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2. Rigid transformation - Wikipedia

   en.wikipedia.org/wiki/Rigid_transformation

   In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. [1] [self-published source] [2] [3] The rigid transformations include rotations, translations, reflections, or any sequence of ...

3. Dehn plane - Wikipedia

   en.wikipedia.org/wiki/Dehn_plane

   Hence, if the model is restricted to the finite part of the plane (points (x,y) with x and y finite), a geometry is obtained in which the parallel postulate fails but the sum of the angles of a triangle is π. This is Dehn's semi-Euclidean geometry. It is discussed in Rucker (1982, pp. 91–2).

4. Motion (geometry) - Wikipedia

   en.wikipedia.org/wiki/Motion_(geometry)

   For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. [1] More generally, the term motion is a synonym for surjective isometry in metric geometry, [2] including elliptic geometry and hyperbolic geometry.

5. Category:Euclidean geometry - Wikipedia

   en.wikipedia.org/wiki/Category:Euclidean_geometry

   Print/export Download as PDF; Printable version; ... Pages in category "Euclidean geometry" The following 103 pages are in this category, out of 103 total. ...

6. Hinge theorem - Wikipedia

   en.wikipedia.org/wiki/Hinge_theorem

   The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...

7. Euclidean geometry - Wikipedia

   en.wikipedia.org/wiki/Euclidean_geometry

   Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions ( theorems ) from these.