With the usual L2-norm for computing distances and angles we use pi for measuring angles, pi = 180 degrees implies the opposite direction, and pi/2=90 degrees is used to express independence. Here the importance of pi is related to the importance of independence, in particular we are considering linear independence. Curiously, the most famous statistical distribution, the normal distribution, satisfies that two normal that are linearly independent are in fact independent. Bayes Theorem for independent events reduce to product of probabilities. In many contexts independence is related to a cartesian product. In topology, the generalization of a product is a fiber bundle. Pi number perhaps appears in context where linear independence and products are good approximation. Also linear independence allow us to apply the generalized Pythagorean theorem in R^n, for example it gives a way to measure the goodness of fit of linear models. So in many contexts pi is related to independence and product that are the easy concepts of dependence and curvature and non linearity.