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
Emery's rule Emery's rule In 1909, the entomologist Carlo Emery noted that social parasites among insects (e.g., kleptoparasites) tend to be parasites of species or generation to which they are closely related. Over time, this pattern has been recognized in many additional cases, and generalized to what is now known as Emery's rule. The pattern is best known for various taxa of Hymenoptera. For example, the social wasp "Dolichovespula adulterina "parasitizes other members of its genus such as "Dolichovespula norwegica "and "Dolichovespula arenaria." Emery's rule is also applicable to members of other kingdoms such as fungi, red algae, and mistletoe. The significance