GEOMETRIC AND OPTICAL PROPERTIES OF CONIC SECTIONS: AN INTERDISCIPLINARY APPROACH TO THE CONSTRUCTION OF LOW-COST SCIENTIFIC APPARATUS

Abstract

This paper proposes an in-depth analysis of the reflection properties inherent to conic sections — ellipse, hyperbola, and parabola — from an interdisciplinary perspective that integrates Analytical Geometry with Optical and Acoustic Physics. The fragmentation of knowledge in High School is identified as an obstacle to the understanding of complex phenomena; in this sense, the present work articulates rigorous theoretical foundation with phenomenological application. A historical survey of conics is presented, from Ancient Greece to the laws of Kepler and Newton, followed by the mathematical deduction of their reflective properties based on Fermat's Principle. Finally, the construction methodology and results of two experimental prototypes are described: a parabolic solar concentrator and an acoustic communicator (parabophone). The results indicate that experimentation based on precise mathematical models enhances didactic transposition and scientific literacy.