Why Chalk Breaks into Three Pieces When Dropped

It has been the author's experience over many years, no doubt shared by others, that a stick of chalk usually breaks into three pieces when accidentally dropped onto the floor. I rarely gave it any thought, apart from noting that the fundamental mode of vibration of a freely supported, rigid rod has two nodes at an equal distance from each end. For example, a baseball bat has a node in the barrel (the sweet spot) about 15 cm from the end and another node in the handle. However, chalk is not expected to break at the node points, since maximum stress arises at the antinode in the middle of the chalk where bending is a maximum. Richard Feynman described a similar problem with long sticks of spaghetti.¹ He found that they always break into three or more pieces when bent slowly beyond their breaking point, rather than simply breaking in half. He was unable to figure out why, although the problem was solved many years later² and is nicely illustrated by Vollmer and Mollmann.³