Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Rule of Saint Francis Rule of Saint Francis As known, Saint Francis founded three orders and gave each of them a special rule. Here, only the rule of the first order is to be considered, i.e., that of the Order of Friars Minor. There are, as in so many other points in the life of St. Francis, not a small amount of doubt and controversy about the Rule of St. Francis. Whether St. Francis wrote several rules or one rule only, with several versions, whether he received it directly from heaven through revelations, or whether it was the fruit of his long experiences, whether