Just an English language question from a non-native speaker. I know there are round public spaces whose names indicate that shape, such as Columbus Circle in Manhattan or Piccadilly Circus in London. But if I were to help someone who’s asking for directions, would I say something like “At that large circle over there, turn left”? Would sound odd, but so would “At that large round square over there, turn left”.
Just call it a plaza, or something.
I would call it a junction. Piccadilly circus isn’t an open square, more like a large traffic island where loads of roads intersect.
A genuinely open space would likely be called a park, I should think. Plaza would also work for a paved area.
It depends.
A ‘town square’ or ‘market square’ doesn’t have to square to get the name, and there’s no shortage of places called ‘*** square’ which aren’t in the least square, although they may have kept the name from a time when they were, before the layout changed.
On the other hand, I wouldn’t call a place just ‘the square’ without the rest of the name unless it was pretty much… well… square. For giving directions, there’s nothing wrong with your ‘large circle’ description, if it is indeed a circle. You could say circular plaza, I guess.
I would use the specific name of the public space (e.g. Sankofa Square, which is kind of trapezoidal) when giving directions. If I don’t know the name of the place, then they’re probably not going to be good directions no matter what I call it!
I might call it “the green” (as in “village green”).
It’ll have a local name; which may or may not include the word “square”, whatever shape it is. I’ll call it the name, which they’ll recognize if they’re local and will probably have on their maps if they don’t. If they’re not local, I’ll mention that it isn’t square if that’s in the name.
Madison Square Garden: not square, not a garden, and not on Madison Avenue.
The center of Indianapolis features a large Civil War monument on a circle. It is called, fittingly, Monument Circle. I probably wouldn’t tell people “turn left at the Circle”, I’d say “turn north/south/east/west at the Circle”. If they say they’re not good with directions, I might tell them to take the second exit or something.
Cleveland’s Public Square has been a square since 1796 (4 squares, actually). It was renovated in 2016 and is now more butterfly-shaped, but it is still called Public Square.
Ah but the original venue from the 1870s was in Madison Square. It’s been rebuilt 3x in other locations since and kept the name.
“What if there were a big street, like a broad way, that went in a diagonal?”
“Ooh, I love it, because it would leave all these random triangles!”
“Yes, but - we call the triangles ‘squares’!”
“Oh, like Times Square, Herald Square?”
From the SNL animated short on Planning New York - https://youtu.be/8PqowwECuUA?si=JC4vlAUBZrgYK5Bm
If a public space is round, it’s known as a “Tuit”.
Absolutely FALSE; a tuit is the chit you get in a bar when someone buys you a drink to be consumed after your current one; as in they buy the bar a round, everyone sitting there gets a tuit.
Aha.. Round tuit. Gotcha 
Always bothered me as a kid, until I stumbled across a magazine article about the history of MSG.
And to me, so would “at that large square over there, turn left” . I don’t think I’ve ever referenced a shape when giving directions. I might say to turn left at the intersection, the next block , at a particular street, at the park. I might say “Turn left a the (Name ) Square” if I think it’s going to be clear to the person I’m giving directions to - which it probably won’t be. Because none of the ones I can think of are actually square , They’re mostly bowties, or actually some are two separate triangles with different names and if I tell someone to turn at Greeley Square, they might actually turn at Duffy Square. And most of them don’t have signs around the perimeter.
Cincinnati has a handful of non-square squares. Hyde Park Square, Oakley Square, and Mt. Lookout Square are all lozenge shaped wide medians (people have used the term esplanade but it’s not exactly correct) that are wide enough to accommodate a small park, or parking in the case of Mt. Lookout. If you ignore the street/pavement layout and just look at the building/non-building figure/ground layout then they better fit the more typical conceptualization of a public square like you might see in Medieval European cities. Fountain Square downtown is a legit square, though it used to be a lozenge like the others.
All that said, if someone wasn’t familiar with Hyde Park Square, I wouldn’t just call it “that square” or “that round thing” unless maybe it was literally within view. I’d add some qualifiers.
Blue Rapids, Kansas, a tiny farming town (where my mother-in-law lives) in northeastern KS, is exceedingly proud of their round town square.
Home of the Round Town Square and the oldest Public Library in Kansas. We are the only Blue Rapids in America!
Not really, no. East 26th and Madison Avenue is about 900 feet northeast of Madison Square (and the venue itself was cattycorner to the park).