the counting numbers from 3:
| Sides | Name |
|---|---|
| 3 | triangle |
| 4 | quadrilateral (the regular one is the square) |
| 5 | pentagon |
| 6 | hexagon |
| 7 | heptagon |
| 8 | octagon |
| 9 | nonagon |
| 10 | decagon |
'Regular' means two things: all the sides are the same length, and all the angles are equal, so every corner looks the same. A square is a regular quadrilateral. A long, thin rectangle also has 4 sides, but they are not all the same length, so it is not regular.
Each of these shapes has as many corners as sides. Walk round the edge: every side ends at a corner, and the next side starts there. So a hexagon has 6 sides and 6 corners; a decagon 10 and 10. Something to think about: as you keep adding more and more sides, what does a regular polygon start to look like?
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