Linked from

The 44 pages that link to Euclidean distance, each with the reason it gives.

• Pythagorean theoremRelated: The theorem derives this distance formula by applying the right-triangle relation to coordinate differences.

• Metric spaceRelated: It is the standard geometric metric and a familiar model for the axioms.

• Arc lengthRelated: Each short segment in a curve-length approximation uses this distance.

• Principal component analysisRelated: Ordinary PCA preserves Euclidean geometry in the retained subspace by minimizing squared reconstruction error.

• Right triangleRelated: In a plane, horizontal and vertical coordinate differences are legs of a right triangle.

• Rigid bodyRelated: Fixed pairwise Euclidean distances define the ideal body's rigidity.

• Square rootRelated: The distance formula takes the square root of a sum of squared differences.

• Congruence (geometry)Related: Preservation of Euclidean distances ensures corresponding points remain equally far apart.

• Unit circleRelated: Every point on the unit circle is exactly one unit from its center.

• Color differenceRelated: The simplest color-difference calculation treats color-space coordinates as points and measures their distance.

• DiameterRelated: The diameter is the greatest distance between any two points of a circle.

• Polar coordinate systemRelated: The radial coordinate measures distance from the origin.

• Euclidean planeRelated: It supplies the plane’s standard notion of how far apart two points are.

• Focus (geometry)Related: Distances from a focus determine which points belong to a conic.

• Radical axisRelated: Circle power is computed from the distance between a point and the circle’s center.

• Parallelogram lawRelated: The vector difference in the identity has length equal to the distance between its endpoints.

• Rotation (geometry)Related: A rotation preserves the distance between every pair of points.

• Unit sphereRelated: The defining condition selects points whose Euclidean distance from the origin equals one.

• Euclidean vectorRelated: Subtracting position vectors turns geometric separation into a vector length.

• Kirszbraun theoremRelated: Finite-dimensional Euclidean spaces are the classical setting of the theorem.

• Stewart's theoremRelated: Every length in Stewart’s theorem is a Euclidean distance.

• Square root of 2Related: The distance between (0, 0) and (1, 1) is square root of 2.

• Apollonius's theoremRelated: The theorem can be derived by expressing each side and the median as distances between points.

• Finsler–Hadwiger theoremRelated: Equal Euclidean lengths establish the sides of the resulting square.

• Barrow's inequalityRelated: The vertex terms are ordinary straight-line distances in the plane.

• MarginRelated: A geometric margin may use this distance from an example to a boundary.

• Two-dimensional spaceRelated: It measures separation between points in a flat two-dimensional plane.