Nested Regular Polygons
Nested Regular Polygons
This Demonstration shows an interesting nesting of successive regular polygons, starting with an equilateral triangle up to a chosen -gon. If the side length of the triangle is 1, can you show that the side of the square is equal to (approximately 0.966) and that the side of the pentagon equals (approximately 0.905)?
n
2+
3
2
(2+
3
)(3-5
)5
+5-2
5
2(5-
5
)