TEACHING THE VISUAL EFFECTS OF RELATIVITY TO JUNIOR HIGH SCHOOL STUDENTS USING ONLY A RULER AND COMPASS

To popularize relativistic visual knowledge among middle school students, this paper is based on the core theories of relativistic vision and reviews its historical development. It points out that the cosine formula for relativistic aberration proposed by Einstein in 1905 fails to demonstrate clear planar geometric significance. Building upon the field of relativistic vision research initiated by Terrell's 1959 paper, the author derives a tangent function version of relativistic aberration, which possesses a distinct planar geometric interpretation. Starting from this tangent formula, the paper utilizes straightedge and compass constructions, combined with knowledge of central angles, inscribed angles, and stereographic projection from middle school geometry, to transform relativistic aberration into an intuitive and operational geometric construction problem. It elucidates the essential nature of relativistic vision as a compression mapping—that is, when a rocket travels at near-light speed, the celestial angle θ observed by the pilot compresses to θ'. Through specific numerical examples of velocity, the paper demonstrates the method of using straightedge and compass to locate the observed position B from the original celestial position A, thereby achieving the goal of explaining relativistic vision through elementary geometric methods.