This Demonstration illustrates deformations of the plot of
in the complex plane. The real and imaginary contours of the cosine form a conformal grid and are locally homeomorphic to the two-dimensional Euclidean grid. The magenta contours show linearly spaced values of the real variable
, a family of hyperbolas. The blue contours show confocal ellipses corresponding to linearly spaced values of
. The left panel plots the contours of the cosine function, while the right panel plots
, which is an adaptation of Euler's formula. With distinct values of
, you can create hinge-like folds at the focal points. If the coefficients
are equal with integers
, the folding process yields multiple perfectly aligned sheets.