Fold over itself' and 'the boundary of the paper'?

Question

I'm having trouble comprehending a problem statement (I'm assuming that the problem statement is clear). The first two sentences I can understand (I've added them for context) but the 3rd is giving me problems.> You would like to mail some origami you have made to your mom.> > The price of mailing is dependent on the area of the envelope used to> mail it: the smaller the envelope area, the less cost to ship. You> cannot fold the origami shape to make it smaller. Of course, the> envelope you are shipping the origami in must be rectangular.> > Consider the vertices which represent the points along the boundary of> the paper in order, such that the edge of the paper may fold over> itself. Given the vertices describing the origami shape, what is the> area of the smallest envelope that you can use to mail the origami?I'm confused as to what means for the 'edge of the paper to fold over itself' and what is meant by 'the boundary of the paper'. I assume that fold over itself means to connect two opposite edges of paper and that along the boundary of the paper means along the edges of the paper but I still don't understand the sentence.

Answer 1

This is a toughie. I think what they're trying to get you to think about all the different ways you can fold the corners versus the sides of the paper. For instance, whether to connect the corners to each other or to fold edge-to-edge. I agree the wording is pretty opaque, but I also assume people writing math problems don't necessarily know all the right terms to describe the art of origami! Of course a mathematician wouldn't say "corners" of paper but instead "vertices"; they've probably never done origami before in real life, since this is a conceptual geometry question. Let me know if that was helpful, and best of luck!

-Elk