Why aren't our squares square, and other questions from a fruitless trip across the river

I've been asking that question since I moved to New England

...Powderhouse Square which is round, and Ball Square, named for a round object, but shaped like a bunch of randomly intersecting streets.

They stop right on Mass. Ave, between the Central Square T station and Foot Locker. The stop is not hard to find, and I think it's well marked.

The term square has long referred to a geographical feature in cities and towns and not necessarily one that is square-shaped. According to the OED, the term has been in use since 1680 and is defined:

An open space or area (approximately quadrilateral and rectangular) in a town or city, enclosed by buildings or dwelling-houses, esp. of a superior or residential kind, freq. containing a garden or laid out with trees, etc.; more generally, any open space resembling this, esp. one formed at the meeting or intersection of streets; (also) the group of houses surrounding an area of this kind. (emphasis mine)

And it's not just New England. London, where the term was first used, has Trafalgar Square and Leicester Square, neither of which is square shaped. Closer to home New York has Times Square and Herald Square for starters, both of which are triangular.

On the first page, Felber describes our area's roads:

Boston’s roads were never meant to be urban thoroughfares — they intersect at odd, often precipitous angles, with frequently interesting results from an urban-design standpoint. Often, three or four roads will intersect in more or less the same place.

When this happened in an area unburdened with history, landmarks, or valuable real estate, the twentieth-century Bostonians created enormous disks of pavement where the roads collided, which they called “rotaries”...

However, when many roads intersect in places that are historic, landmark-laden, or filled with valuable real estate (a set of conditions that can be best described as “almost everywhere”), the planners and pavers of Boston opted to create Squares. From a design standpoint, this roughly means, “Do nothing and name the place after the principal reason why we can’t have a rotary here.”