How to determine if a sphere is locally isometric to a plane? 
Is a sphere of radius one locally isometric to a plane? (Briefly justify your answer.)

How do I go about answering this question. Could someone provide an explanation to what exactly locally isometric means? Also is the radius value of 1 an irrelevant piece of information so basically what they are asking is whether sphere , regardless of the radius locally isometric to a plane?
Any help would be much appreciated.

Hint:
1) We say that a smooth map $F : S_1 →\rightarrow S_2$ between the two surfaces $S_1$,$S_2$ is a local isometry if it preserves distances between two points close to each other.
2) From the Teorema egregium of Gauss we know that the gaussian curvature of a surface is invariant under isometries. And the gaussian curvature of a sphere  of radius $R$ is $1/R^2$ but the gaussian curvature of a plane  is $0$.
