I was watching the flight patterns the other day and it occured to me that they only fly in straight lines. No curves at all. They just fly along straight, change direction, then continue on in another straight section until it is time to turn again. I know that at the intersections there is a small arc, but in general the fly always straight. It seems kind of odd to do that instead of a sort of a meandering, cruise.
I hope I described this clearly enough. What gives?
Flat…
Houseflies also fly in circles. Haven’t you ever seen them buzzing around a steaming heap of manure? They sure as heck don’t make repeated, straight path fly-bys, they circle it.
What you may be observing is a stimulus-response situation. In the absence of an attractor (i.e., corpse, excrement, garbage) they continue in a straight line to maximize their chance of encountering something.
Flies don’t live for very many days so they need to have sex and find a place to lay their eggs in a hurry.
Zenster
Yes I’ve seen them circling…but if you watch closely it’s a series of straight sections with quick direction changes inbetween. Really!
Flat…
there have been flies i’ve seen that fly in straight lines only.
I say one flying in squares… SQUARES!
I think Zenster has hit the nail on the head. Flies minimize energy expenditure until the sensory input says TURN! I know I have seen mayflies going back and forth over a stream looking for love. They always seem to be flying a foot long pattern back and forth. Probably sniffin’ out the action, but then again I am not a mayfly.
It says here that they fly in straight lines and squares.
I have observed this too; typically they will fly at about head-height in more or less the centre of the room, flying in a straight line for up to a metre (but most often less), then turning sharpy. If there is more than one fly there, they will occasionally encounter one another, then go into a sort of tight downward co-spiral.
Flies fly in straight line because the differential equations required to plot a parabolic flight path are too complex for their tiny brains. 
If the path is unobstructed a human***** will walk in a straight line to his/her destination. Why would you walk or drive in a circle, if you could go straight?
[ul]*
[sup]Unless he’s had too much to drink.[/sup][/ul]
The point is that the flies are not going from A to B, they are circling (except not in a circle) at the middle of the room for prolonged periods.
[ul]
[sup]That clears everything up.[/sup][/ul]
I’m no expert (no flies on me), but I think you’d find this behavior in most creatures. If you put a bunch of humans out in a field and told them to run, most would run straight lines. Sure we run in circles/ovals on a track, but that’s an external constraint. Left to our own devices, we tend to go in straight lines even when wandering aimlessly (e.g. nervous pacing).
Sometimes I feel like I’m flying in circles, but I’m really making progress. But other times I feel like I’m flying straight, but I’m really going in circles. Then, when I try to go in hexagons…
kniz What I mean is that rather than starting somewhere, travelling in a straight line and stopping at the end, like the unobstructed human in your post, these flies are making circuits continuously - they fly a foot or two, turn sharply, fly a foot or two, turn sharply, fly a foot or two… you get the idea. It isn’t that they are taking the shortest route on a journey from point A to point B; they aren’t actually on their way anywhere.
Also, flies have such little mass that they have no need to turn gradually.