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 recognition if the rule of recognition were "what Professor X says is law", then any rule that Professor X spoke would be a valid legal rule. It follows that the rule of recognition is but a factual acknowledgement of what is indeed law; as per the classic illustration of a bill passed by the legislative authority and assented to by a Head-of-State. The fact that the bill has been made law in accordance with proper parliamentary procedure shall, in accordance with the Rule of Recognition, render it valid law. Again, this is primarily based on the fact of its existence in