Galilean relativity – Explained by means of the triangle solutions

This paper presents a novel approach to understanding relativity through the lens of the triangle solutions. Triangle solutions will serve as a mathematical model for relativity. Using these very reliable and straightforward solutions ensures us that often-overlooked complexities in relativity can be clarified. Through comparative analysis between triangle solutions and situations in relativity, the fundamental concepts of this phenomenon such as the principle of relativity, Galilean transformation, velocity addition formula, relativity of time, and the origin and role of the Lorentz factor are elucidated. All these achieved results are supported with concrete explanations and examples. These results, shedding light on relativity, lead to several important conclusions, four of which stand out as both novel and significant. Firstly, while modern physics portrays light as possessing extraordinary properties, this paper argues that light behaves consistently with the laws of Galilean relativity, quite like other bodies. Secondly, contrary to the prevailing stance since the early 20th century, wherein time is considered absolute within the framework of Galilean relativity, this paper demonstrates that time is indeed relative within this framework, yielding a novel Galilean transformation (the transformed Galilean transformation). Thirdly, the Lorentz factor, until now was used as an "ace up one's sleeve", for all situations, without adequate analytical and physical reasoning, leading to wrong concepts and equations. The triangle solutions analysis led to the general equation of the transformation factor of physical quantities in relativity, whereas the Lorentz factor is only a special case of this general transformation factor. Fourthly, this study's general conclusion challenges modern Physics' stance that Galilean relativity is an approximate theory applicable only for small velocities; rather, it posits that Galilean relativity constitutes a complete theory, which offers realistic solutions for all relativity situations.