Linked from

The 63 pages that link to Pythagorean theorem, each with the reason it gives.

• Euclidean spaceRelated: Orthogonal displacement components combine by this rule to give squared distance.

• Euclidean distanceRelated: Repeated applications of this theorem yield the coordinate formula for distance.

• Equilateral triangleRelated: Splitting the triangle by an altitude gives a right triangle for deriving its height.

• Inner productRelated: Orthogonal vectors satisfy this length-addition law under an inner-product norm.

• Heron's formulaRelated: A perpendicular height and the triangle's sides form right triangles in a standard derivation.

• Right triangleRelated: It gives the defining length relationship among the triangle’s three sides.

• Square rootRelated: Finding a side length from the other two requires taking a square root.

• DistanceRelated: It yields the familiar distance formula by combining perpendicular coordinate differences.

• OrthogonalityRelated: Orthogonal vectors satisfy the same sum-of-squares relation for their lengths.

• TrigonometryRelated: It links the sine and cosine of an angle through their squared values.

• Unit circleRelated: For unit-circle coordinates, it yields cos² θ + sin² θ = 1.

• Orthogonal projectionRelated: Perpendicularity makes projection error split into a right-triangle distance identity.

• DisplacementRelated: For perpendicular components, it gives displacement magnitude.

• Euclidean normRelated: The norm formula extends this theorem from two perpendicular components to any number of coordinates.

• Isosceles triangleRelated: The altitude splits the triangle into right triangles whose side lengths can be calculated with this theorem.

• Power of a pointRelated: A perpendicular from the center to a secant derives the center-distance formula.

• Babylonian mathematicsRelated: Babylonian numerical problems include right-triangle relations centuries before Pythagoras.

• Perpendicular linesRelated: Perpendicular sides form the legs in the theorem's right-triangle applications.

• RectangleRelated: It gives a rectangle’s diagonal length from its side lengths.

• Inner product spaceRelated: Orthogonal vectors satisfy this identity through the inner-product norm.

• SquareRelated: Applied to a square’s diagonal, it gives the diagonal-to-side relation.

• Chinese mathematicsRelated: Chinese texts applied the right-triangle relation to surveying and geometric problems.

• Thales' theoremRelated: Thales' theorem identifies right triangles to which this relation applies.

• Euclidean planeRelated: It yields the distance formula for points in perpendicular coordinates.

• Right angleRelated: Its converse can establish that a triangle contains a right angle.

• Algebraic identityRelated: Its equation holds for every right triangle, linking geometric relations to algebraic equality.

• Complex modulusRelated: Applied to the real and imaginary coordinates, it gives the modulus formula.

• Distance formulaRelated: The distance formula applies this theorem to horizontal and vertical coordinate differences.

• Perfect squareRelated: Its integer solutions connect perfect squares through sums of two squares.

• The Nine Chapters on the Mathematical ArtRelated: The gougu chapter applies this relation to inaccessible lengths and right-triangle problems.

• Unit sphereRelated: Applied along three perpendicular axes, it gives the sphere's equation.

• Bessel's inequalityRelated: The inequality follows by applying this relation to a vector and its orthogonal projection.

• Fermat's theorem on sums of two squaresRelated: The same sum-of-squares expression appears, though the theorem concerns prime hypotenuses.

• Hippocrates of ChiosRelated: Right triangles provide the side-length relationships used in classic lune constructions.

• Sum of squaresRelated: Orthogonal fitted and residual components yield an analogous sum-of-squares decomposition.

• Van Aubel's theoremRelated: Length comparisons in geometric proofs often reduce to this relation.

• Nth rootRelated: Recovering a side length from the other two requires taking a square root.

• Pythagorean trigonometric identityRelated: Dividing this theorem by the hypotenuse squared yields the sine-cosine identity.

• Fermat's right triangle theoremRelated: It converts integer side lengths into the Diophantine equation underlying the proof.

• Square root of 2Related: A right triangle with unit legs has a hypotenuse of length square root of 2.

• Apollonius's theoremRelated: A perpendicular construction proves the median relation by applying this identity twice.

• Brahmagupta–Fibonacci identityRelated: The identity combines the square-coordinate structure underlying right-triangle integer solutions.

• British flag theoremRelated: Each squared distance in the theorem follows from this relation.

• Geometric mean theoremRelated: It gives an algebraic route to the same altitude relation using the smaller right triangles.

• De Gua's theoremRelated: De Gua's theorem extends this sum-of-squares pattern from lengths to face areas.

• Erdős–Anning theoremRelated: Its integer solutions give familiar finite configurations with integer distances.

• Inverse Pythagorean theoremRelated: Its side-length equation becomes a test for whether a triangle has a right angle.