Is there a single word that describes starting out and moving in some direction(s) but eventually ending up right back where you started?

Retrace

Holiday.

Revert?

Boomerang effect?

Circumnavigation?

come full circle (3 words, closest I can get)
retreat

Fool’s journey?
busman’s holiday?

Circular

Come full circle. Some one has already mentioned this and it is the thing I can come up with.

“must not imply wandering aimlessly”

Hmm… sorry, I misread that as must imply wandering aimlessly.

Round trip

neandering?

Loopback
Deja vu

Hmmm. Thank you all for your contributions.

I like “loopback” best, but it’s still not quite what I’m looking for. Maybe it doesn’t exist.

Here’s some background. I was just thinking the other day about a concept from elementary college physics (though that was many decades ago, so I don’t know if I remember correctly) that “work” is defined as a force applied over a distance. But when you take into account the directions (vectors), if you return to your starting point, the sum is zero. I wondered if there is a single to describe all of this.

I’ve thought of “zero-sum”, but that seems to be a concept out of game theory, where “my gain is equal to your loss”, which in turn is related to “there is no free lunch” in economics.

I’m trying to neatly summarize in a single word a series of dance movements, the end result of which is you wind up where you started.

Perhaps a phrase is required and there is no single word?

@2davidc8 Knowing how the world of dance loves its terminology, you’d think that would be easy! But I can’t seem to find a word or phrase for a return to the initial position.

@dappled_leaves Yes, I just thought that it would be useful know that if you performed, say, movements A, B, C, D, and E, you would be back at your starting position. So the “sum” of all those movements is zero, as it were.

@2davidc8 Being a physics person, I can totally understand wanting to make a vector sum analogy, but perhaps the intended audience would not appreciate it as much. ;)

What about cycle back? The idea of cycles, as in lifecycle or succession of the seasons, is an historically powerful concept and has many artistic depictions. The dance does not end. It is just completing a cycle.

@LostInParadise I like your idea of cycle, except that I do want to imply that there is necessarily any kind of circular movement. Thank you for your input.

Cycling: “going someplace(s) and then returning exactly where you started.”

Cycled: “gone somewhere and returned exactly where you started from.”

I’d go with something like “treadmilling”. Even if it’s not a word… yet.

Quixotic journey?

Or revert?

You want to look at dance terminology—in ballet, there is a French term for returning to the original position. I used to have a ballet terminology book but have no idea where it is now.

@Bill1939 Wow, I didn’t know that! Now I like “cycle” best.

Thank you all for your suggestions!

Nice! A piston cycles in an engine. E.g. Most cars have 4-cycle engines. Some motorcycles have 2-cycle engines.

Retrogress.