The curve of the bent wafer will be the one which minimizes integral curvature(s)^2 * width(s) ds i.e. total elastic energy. Here s is arclength along curve. This is subject to the constraint that the 2 endpoints of the curve must lie some fixed distance apart. I think an effectively equivalent constraint is that integral curvature(s) ds = fixed constant. You can now write down Euler-Lagrange equation, solve it, etc. to find the shape of the bending curve. The location of breakage will be the point where |curvature| is maximized. The "optimum design" width(s) curve will be one which uniformizes curvature, therefore, and will be simply width=constant, i.e. a strip; then the bending curve will be an arc of a circle. [ http://people.csail.mit.edu/bkph/AIM/AIM-612-OCR.pdf considers a curve with given endpoints and orientations there, and variable arclength. Not the problem we want. ] Re the claim spaghetti always breaks into 3 pieces, this seems inexplicable with above model. So need a better model. I think it must have to do with some kind of "nonlinear and/or time-dependent elasticity" property of spaghetti. i.e. crack formation. (Above model had been linear, i.e. energy is integral of quadratic.) Possibly dynamical effects involved too. Suggest seeking insight via a high speed video camera.