On the geometry of the Frobenius problem

The geometrical method to find the Frobenius number indicated by Arnold (Funct. Anal. Other. Math. 2, 2007) in the case of 3 generators can be extended to any number of generators. The method provides not only the Frobenius number but also a set of numbers, from which all the nonrepresentable numbers can be generated. In the case of three generators, we show some geometrical implications of the conditions for a semigroup to be symmetric or nonsymmetric.