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Angle. A green angle formed by two red rays on the Cartesian coordinate system. In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [1] Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays.
In mechanics and geometry, the 3D rotation group, often denoted SO (3), is the group of all rotations about the origin of three-dimensional Euclidean space under the operation of composition. [1] By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry ), and orientation ...
In mathematics, a Lie algebra (pronounced / liː / LEE) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the ...
The affine group of one dimension is a two-dimensional matrix Lie group, consisting of. 2 × 2 {\displaystyle 2\times 2} real, upper-triangular matrices, with the first diagonal entry being positive and the second diagonal entry being 1. Thus, the group consists of matrices of the form.
Carnegie stages. In embryology, Carnegie stages are a standardized system of 23 stages used to provide a unified developmental chronology of the vertebrate embryo . The stages are delineated through the development of structures, not by size or the number of days of development, and so the chronology can vary between species, and to a certain ...
Lie groups and Lie algebras. In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n -by- n invertible matrices, then the adjoint ...
The 8,640-kilometer coastline is highly indented. Some 3,579 islands lie adjacent to the peninsula. Most of them are found along the south and west coasts. After World War II and before June 25, 1950, the line between the two Korean states was the thirty-eighth parallel of latitude.
Direct repeats are a type of genetic sequence that consists of two or more repeats of a specific sequence. [1] In other words, the direct repeats are nucleotide sequences present in multiple copies in the genome. Generally, a direct repeat occurs when a sequence is repeated with the same pattern downstream. [1]