Regular n-Gons as Polygons and Stars

This Demonstration shows regular -gons that can be convex polygons or stars.
Polygons with sides correspond to step size 1: the sides are connected in sequence around the inscribed circle, which they approximate as the number of sides increases.
With sides and a larger step size , the figure is a star or a polygon with sides if this is a whole number.

THINGS TO TRY

SNAPSHOTS

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DETAILS

It's an interesting job to look for all the pentagons and pentagrams and to take note of the relationships between the number of sides and the divisor (step size).
The series of pentagons is , , , , …, , which are all equal to 5. Beginning with , double the values of the divisor in order to get pentagrams.
The series of pentagrams is therefore , , , , , …, .
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Related Curriculum Standards

US Common Core State Standards, Mathematics