Simpson and His Donkey

"Simpson and His Donkey" is a humorous mathematical story illustrating how different methods of approximating an integral can yield varying results. Simpson’s Rule uses a quadratic polynomial to estimate the area under a curve, providing accurate results for smooth functions. The story shows that applying Simpson’s Rule to a function or a similar shape (like a donkey) can produce different estimates depending on the method's setup. It highlights the importance of choosing appropriate approximation techniques in calculus and how assumptions in these methods affect accuracy, emphasizing the need for understanding the context and limitations of numerical integration.