Euclidean distance, in fact, is the application of the Pythagorean theorem to calculate the distance between two points is a straight line
Two-dimensional space of the formula
among them,
Point 
to point 
Euclidean distance between; 
point to the origin of the Euclidean distance.
Formula three-dimensional space
Formula n-dimensional space
Manhattan distance is absolutely represent two points on the standard wheelbase of the coordinate system and:
Representative Manhattan distance in the red, green represents the Euclidean distance , i.e. the linear distance , and the blue and yellow for equivalent Manhattan distance. Manhattan distance - the distance between two points in the north-south direction plus the distance in the east-west direction, i.e., d (i, j) = | xi-xj | + | yi-yj |.