This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity in geometry. Through the formulae, the author describes how the velocity and distance from the ground change with respect to time when a body is left to fall from a height above the ground. The author emphasizes that this activity has some didactic theoretical properties: (1) It is cross curricular thematic in physics and mathematics; (2) It requires inverse thinking and inverse construction abilities; (3) It contains group work and experimentation; (4) It facilitates NT in the classroom or at home for extended results; and (5) It is visual. The students can simulate their own constructions in ways that can even be seen as artistic. (Contains 7 figures.)