Philip Mallinson introduced me to the geometry of salt piles at the 2015 Anja S. Greer Conference on Mathematics and Technology at Phillips Exeter Academy.

Predicting the shape of the ridge they will get prior to experimental verification. Students refined their model of ridge formation with each experiment.

For this polygonal card stock, the ridge appears to be a union of straight line segments.

Is the ridge circular in shape? Or is it an ellipse? Perhaps it is not even a conic section?

Given the shape of a card stock, is there a way to use geometry to predict the shape of the ridge we get by pouring salt?