An offbeat geometry question

[Korintar]

I was working with a student the other day and he asked an interesting question which has perplexed me. One of the problems involved a square inside another square- in effect, creating a hole in the larger, shaded in, square. What this student wanted to know was what is the technical term the shape formed by the shaded area. My best guess was a fractal- but that clearly was not right, and he did not think it could possibly be a concave polygon, but we agreed it was a polygon. To the mathematicians of NSG, what are your thoughts?

[Mike the Progressive]

42

[The Corparation]

42

6 x 7

[Korintar]

42

Seriously, guys

The equations for area and perimeter (my best guess) are as follows:

A=S₁²-S₂²

P=4S₁+4S₂

Where A is the area of the shaded region, P is perimeter, S₁ is the length of the side of the outer square and S₂ being the side length of the inner square.

[Buffett and Colbert]

I don't see how that'd be concave...

[Vetalia]

Wouldn't it be a...square? As far as I know, any square ever drawn in the history of geometry is in theory contained within a larger square, ad infinitum.

For the larger square containing it, I believe it would be a polygon. Nothing suggests otherwise.

[Risottia]

I would call it a square annulus, in analogy with the (circular) annulus.

[The Corparation]

A sqaure picture frame?

[Korintar]

I would call it a square annulus, in analogy with the (circular) annulus.

Thanks, the kid I'm working with asks some very interesting questions sometimes, and sometimes they are beyond my understanding or about things that I haven't thought about that deeply.