u . v = |u| |v| cos θ, so cos θ = (u . v) / (|u| |v|) = (u . v) / (sqrt(u . u) * sqrt(v . v))
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when f(x) = x and g(x) = x^x_1, C = y_1 = sqrt(z_1) / w_1
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when f(x) = 1 and g(x) = x^x_2, C = y_2 = sqrt(z_2) / w_2 = cos(u_2), sin(u_2) = p_2 / q_2
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equals
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sin(u_2) is a simple fraction?
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conjecture: the sine of the functional angle between x ↦ 1 and x ↦ x^(2n) is (2n) / (2n + 1)
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