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Klein's line or the line of Klein is a virtual line that can be drawn on an X-ray of an adolescent's hip parallel to the anatomically upper edge of the femoral neck.It was the first tool to aid in the early diagnosis of a slipped capital femoral epiphysis (SCFE), which if treated late or left untreated leads to crippling arthritis, leg length discrepancy and lost range of motion.
Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection. In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit ...
V is the symmetry group of this cross: flipping it horizontally (a) or vertically (b) or both (ab) leaves it unchanged.A quarter-turn changes it. In two dimensions, the Klein four-group is the symmetry group of a rhombus and of rectangles that are not squares, the four elements being the identity, the vertical reflection, the horizontal reflection, and a 180° rotation.
A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.
In that 5-space, the points that represent each line in S lie on a quadric, Q known as the Klein quadric. If the underlying vector space of S is the 4-dimensional vector space V, then T has as the underlying vector space the 6-dimensional exterior square Λ 2 V of V. The line coordinates obtained this way are known as Plücker coordinates.
A Klein geometry is a pair (G, H) where G is a Lie group and H is a closed Lie subgroup of G such that the (left) coset space G/H is connected. The group G is called the principal group of the geometry and G / H is called the space of the geometry (or, by an abuse of terminology, simply the Klein geometry ).
The Cayley–Klein metrics provided working models of hyperbolic and elliptic metric geometries, as well as Euclidean geometry. Klein is responsible for the terms "hyperbolic" and "elliptic" (in his system he called Euclidean geometry parabolic, a term that generally fell out of use [16]). His influence has led to the current usage of the term ...
In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by Clebsch (1871) and Klein (1873), all of whose 27 exceptional lines can be defined over the real numbers. The term Klein's icosahedral surface can refer to either this surface or its blowup at the 10 Eckardt points.