Definition, Betydelse & Anagram | Engelska ordet ISOMETRY

Definition av ISOMETRY

1. (matematik) isometri

Exempel på hur man kan använda ISOMETRY i en mening

• However, any Lipschitz map between metric spaces is uniformly continuous, in particular any isometry (distance-preserving map).
• More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.
• As a linear transformation, an orthogonal matrix preserves the inner product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation, reflection or rotoreflection.
• The most common version uses the concept of "equidecomposability" of polygons: two polygons are equidecomposable if they can be split into finitely many triangles that only differ by some isometry (in fact only by a combination of a translation and a rotation).
• The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime.
• An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of −1.
• In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
• Thus isometry is simply bending and twisting of a surface without internal crumpling or tearing, in other words without extra tension, compression, or shear.
• Charnia is an extinct genus of frond-like lifeforms belonging to the Ediacaran biota with segmented, leaf-like ridges branching alternately to the right and left from a zig-zag medial suture (thus exhibiting glide reflection, or opposite isometry).
• In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
• A special case of this is when the group G in question is the automorphism group of the space X – here "automorphism group" can mean isometry group, diffeomorphism group, or homeomorphism group.
• Frieze groups and wallpaper groups are discrete subgroups of the isometry group of the Euclidean plane.
• Additionally, both Catalan solids rhombic dodecahedron and rhombic triacontahedron are edge-transitive, meaning there is an isometry between any two edges preserving the symmetry of the whole.
• In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold.
• The polar decomposition for matrices generalizes as follows: if A is a bounded linear operator then there is a unique factorization of A as a product A = UP where U is a partial isometry, P is a non-negative self-adjoint operator and the initial space of U is the closure of the range of P.
• This case is potentially physically interesting in the case that the shape of the universe is a multiply connected 3-manifold, since finding the angles of the eigenrotations of a candidate isometry for topological lensing is a way to falsify such hypotheses.
• In mathematics, the isometry group of a metric space is the set of all bijective isometries (that is, bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation.
• If dom(AA) = dom(BB) and AAh = BBh for all h ∈ dom(AA), then there exists a partial isometry U such that A = UB.
• Hjelmslev's theorem, the statement that the midpoints of corresponding pairs of points in an isometry of lines are collinear.
• Among his contributions to dentistry are the rules of isometry that allow for the bisecting angle to accurately reproduce dimensions in x-radiology, and extraoral anæsthetising techniques.

Förberedelsen av sidan tog: 481,05 ms.