Why chalks typically break into three pieces when dropped from a sufficient height? Why spaghetti also break into more than two pieces, typically three? I read some papers, but those only made me more confused.
Here is another point of view: When a chalk is dropped to ground, only one end touches the ground, and this end instantly receives a forces, exerted by the ground, and consequently longitudinal and bending stress waves (I assume they travel at the same speed) is spreading along the chalk. The speed of the elastic wave is estimated to be around 3km/s. If we solve the wave equation for the displacement of a point on the chalk from its equilibrium position, plus the boundary conditions, we find that if we plot it, it looks like a sine function in one period, but with the other end flat out. This is so because the boundary conditions, one end is fixed, and the other end is (stress) free. Therefore we see that along the chalk there should be two points that have maximum displacement, which correspond to locations the chalk breaks. The first is slightly less 1/3 along the length of the chalk, and the second is slightly less than 2/3. The numerical values of these locations can easily obtained, and be compared to experimental results. The cross-sections of the breaking pieces should also tell a lot of details about the nature of the force. Combined all these things together, we should be able to derive a reasonably good theory of it. The case with spaghetti is similar. Anyway, more insightful experiments are needed to clarify the situation.