SymmetrySymmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Structural isomerIn chemistry, a structural isomer (or constitutional isomer in the IUPAC nomenclature) of a compound is another compound whose molecule has the same number of atoms of each element, but with logically distinct bonds between them. The term metamer was formerly used for the same concept. For example, butanol , methyl propyl ether , and diethyl ether have the same molecular formula but are three distinct structural isomers. The concept applies also to polyatomic ions with the same total charge.
Chemical propertyA chemical property is any of a material's properties that becomes evident during, or after, a chemical reaction; that is, any quality that can be established only by changing a substance's chemical identity. Simply speaking, chemical properties cannot be determined just by viewing or touching the substance; the substance's internal structure must be affected greatly for its chemical properties to be investigated. When a substance goes under a chemical reaction, the properties will change drastically, resulting in chemical change.
Molecular orbitalIn chemistry, a molecular orbital (ɒrbədl) is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.
Optical rotatory dispersionOptical rotatory dispersion is the variation in the optical rotation of a substance with a change in the wavelength of light. Optical rotatory dispersion can be used to find the absolute configuration of metal complexes. For example, when plane-polarized white light from an overhead projector is passed through a cylinder of sucrose solution, a spiral rainbow is observed perpendicular to the cylinder. When white light passes through a polarizer, the extent of rotation of light depends on its wavelength.
EpimerIn stereochemistry, an epimer is one of a pair of diastereomers. The two epimers have opposite configuration at only one stereogenic center out of at least two. All other stereogenic centers in the molecules are the same in each. Epimerization is the interconversion of one epimer to the other epimer. Doxorubicin and epirubicin are two epimers that are used as drugs. The stereoisomers β-D-glucopyranose and β-D-mannopyranose are epimers because they differ only in the stereochemistry at the C-2 position.
Chirality (mathematics)In geometry, a figure is chiral (and said to have chirality) if it is not identical to its , or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be achiral. A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'.
Organic chemistryOrganic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms. Study of structure determines their structural formula. Study of properties includes physical and chemical properties, and evaluation of chemical reactivity to understand their behavior.
Symmetry groupIn group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space.
Rotational symmetryRotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids.
Chemical substanceA chemical substance is a form of matter having constant chemical composition and characteristic properties. Chemical substances can be simple substances (substances consisting of a single chemical element), chemical compounds, or alloys. Chemical substances that cannot be separated into their simpler constituent elements by physical means are said to be 'pure'; this notion intended to set them apart from mixtures.
Reflection symmetryIn 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 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called . In conclusion, a line of symmetry splits the shape in half and those halves should be identical.
