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
Two-third rule Two-third rule Two-third rule is British railway safety rule. For safety reasons, speed limits are imposed on trains running on a railway line. Many factors can affect the speed limit of a particular line including the state of the track, the curvature of the track, the number of stations, the individual features of stations or junctions and the stopping distances of trains running on that track. On some lines in southern England, speed limits for passenger trains are higher than for freight trains, because the electric multiple units (EMUs) on those lines are capable of slowing down much more quickly