Addressing the Solution of Triangles through the Lens of Python

In the present work we are interested in finding missing characteristics of triangles and discovering relationships between them by following an intuitive approach based on experimentation. The experimentation is facilitated by the Python environment in which we assume the role of an actor which can move as instructed. Through observation and calculation we gain intuition for the formulation of the law of sines and establish formal proofs ending finally to a proof of the law of cosines by following an approach related to the equality of areas. Acting complementarily to the official book of Mathematics of the second grade of greek upper high school we work together with the students in order to end up to the formulation of the law of cosines using the proving method inspired by the ancient Persian Mathematician Al-Kashi. Our teaching approach in based on constructivist approaches that are implemented in the environment of Python where LOGO-like instructions are executed. Combining the method of Al-Kashi with the use of software belonging to the LOGO family we achieve the visualization of the geometric constructions and the determination of the geometric quantities through computational methods. Following an experimental approach in Geometry we expect to highlight the restrictions and the strong points characterizing each approach, either this is founded on the classical geometric techniques or on the employment of software tools. The environment of Python offers students the opportunity to associate the gained experience with previous knowledge and experience, a procedure which is not easily feasible through face-to-face learning.