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A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

The theory of analyzing a decision between a collection of alternatives made by a collection of n voters with separate opinions. Any choice for the entire group should ...

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

A product of a reflection in a line and translation along the same line.

The only irreducible spherical simplexes generated by reflection are A_n (n>=1), B_n (n>=4), C_n (n>=2), D_2^p (p>=5), E_6, E_7, E_8, F_4, G_3, and G_4. The only irreducible ...

Consider a reference triangle DeltaABC with circumcenter O and orthocenter H, and let DeltaA^*B^*C^* be its reflection triangle. Then Musselman's theorem states that the ...

Of opposite symmetry under reflection; mirror images.

Objects which are identical except for a mirror reflection are said to display handedness and to be chiral.

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...