Compactness measure of a shape

Imagine you have a bunch of shapes like squares, circles, and triangles. When we talk about the compactness measure of a shape, we want to know how squished or spread out the shape is.

For example, a circle is a very compact shape because it is perfectly symmetrical and all the points on the edge are at the same distance from the center. In contrast, a long and skinny rectangle would be less compact because it looks stretched out and doesn't have the same symmetry as a circle.

To measure compactness, we usually look at the ratio of an object's perimeter (the distance around the outside edge) to its area (the space inside the edge). The smaller this ratio is, the more compact the shape is.

So basically, a high compactness measure means the shape is more squished and symmetrical, while a low compactness measure means the shape is more spread out and asymmetrical.