It is possible to construct a regular pentagon with compass and straightedge:
- Draw circle (red).
- Draw diameter and construct a perpendicular radius through .
- Construct the midpoint of , and label it .
- Draw (green).
- Construct the angle bisector of , and label its intersection with as (pink).
- Construct a perpendicular to at .
- Adjust your compass to length , and mark off points , and on circle .
- is a regular pentagon.
The Golden Ratio and the Pentagram
The pentagon is closely associated with the Golden Ratio. More specifically, the ratio of a diagonal to an edge is . By drawing each of the diagonals, one can form a pentagram, or five-pointed star, in which each of the internal angles is .\\
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