Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian
packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is
folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical
frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and
the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically
deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and
oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with
oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is
corroborated by numerical simulations that allow us to generalize our analysis to study structures with
multiple curved creases.