## affinely

13 examples (0.01 sec)
• Positive infinity is one of the non real number elements in the affinely extended real number system.
• In particular, x t is a geodesic if and only if its development is an affinely parametrized straight line in T x 0 M.
• The IEEE standard employs (and extends) the affinely extended real number system, with separate positive and negative infinities.
• Just as members of a set of vectors are linearly independent if none is a linear combination of the others, so also they are affinely independent if none is an affine combination of the others.
• Similarly they are affinely dependent if in addition the sum of coefficients is zero: a condition that ensures that the combination makes sense as a displacement vector.
• One application of the torsion of a connection involves the geodesic spray of the connection: roughly the family of all affinely parametrized geodesics.
• A manifold having a distinguished affine structure is called an affine manifold and the charts which are affinely related to those of the affine structure are called affine charts.
• Every possible bit combination is either a NaN or a number with a unique value in the affinely extended real number system with its associated order, except for the two bit combinations negative zero and positive zero, which sometimes require special attention (see below).
• Given a convex r-dimensional polytope P, a subset of its vertices containing (r+1) affinely independent points defines an r-simplex.
• In geometry, an affine-regular polygon or affinely regular polygon is a polygon that is related to a regular polygon by an affine transformation.
• In the theory of general relativity, and differential geometry more generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only affinely parametrized geodesics.
• A set of points in general linear position is also said to be affinely independent (this is the affine analog of linear independence of vectors, or more precisely of maximal rank), and d+1 points in general linear position in affine d-space are an affine basis.
• An affine connection is determined by its family of affinely parameterized geodesics, up to torsion, The torsion itself does not, in fact, affect the family of geodesics, since the geodesic equation depends only on the symmetric part of the connection.