What a great collection of ideas! (I just hope a fly or something doesn't get in with the object I'm teleporting...!)
I may be off base, but here's a different spin on the question if you're looking for a rationale to use in assembling the Square/Circle parts. And at least it's a Chinese yarn based in fact...
"You may have heard how opposites attract. The idea dates back to the Han Dynasty in China. They believed that the universe was ruled by two opposing forces. The masculine force is called 'yang.' It represents activity, light, and heat. By itself, it's not too impressive."
Here you'd show one of the pieces to be empty.
"The opposite force is feminine and called 'yin.' It represents passiveness, darkness, and cold. (This is probably why I married a brunette who won't leave the thermostat alone.) Again, it isn't much to look at."
Show the other piece to be empty.
"The interesting thing about the universe is that nothing at all would exist if yin and yang had never gotten together. (They probably met over the internet.) But when activity and passiveness combine, when light and dark coalesce, and when heat meets cold then...only then...do you have life and beauty and magic."
Just an idea. By the way, for decorating purposes, yin and yang aren't black and white. Yin was originally black all right but yang was originally red. I'm sure there are other "combination" plots that would make sense as well and give you a purpose for putting the square with the circle.