Minimum Area for Odd-Sided Equilateral N-Gons

Geometry Level 3

Consider equilateral n-gons with an odd number of unit length sides. When n = 3, an equilateral triangle is formed, and its area = 3 4 \dfrac{\sqrt{3}}{4} . As n increases beyond 3, starting with n = 5, the minimum possible areas of these special polygons will:

have a limit of 3 4 \dfrac{\sqrt{3}}{4} from above. approach 0. eventually increase without bound.

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