Euclidean Distance

Euclidean distance finds the distance between two points in multidimensional space, which is the kind of distance you measure with a ruler. If the points are written as (p₁, p₂, p₃, p₄, ...) and (q₁, q₂, q₃, q₄, ...), then the formula for Euclidean distance can be expressed as shown in Figure B-1.

A clear implementation of this formula is shown here:

def euclidean(p,q):
  sumSq=0.0

  # add up the squared differences
  for i in range(len(p)):
    sumSq+=(p[i]-q[i])**2

  # take the square root
  return (sumSq**0.5)

Euclidean distance is used in several places in this book to determine how similar two items are.