ABSTRACT
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 the concept of “shape”? What does it mean to say that an object has a “hole” in it (certainly having a hole is part of the concept of shape)? And 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 both 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?
