Does Pi change when gravity changes

$pi$ is just a number. It doesn't vary with anything.

The ratio of the circumference to the diameter of a circle varies with geometry, so in the general case, this definition doesn't hold. But there are other definitions, such as

$$pi = int_{-1}^{1}frac{dx}{sqrt{1-x^2}},$$
or
$$mathrm{The,smallest,positive,number} , x , mathrm{for,which}, arccos(2x) = 0.$$
The latter definition can also be expressed a power series, which is independent of geometry.

• Next soft question - Best online mathematics videos?
• Previous fa.functional analysis - Characterisation of positive elements in l¹(Z)