  We propose a curvature-based approach for choosing good values for the
time-delay parameter $\tau$ in delay reconstructions. The idea is based on the
effects of the delay on the geometry of the reconstructions. If the delay is
chosen too small, the reconstructed dynamics are flattened along the main
diagonal of the embedding space; too-large delays, on the other hand, can
overfold the dynamics. Calculating the curvature of a two-dimensional delay
reconstruction is an effective way to identify these extremes and to find a
middle ground between them: both the sharp reversals at the ends of an
insufficiently unfolded reconstruction and the folds in an overfolded one
create spikes in the curvature. We operationalize this observation by computing
the mean over the Menger curvature of 2D reconstructions for different time
delays. We show that the mean of these values gives an effective heuristic for
choosing the time delay. In addition, we show that this curvature-based
heuristic is useful even in cases where the customary approach, which uses
average mutual information, fails --- e.g., noisy or filtered data.
