Planificação de superfícies poliédricas no cálculo de distâncias

Abstract

This work proposes the calculation of the length of the shortest possible trajectory connecting two points on the surface of a straight rectangular parallelepiped. One of the points belongs to a face and the other belongs to another face, adjacent to the first. The initial step of the solution is to identify the minimum trajectory, that is, to know exactly where it passes, and the other is to obtain its measurement. To identify the trajectory, a plan is carried out, so that the two adjacent faces are contained in the same plane. As a resource for calculating the length of this trajectory, this work suggests the Pythagorean Theorem or the Similarity of Triangles as a tool. A mathematical modeling of this problem will be proposed by calculating the shortest length of a conduit running from a lamp on a room's ceiling to the lamp switch on one of the room's walls. The concepts of Plane and Spatial Geometries accessed in the consideration and resolution of the problem are considered and presented, which serves as motivation for teaching and learning such concepts. Other similar situations will be suggested, such as, for example, the measurement of a minimum trajectory traveled on the lateral surface of a straight cylinder.