We introduce a new geometric framework for arithmetic functions belonging to the class \mathcal{V},where each function f\in\mathcal{V} is associated with the discrete orbit A_n=(n,f(n))\in\mathbb{Z}^2. From this perspective, arithmetic properties of fare interpreted through Euclidean geometric configurations generated by points on the discrete graph of the function, and one studies whether such configurations exist finitely or infinitely often.
