Polygons in polygons
An n-sided regular polygon is inscribed in a similar regular polygon.
You can choose the number of sides [from 3 to 20] using the slider.
You can vary the inscribed polygon by dragging the GOLD dot.
As a function of the number of sides and the position of the GOLD dot
can you derive expressions for -
- the ratio of the perimeters of the two polygons?
- the fraction of the area of the Blue polygon is covered by the
Green polygon?
Adapted from an applet by Jessica Layton