Finding an Interesting Locus Through the use of Wolfram Mathematica

Being able to look at something in more than one way is crucial in all branches of mathematics. This fact, however, is often disregarded. Learning to view the world differently implies through a change in perspective, that can have a relevant impact on the capability to solve problems (see [2]). Based on our experiences of Wolfram MathematicaTM, we propose an approach to identify the locus, and its related conic section, of all the points that trisect an arc of circle having its center on the axis which passing through the medium point of the chord subtended by the arc. In this paper, it is shown that it is possible, without any conflict with the proved impossibility of the classical trisection of the angle, to trisect an arc that opposes the angle at the center of a circle, using only a straightedge and a compass. After setting out the conditions for the evaluation of a conic, first, by using MathematicaTM, we numerically determine that the curve is a hyperbola; then we prove that, given any generic segment, it is always possible to identify a hyperbola locus of points which lies on the intersections of the arcs of circumference having the center on the axis of the segment. Knowing that when someone looks at a Math problem, it is very common that they try to "figure it out" in their head before writing anything down, two possible lines of research are presented with the conclusions: the first one concerning the logical justification that the revenue place is a conic, and the second one connected with the need to explain how, and if, the segment size may alter the value of the minimum angle determined by the displacement of the center of the circle toward the infinite.