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On a circular island we build n straight dams going from sea to sea so that every two intersect but no three go through the same point Use Euler's Formula to determine how many parts we get?
Wiki User
∙ 11y ago
Consider following figure with n = 4.
Clearly, number of vertices (v) = 14, number of edges (e) = 24 and number of faces (f) = 12.
According to Euler's formula, v + f = e + 2
i.e. v + f = 14 + 12 = 26 = e + 2.
In general we have, v = 2n + nC2 and e = 2n + n2.
Hence, using Euler's formula,
f = e + 2 - v
= 2n + n2 + 2 - 2n + nC2
After simiplication we have,
Wiki User
∙ 11y ago
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