Depends on what you mean by setting pi = 1. You can subtract (pi - 1) from every number, giving you a translation of the real numbers. You can divide everythi

Depends on what you mean by setting pi = 1. You can subtract (pi - 1) from every number, giving you a translation of the real numbers. You can divide everything by pi, giving you a slight compression that ultimately doesn't mean anything. You could use it to create a field extension of the rationals, giving you a http://en.wikipedia.org/wiki/Algebraic_number_field http://en.wikipedia.org/wiki/Algebraic_number_field where {1, pi} is the basis. But to answer your question: probably nothing.