Euclidean Distance

In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.

Distance formulasCopy Anchor Link

One dimensionCopy Anchor Link

The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates

Two dimensionsCopy Anchor Link

Higher dimensionsCopy Anchor Link

In three dimensions, for points given by their Cartesian coordinates, the distance is

Example: the distance between the two points (8,2,6) and (3,5,7):

In general, for points given by Cartesian coordinates in n-dimensional Euclidean space, the distance is

CodeCopy Anchor Link

/**
 * @typedef {import('../matrix/Matrix.js').Matrix} Matrix
 */

import * as mtrx from '../matrix/Matrix';

/**
 * Calculates the euclidean distance between 2 matrices.
 *
 * @param {Matrix} a
 * @param {Matrix} b
 * @returns {number}
 * @trows {Error}
 */
const euclideanDistance = (a, b) => {
  mtrx.validateSameShape(a, b);

  let squaresTotal = 0;

  mtrx.walk(a, (indices, aCellValue) => {
    const bCellValue = mtrx.getCellAtIndex(b, indices);
    squaresTotal += (aCellValue - bCellValue) ** 2;
  });

  return Number(Math.sqrt(squaresTotal).toFixed(2));
};

export default euclideanDistance;

ReferencesCopy Anchor Link

• Euclidean Distance on MathIsFun
• Euclidean Distance on Wikipedia