AT work, we were wondering about exotic geometries, and we ended up to a question.
Can we make a 2D closed surface (in a 3D space, like a sphere) called S such that there exists a point on that surface, called O, such that for any other point P on S, there exist a "straight" line on S that goes from P to L?
I guess that such surface S will follow an equation (like x² + y² + z² = 1), but I don't really see how to formulate the condition of the straight line existence. I think that the "straight line on S from point P toward direction D" might be considered as the intersection of the surface S and the plane F that contains both the normal of S on P and the chosen direction D. But the calculus seems heavy.
So, is there such surface? Maybe in higher dimensions? What is the search field in mathematics that explores this kind of question?