In mathematics and the physical sciences, it is important to be able to compare the shapes or forms of objects. Just what do we mean by “shape”? What does it mean to say that an object has a “hole” in it? Is the hole in the center of a basketball the same as the hole in the center of a donut? Is it correct to say that a ruler and a sheet of paper have the same shape—both are, after all, rectangles? What is a rigorous and mathematical means of establishing that two objects are equivalent from the point of view of shape or form?