Each non-zero point in Rd identifies one closest point x on the unit sphere Sd−1. We are interested in computing an ε-approximation y ∈ Qd for x , that is exactly on Sd−1 and has low bit size. We revise lower bounds on rational approximations and provide explicit, spherical instances. We prove that floating-point numbers can only provide trivial solutions to the sphere equation in R2 and R3. Mo...
