By rotating a half-line around its origin, we accomplish the scanning of a part of the plan. We get thus a right angle when this scanning covers one quarter of the plan. We also get a flat angle when it covers half of the plan when the covered part is one eighth of the plan, etc. As it is for the right angle of a right-angled triangle, each one of its two other angles is the part of the plan which is covered by the scanning accomplished by bringing the half-line support of the adjacent side of the angle, to the half-line, support of the hypotenuse of the triangle, and vice versa. Thus, it is possible to act on those scans by computing on the connections of the right-angled triangles right angles sides. In this article, we demonstrate that the movement on the grid also makes sense when it is conceived as an essence for this operation and those calculations. However this way is still a blind point of the successive didactical contracts that the didactical systems ties around the notion of angle particularly, and the trigonometry generally speaking.
Praxeology, intelligibility, traceability of objects of knowledge, movement on the grid