Assume hypothetically that π = a/b for some integers a and b. What downstream effects would this have on geometry, analysis, or physical theories? Would the foundations of math crumble? Would anything in the physical universe actually change?

Well, for a start it breaks Euler's Identity

>>16700432 (OP)
Math can not crumble because π is just a constant tied to a specific definition of distance, but a universe with a different definition of distance would be dramatically different.