Consider an equilateral triangle, with sides of length L, drawn on a two-dimensional surface of uniform curvature. Can you draw an equilateral triangle of arbitrarily large area A on a surface with κ=+1 and radius of curvature R? If not, what is the maximum possible value of A? Can you draw an equilateral triangle of arbitrarily large area A on a surface with κ=0? If not, what is the maximum possible value of A? Can you draw an equilateral triangle of arbitrarily large area A on a surface with κ=−1 and radius of curvature R? If not, what is the maximum possible value of A?