How to compute Euclidean distance in C#

Definition

The Euclidean distance, in any n-dimensional plane, is the length of a line segment connecting the two points.

Formula

The Pythagorean Theorem can be used to calculate the distance between two points, as shown in the figure below. If the points $(x_1,y_1)$ and $(x_2,y_2)$ are in 2-dimensional space, then the Euclidean distance between them, represented by d, is: $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

In higher dimensions

Similarly, if the points are in a 3-dimensional space, the Euclidean distance will be represented by: $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}$

In general, for two points p and q given by Cartesian coordinates in an n-dimensional space, p is represented by $(p_1,p_2, ..., p_n)$, q is represented by $(q_1, q_2,...,q_n)$, and the Euclidean distance is: $\sqrt{(p_1-q_1)^{2}+(p_2-q_2)^{2}+(p_3-q_3)^{2}+....+(p_n-q_n)^{2}}$

Implementation in C#

For reference, below is the implementation of Euclidian distance calculation in C#, using the Math class to take the square and square-root.