I think it's a really good demonstration of how harmony can be made without any of the normal major/minor chords.

Hey, if you have a square with integer coordinates of (0,0) and (1,1): Does it have a width of 1 or 2?

You're gonna have to elaborate on that.

like, does it include all of the sub-squares at (0,0), (0,1), (1,0) and (1,1), or just the subsquare (0,0)?

with real coordinates, its obvious, but not with integer coordinates

I personally think that it should have width of 1, but people are arguing that (1,1) should be inclusive

Would an integer point then have width 1 rather than 0?

the square from 0,0 to 0,0 would have width 1, yeah

I suppose it makes some sort of sense if you think of [] (no integers) as having width 0, and [5] (one integer) as having width 1. Then in 2D it would make corresponding sense

But that's for lists of consecutive integers, not lines (or squares). I can't see how the width of a shape can be 1 if it has no interior

Although I suppose as long as it is defined unambiguously at the start of whatever you're doing, it doesn't matter too much

well, I've already implemented it the width=1 way

I've just gotten feedback that the endpoints should be inclusive, so I was bouncing it off of you guys

What's the context?

starting there :)

ok, another related question: does the square from (0,0) to (1,1) include the point at (1,1)?

I don't think there's a right or wrong answer here... if you're talking about geometry there's the concept of open vs closed disk.

right, but intuitively, what would you think?

if you didn't know how the implementation worked, which way would you guess it to work?

Intuitively I'd say yes... but more in the context of programming it would also make sense if the answer is no, that the square includes its lower edges (x=0 and y=0) but excludes its upper edges (x=1 and y=1).

@NathanMerrill: If we're talking about a game board here with discrete square cells, then I think it makes sense to say that the square from (0,0) to (1,1) has four cells altogether since there's a cell centered on each of (0,0), (0,1), (1,0), (1,1). I feel like that's the most intuitive and satisfactory, and that does mean you'll probably have to adjust your code/definitions a bit so that outer boundaries are inclusive.

Another thing that might be throwing you/others off is starting at 0. A chess board goes from (1,1) to (8,8), just in different notation (a1 to h8).

That's neat.