  Minding's most celebrated result is his namesake theorem of 1839 which
established that all surfaces having the same constant curvature must be
locally isometric. Today, Minding's theorem is a staple in differential
geometry textbooks. But, to the best of our knowledge, all published proofs of
it, inclusive of Minding's original argument are existential in nature. In this
note, we give a constructive proof of Minding's theorem in the flat case. The
proof requires only some basic facts about harmonic functions and complex
analytic functions.
