  Using a geometric formalism of elasticity theory we develop a systematic
theoretical method for controlling and manipulating the mechanical response of
slender solids to external loads. We formally express global mechanical
properties associated with non-euclidean thin sheets, and interpret the
expressions as inverse problem for designing desired mechanical properties. We
show that by wisely designing geometric frustration, extreme mechanical
properties can be encoded into a material using accessible experimental
techniques. To test the methodology we derive a family of geometries that
result with anomalous mechanical behavior such as tunable, an-harmonic, and
even vanishing rigidities. The presented formalism can be discretized and thus
opens a new pathway for the design of both continuum and discrete solids and
structures.
