Laboratorio di matematica in classe: due nuove macchine per problemi nel continuo e nel discreto

In this work we will introduce two mathematical machines (originally invented by the authors) that can be useful in class during laboratorial activities. We decided to introduce them together because they appeared us complementary about the subtended contents, in fact one of them solves a discrete problem (diophantine equations) involving concepts as integers, divisibility, and in general discrete math, while the other machine (solving differential equations in a grapho-mechanical way) involves the complementary concepts of continuous math: curves, tangents, derivatives. In this paper we will just present the machines, deepening the ideas and the subtended mathematical contents, but we will not introduce didactical questions that will be treated in future works.