Revision #368 → #1198 · back to history
addedEuclidean space (informal)08ba543e364a
addedUniqueness up to isomorphism89c088a49be9
addedEuclidean vector space1746619ee855
addedEuclidean space (affine)ebb4490a020b
addedDimension of a Euclidean space7e69365f1395
addedPoints and Euclidean vectors6ddf64025086
addedTranslation action on a point0a7e279f7c42
addedUnique displacement vectora3b55a8bb373
addedVector space as Euclidean space1f8676259c82
addedStandard Euclidean spacefe2f0367d96d
addedIsomorphism from a Euclidean framec7f2f339099d
addedFlat / Euclidean subspace7b1c980c41c3
addedDirection of a subspaced5d194d5ebfd
addedSubspace through a point with given direction7377628a2757
addedLinear vs Euclidean subspacesb85652f78e82
addedLine in Euclidean space759542abec3e
addedLine through two points0a27977990e0
addedLine segment778f70710724
addedParallel subspaces (same dimension)befe350f7b48
addedPlayfair's axiom4e37e21c8a7e
addedTwo lines in a plane meet or are parallelf58f7f0c56e4
addedParallel subspaces (different dimension)db9a4ffa468e
addedInner product / dot product notation42386f455257
addedEuclidean norm34855a9729e3
addedEuclidean distance00b609169f4e
addedLength of a segment6e1757a1196e
addedTriangle inequality593ed4314ab7
addedEquality case of triangle inequality08bbfe59818d
addedEuclidean space is complete7794488bb1ef
addedOrthogonal vectors3b57ff65009f
addedOrthogonal subspacesda510ed0d611
addedOrthogonal Euclidean subspaces / perpendicular lines5a3e8a25ec37
addedPerpendicular segments / right anglea5c9e48ed7b7
addedPythagorean theoremc2d4391d338b
addedAngle between two vectors237aa1224f3f
addedAngle is well defined via Cauchy–Schwarzac2174598a59
addedOriented angle in the plane5e27a8212653
addedAngle invariant under positive scalingf419fd4ffa8a
addedAngle of segments / half-linesf355f68067a9
addedAngle of two lines5af39bfd35ba
addedExistence of orthonormal basis / Gram–Schmidtc41a2a194f27
addedCartesian frame1ee1515e7002
addedCartesian coordinates of a vectorb5564837a01c
addedCartesian coordinates of a point35eb494787f9
addedAffine / skew coordinates8d714073842f
addedAffine basis and barycentric coordinatesd965036a9c8b
addedCoordinates via homeomorphisme40992068410
addedIsometry between metric spaces6bb26b88baad
addedOrigin-preserving isometry preserves norm and inner product1050b0358443
addedIsometry of Euclidean vector spaces is linearb7327da95a18
addedIsometric Euclidean spaces have same dimension9779d79169f0
addedIsometry maps subspaces to subspaces081e087f1ee9
addedCanonical isometry from origin choiceb2de15e63622
addedIsometry via Euclidean frame6e2fe31a5fd6
addedUnique Euclidean space of each dimension up to isomorphismd76829e398a7
addedEuclidean group505a30ea1a61
addedTranslations form a normal subgroupdfa469db3caf
addedAssociated linear isometry of an isometry48a623df0d5b
addedHomomorphism onto orthogonal groupbbe3a4acf4df
addedStabilizer isomorphic to orthogonal groupf8e72f595cf6
addedEuclidean group as semidirect producte6cf1878a824
addedSpecial Euclidean group / displacements5cc9e61f64e8
addedReflectionsc6cc452415eb
addedNon-motion equals reflection times motionc9c31bba48df
addedEuclidean topologyd47b0d5c98f6
addedOpen sets via open ballsdc4d2c3c8c11
addedTopological dimension equals dimension67f55a7fbf94
addedInvariance of domaine22b783e5f11
addedHeine–Borel: closed and bounded is compact05cd5c5a41e7
addedEquivalence of axiomatic definitions (Artin)ad85ed0df24a
addedPseudo-Euclidean space4b867176565a
addedMinkowski spacec8625ef3c9c1