Euclidean Distance

Name: - Aditya Narayanan

Roll Number: 14125

Group B (Operations Batch)

Today’ Business Analytics lecture looked Euclidean distance among the many topics. In mathematics, the Euclidean distance or Euclidean metric is the ordinary distance between two points that one would measure, and is given by the Pythagorean formula. The Euclidean distance between two points ‘p’ and ‘q’ is the length of the line segment connecting them.

In the Cartesian system of coordinates the Euclidian distance between two points ‘p’ and ‘q’ is given by the distance between its respective ‘x’ and ‘y’ coordinates. The formula for this calculation is represented by:

Distance (p, q) = Distance (q, p) = ((x1 - x2) ^2 + (y1 - y2) ^2) ^ (1/2)

The position of a point in a Euclidean n-space is a Euclidean vector. So, p and q are Euclidean vectors, starting from the origin of the space, and their tips indicate two points. The Euclidean norm, or Euclidean length, or magnitude of a vector measures the length of the vector.

|P| = (P1^2 + P2^2 + .....+ Pn^2) ^ (1/2)

The Euclidean distance between two points in multiple dimensions can be calculated by using the following formula.

One Dimension

Distance (p, q) = ((p – q) ^2) ^ (1/2)

Two Dimensions

Distance (p, q) = ((p1 - q1) ^2 + (p2 - q2) ^2) ^ (1/2)

N-Dimensions

Distance (p, q) = ((p1 - q1) ^2 + (p2 - q2) ^2 + (pn – qn) ^2) ^ (1/2)