From a historical point of view, mathematics and physics are closely related and interconnected fields of knowledge. However, the division present in academic and scholastic worlds leads to a separation of knowledge that limits the ability to develop a comprehensive view that grasps the important commonalities and boundary aspects. Special relativity can be taken as an example to highlight the deep connections between the two disciplines. This paper presents an activity, reserved for pre-service mathematics and physics teachers, based on an analysis of the mechanisms of boundary crossing between the two disciplines within the theory. This work highlights how specific and well-detailed attention to these mechanisms can shed light on nuances that are very important in enabling learning about the multifaceted nature of Lorentz transformations.