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Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
The Structure of Evolutionary Theory (2002) is Harvard paleontologist Stephen Jay Gould's technical book on macroevolution and the historical development of evolutionary theory. [1] The book was twenty years in the making, [2] published just two months before Gould's death. [3] Aimed primarily at professionals, [4] the volume is divided into ...
Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation ).
While the idea of dorsoventral axis inversion appears to be supported by morphological and molecular data, others have proposed alternative plausible hypotheses (reviewed in Gerhart 2000). [1] One assumption of the inversion hypothesis is that the common ancestor of protostomes and chordates already possessed an organized central nervous system ...
The idea of a tree of life arose from ancient notions of a ladder-like progression from lower into higher forms of life (such as in the Great Chain of Being).Early representations of "branching" phylogenetic trees include a "paleontological chart" showing the geological relationships among plants and animals in the book Elementary Geology, by Edward Hitchcock (first edition: 1840).
Evolution is the change in the heritable characteristics of biological populations over successive generations. [1] [2] It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. [3]
In biology, a substitution model, also called models of sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules, such as DNA sequences or protein sequences, that can be represented as sequence of symbols (e.g., A, C, G, and T in the case of DNA or the 20 "standard" proteinogenic amino acids in the case of ...