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In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry
They also classify spacetimes using symmetry vector fields (especially Killing and homothetic symmetries). For example, Killing vector fields may be used to classify spacetimes, as there is a limit to the number of global, smooth Killing vector fields that a spacetime may possess (the maximum being ten for four-dimensional spacetimes).
Modern physics deals with three basic types of spatial symmetry: reflection, rotation, and translation. The known elementary particles respect rotation and translation symmetry but do not respect mirror reflection symmetry (also called P-symmetry or parity).
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
The role of symmetry in grouping and figure/ground organization has been confirmed in many studies. For instance, detection of reflectional symmetry is faster when this is a property of a single object. [29] Studies of human perception and psychophysics have shown that detection of symmetry is fast, efficient and robust to perturbations.
The equation of hydrostatic equilibrium may need to be modified by adding a radial acceleration term if the radius of the star is changing very quickly, for example if the star is radially pulsating. [9] Also, if the nuclear burning is not stable, or the star's core is rapidly collapsing, an entropy term must be added to the energy equation. [10]
A simple example illustrating relaxation is two-body relaxation, where a star's orbit is altered due to the gravitational interaction with another star. Initially, the subject star travels along an orbit with initial velocity, v {\displaystyle \mathbf {v} } , that is perpendicular to the impact parameter , the distance of closest approach, to ...
A point reflection is an involution: applying it twice is the identity transformation. An object that is invariant under a point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among its symmetries is called centrosymmetric.