# 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: $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}$ </br>

> 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`.

using System;

namespace eucledian_distance
{
    class Program
    {
        static void Main(string[] args)
        {
            double x1, x2, y1, y2;
            x1 = 3;
            x2 = 4;
            y1 = 5;
            y2 = 2;
            var distance = Math.Sqrt((Math.Pow(x1 - x2, 2) + Math.Pow(y1 - y2, 2)));
            Console.WriteLine($"The Eucledian distance between the two points is: {Math.Round(distance, 4)}");
        }
    }
}

How to compute Euclidean distance in C# 

Euclidean distance is computed using the Pythagorean theorem for any n-dimensional space. Implementation uses the Math class in C#.