Question

characteristics of symmetry

Answer 1

symmetry.

A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:

An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]

An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]

An object has translational symmetry if it can be translated without changing its overall shape.[8]

An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]

An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]

Other symmetries include glide reflection symmetry and rotoreflection symmetry.

In logicEdit

A dyadic relation R is symmetric if and only if, whenever it's true that Rab, it's true that Rba.[12] Thus, "is the same age as" is symmetrical, for if Paul is the same age as Mary, then Mary is the same age as Paul.

Symmetric binary logical connectives are and (∧, or &), or (∨, or |), biconditional (if and only if) (↔), nand (not-and, or ⊼), xor (not-biconditional, or ⊻), and nor(not-or, or ⊽).

Answer 2

The symmetric pattern of codon degeneracies is discussed by using empirical arguments processed within a group-theoretic framework. It is reasoned that the genetic code is a relation rather than a mapping, and the symmetry of a relation defined on the codons is investigated. The principal results are:

(i) a new extraction of the basic symmetry inherent in the standard genetic code;

(ii) the unification of the symmetry of ambiguous codon assignments with that of the standard genetic code; and

(iii) the primacy of the concept of a biological context as that device which degenerates the code relation to a mapping.