Relativistic Frame–Dependent Trisection of an Angle and Triangle in Minkowski SpaceTime

The classical impossibility of trisecting an arbitrary angle using an unmarked straight- edge and compass, established by Wantzel in 1837, is formulated within Euclidean geometry, which at the time was widely assumed to describe physical space. Modern physics, however, shows that physical reality is governed by Minkowski spacetime, in which spatial geometry is observer-dependent. In this paper, we extend the notion of geometric construction to in- clude transformations between inertial frames in special relativity. We demonstrate that, by passing to a suitable moving frame, an angle or triangle can be exactly trisected using standard Euclidean constructions within that frame. Although the resulting construction does not yield a Euclidean trisector in the original rest frame, it constitutes a valid trisec- tion in Minkowski spacetime. These results suggest that classical impossibility theorems are framework-dependent and that trisection is operationally achievable in the physically relevant setting of spacetime.