Um estudo sobre a propriedade de reflexão dos bilhares cônicos.

Abstract

In this work, a study is carried out on the conics with the objective of presenting the reflective property using the conical billiards, since it is a direct application of this property, allowing a better interpretation of the same, because when moving the ball trajectory will describe a point about the billiard table, which upon reaching the table will be reflected to the pocket. This reflection property, contained in the conical billiards, is due to the fact that the angle of incidence, ie the angle of arrival when the ball reaches the table, is equal to the angle of reflection. For each billiard it occurs differently. In elliptical billiards if the ball is located on a marking made on the table, to draw it anywhere on the table with enough force, it will only play once in the table and will be reflected to the billiard pocket. If the ball is not over the mark, with sufficient force, towards it the ball will play only once in the table and will be reflected to the pocket. In hyperbolic billiards, regardless of the position, when you hit the ball towards a mark made on the table, it will hit only once the table and will be reflected to the billiard deck. In the parabolic billiard, also regardless of the position of the ball, to stick it parallel to the axis of symmetry, that is, to pick it straight at any point in the table, it will touch only once in the same and will be reflected to the pocket. This property of reflection is demonstrated using definitions of each curve, deducing the canonical equation of the same, deriving implicitly each deduced equation, obtaining the angular coefficient of the tangent and normal lines of each conic, using Angular Trigonometric Tangent, External Angle Theorem , Angular Coefficients and Algebraic Manipulations.