Adjacent Rectangles intersect.
If we have two rectangles, r1 and r2, such that
r1 = new Rectangle(60,60,20,20); r2 = new Rectangle(80,60,20,20);
r1.intersects(r2) returns true; r2.intersects(r1) also returns true.
This doesn't seem quite right to me.
Comments (2)

Zolomon 
Adam Badawy No, you're entirely incorrect. When I create a new rectangle, the constructor parameters are xposition, yposition, width, and height. If I make a rectangle like so:
Rectangle r1 = new Rectangle(0,0,20,16);
This means that the rectangle will occupy all positions from x = 0 to x = 19 (20 pixels, the width) and y = 0 to y = 15 (16 pixels, the height).
Furthermore, if my game is tiled 20x20, my walls should have a width and height of 20 without intersecting each other.
Can you point me to what graphics library has this illogical practice?
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Well, they are intersecting!
If the second rectangle would be place at (81, 60) then they wouldn't intersect.
60+20 = 80, which means that they intersect. You need to add +1 to x position of the second triangle, or 1 to the width of the first, for them not to intersect. This is common practice through all graphics libraries.