Swarm Intelligence

distance. If one point A in an n-dimensional space is defined by coordi-

nates (a

1

, a

2

, ... a

n

), and another, B, has coordinates (b

1

, b

2

, ... b

n

), then the

distance between the two points is (the useful formula, again)

Dab

AB i i

=−

∑

()

2

Distance is the square root of the sum of the squared differences be-

tween pairs of coordinates. In one dimension, the square root of the dif-

ference squared is just the difference itself, which seems like a reasonable

measure of distance. In two dimensions, it is the familiar Pythagorean

theorem, the length of the hypotenuse of a triangle, and in more dimen-

sions this conceptualization is known as the square root of ...