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In statistics, multicollinearity or collinearity is a situation where the predictors in a regression model are linearly dependent. Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship.
In geometry, collinearity of a set of points is the property of their lying on a single line. [1] A set of points with this property is said to be collinear (sometimes spelled as colinear [ 2 ] ). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
A Koch snowflake has an infinitely repeating self-similarity when it is magnified. Standard (trivial) self-similarity [1]. In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts).
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, [1] or its generalization to other kinds of mathematical spaces.As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist.
In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space .
They are encoded in the positive geometry of the amplituhedron, via the singularity structure of the integrand for scattering amplitudes. [1] Arkani-Hamed suggests this is why amplituhedron theory simplifies scattering-amplitude calculations: in the Feynman-diagrams approach, locality is manifest, whereas in the amplituhedron approach, it is ...
Jacob Lurie's under-construction book Spectral Algebraic Geometry studies a generalization that he calls a spectral Deligne–Mumford stack. By definition, it is a ringed ∞-topos that is étale-locally the étale spectrum of an E ∞ -ring (this notion subsumes that of a derived scheme , at least in characteristic zero.)
However, each staircase has length two, while the length of the diagonal is the square root of 2, so the sequence of staircase lengths does not converge to the length of the diagonal. [ 3 ] [ 4 ] Martin Gardner calls this "an ancient geometrical paradox". [ 5 ]