Originally posted by DOHC
2 blocks yes. A circle of radius 1 has diameter 2. The 2 block distance is equivalent to the diameter. The 8 block circumference is 4 times the diameter, hence pi=4.
Yes....a circle with centre 42nd St, 5th Ave consists of all points that can be reached exactly one block from there....41st St, 4th Ave is 2 blocks away, so outside your circle.
Originally posted by DOHC
...plus the streets and Avenues that connect those four points in the shortest possible way (=distance) between those points.
No, because half way from one point to the next point you are at a point that is further than one block away from the centre, hence outside your circle. That's like saying that I can measure the 'circumference/perimeter' of the M25 between the M11 and M1 junctions by driving up the M11, across the the M1 and then back down to the M25 again.
Originally posted by DOHC
Don't forget the streets/avenues that connect the four corners. That makes a square, whose perimeter is a continuous curve.
Again, the streets and avenues that connect them are not part of the circle, as they are more than one block away from the centre.
Originally posted by DOHC
But it applies to the square, which we are talking about here.
No it doesn't actually. A square is not rotationally symmetrical about every angle - think about it, if you rotate a square 5deg, it does not overlay the original square anymore. A sqare is also not reflectionally symmetrical about a line through its centre from a third of the way along one side to two thirds of the way along the opposite side.