GeoGebra

Regular Polygons

Created by User:Zen biker

Demonstrations of how to create Regular Polygons

• 3-gon (also known as an equilateral triangle or regular trigon) is a Regular Polygon with 3 sides.
• 4-gon (also known as a square or regular tetragon) is a Regular Polygon with 4 sides.
• 12-gon (also known as a dodecagon) is a Regular Polygon with 12 sides.

The 3-gon is a regular polygon (P) with 3 (n) sides and vertices A, B, C. A sequence of Regular Polygons can be produced by gradually adding more sides to the 3-gon.

Add a side to a regular polygon in 3 steps. (Example : from a 3-gon to a 4-gon)

1. Step: Redefine n by adding 1 so that 3 becomes 4.
2. Step: Rotate Point C around Point O by angle α counterclockwise. (Use mode: Rotate object around point by angle)
3. Step: Redefine Polygon P by adding an extra vertex D.

So P = Polygon[A, B, C] becomes P = Polygon[A, B, C, D]. This process can be repeated to add more sides and thus create regular polygons with any number of sides. The polygon in the dynamic worksheet can be

• re-sized
• re-oriented
• re-located

by dragging three special points (A, Y and O).