I am not sure if i understand your question right, but of course mathematicians have explored the concept of geometry in non-Euclidean spaces, where the traditional rules of Euclidean geometry do not apply. Non-Euclidean geometries, such as hyperbolic and elliptic geometries, deal with planes that have different properties from those of Euclidean space.
Discussion
I always throw out wildcards whenever I can haha… No mathematician at ALL, but Euclidean geometry has always been a natural for me.
Would need some very weird mathematician to know if any geometry can be done NOT knowing what plane it is on! Or even with a plane that is changing ;-)