What are surfaces and membranes ?

Surfaces are everywhere: the computer screen in front of you has a smooth surface; we walk on the surface of the earth; and people have even walked on the surface of the moon.

By surface we mean something 2 dimensional (*). Clearly objects like a coffee cup or a pencil are 3 dimensional but their edges - their surfaces - are 2 dimensional. We can put this another way by seeing that the surface has no thickness - it is just the places where the coffee cup ends and the air or coffee begins.

Surfaces can be flat, like a table top, or curved like the surface of a football, a balloon or a soap bubble. The surface of water can be either flat without ripples, or curved when it has ripples or waves on it.

We use the word membrane to mean a sheet-like 2 dimensional object, an object with area but very little or no thickness. Good examples are sheets of paper or a piece of plastic food wrap. Just like surfaces, membranes can be flat or curved; rough or smooth.