"gravity and mass are directly proportional to sin...." , yeah, that's rich!
gravity distorts space...any kind of space (yes, even euclidian [2-D, infinite, homogenous, etc] )
you actually need an extreme amount of mass concentrated in a relatively small 'amount of space' to observe the phenomenon
BUT! M_PI (C/C++) will actually have the same value
Let's say we have a tiny black hole (but massive enough to measure space distorsion), and that we have 2 observers: A, in the middle of a metal circle, B, far enough to not be affected by spacial distorsion generated by the black hole, and an infinetisimal small metal circle(that keeps its solid-rigid properties) having A in the center, heading for the black hole. Observer B will see the metal circle as being stretched out of its shape, thus apparently changing PI value while observer A will witness no shape change for the circle.
Thought that was hard to keep up with?... try this:
The amount of space distorsion is reverse-proportional with the square of the distance between the estimated center of the massive mass object doing the stretching and each material point of the object being stretched (infinetisimal small circle).
From the viewpoint of the 'information conservation' approach, space being stretched will not lose any information up to the event horizon(so PI will have the same value), but what happens beyond 'the point of no return' is anybody's guess...
...or we could throw physics into the bin as an 'evil' science and be on our way caring about our 'salivation' ... or something like that..