The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases: Newton-Cotes, Clenshaw-Curtis, Gauss-Legendre, and Gauss-Hermite quadrature. Three further examples are mentioned more briefly.

翻译：二次方程式的标准设计原则是,对于某一类的先辈,例如固定度的多面体,应该精确地使用该方程式。我们展示了这一原则如何未能预测四个案例的实际行为:牛顿-科特斯、克伦肖-科尔蒂斯、高斯-莱根德雷和高斯-赫米特二次体。我们更简要地提到了另外三个例子。