TITLE: Have I made a straight line, or a circle?
QUESTION [28 upvotes]: (Disclaimer: I'm an engineer)
Hi everybody, I found this “riddle” posted on the internet:

It's meant as a joke, but I do think it deserves an answer :)
A bit of background: the orange and blue ellipses are a citation from the videogame Portal. They are "portals" connected so that everything that goes into one of them comes out of the other, mantaining his momentum (this last part is the foundation for the game). For further info, you can also watch the trailer.
So.. is it a circle, a straight line or what else?
(also, feel free to retag)

REPLY [2 votes]: Is the equator of the Earth a line or a circle? 
Well, it's a circle of course. But as you know by now, from Willie Wong's answer and from others, it's also a geodesic, which is very much like a straight line: unless you are ready for some serious digging, the equator is the shortest path between any two places on it.
Your Portal picture is nothing like the Earth, mind you. But in my kitchen I have a cutting board that's a flat rectangle with a thin rectangular hole cut out near one side, as a handle for carrying. The corners are rounded somewhat. Now an ant walking along the top side, if it passed through the handle, would wind up on the bottom side with its momentum reflected. The same if it walked over an edge.
Imagine an orthographic projection of my cutting board. (By the way I'm also an engineer. I learned drafing the old-school way, with a T-square.) I draw a top view which is a rectangle with a thin vertical rectangular hole near the right side. To the right I place a side view which is just a vertical rectangle with a couple of hidden lines, the thickness of the cutting board. It's not normal "third-angle" to also draw the bottom view, but I will, so it is a rectange with a thin vertical rectangular hole near the left side.
An ant walking over the right edge would, on the drawing, pass from the top view to the side view to the bottom view with its momentum unchanged. (From a 2-D perspective, the edges are not actually special. The corners are another matter.) If it walked through the handle, it would pass from one rectangle on the top view through an "interspace" - hidden lines on the side view - to the other rectangle on the bottom view, again with its momentum again unchanged. Imagine if we tied a string through around the handle and the right edge of the cutting board. On the drawing, it would be a straight line between the two rectangles passing through the three views. 
So the area around the handle and right edge of my cutting board is very much like a 2-D version of Portal. 3-D Portal can then be thought of as being played on the hypersurface of a higher dimensional cutting board. (To visualise a higher dimensional cutting board, ponder an ordinary cutting board while enjoying a "herbal cigarette".)