The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n = (9cos^2 ω + 52cos ω + 44)/(36n^2 sin^2 ω), where ω congruent 2π/n (Alikoski 1939; Solomon 1978, p. 109; Croft et al. 1991, p. 54). Prior to Alikoski's work, only the special cases n = 3, 4, 6, 8, and ∞ had been determined. The first few cases are summarized in the following table, where A^__7 is the largest root of 784147392x^3 - 84015792x^2 + 2125620x - 15289 = 0, and A^__9 is the largest root of 24794911296x^3 - 2525407632x^2 + 55366092x - 312427 = 0.
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