Is there a shape for every possible angle?
Mathematicians are currently chasing a conjecture regarding single-angle polyhedra. This video explores a geometric mystery that remains unsolved, despite having all the necessary components for a proof scattered across existing mathematical literature.
The video examines the conjecture that a single-angle polyhedron exists for any angle θ with an algebraic sine. While the mathematical community believes this statement to be true, a complete and elegant proof has yet to be assembled.
The search for a solution involves piecing together existing research, specifically looking at the work of Sydler and Jessen. While their papers appear to contain the essential elements required to validate the conjecture, the final logical bridge remains undiscovered.
Source: The shape that should be impossible.
