Ribbon

A ribbon or riband is a thin band of material, typically cloth but also plastic or sometimes metal, used primarily as decorative binding and tying. Cloth ribbons are made of natural materials such as silk, velvet, cotton, and jute and of synthetic materials, such as polyester, nylon and polyproylene. Ribbon is used for innumerable useful, ornamental and symbolic purposes. Cultures around the world use ribbon in their hair, around the body, and as ornamentation on animals, buildings, and packaging. Some popular fabrics used to make ribbons are satin, organza, sheer, silk, velvet and grosgrain.

Etymology

The word ribbon comes from Middle English ribban or riban from Old French ruban, which is probably of Germanic origin.

Cloth ribbon

Ribbon (mathematics)

In mathematics (differential geometry) by a ribbon (or strip) is meant a smooth space curve given by a three-dimensional vector , depending continuously on the curve arc-length (), together with a smoothly varying unit vector perpendicular to at each point (Blaschke 1950).

The ribbon is called simple and closed if is simple (i.e. without self-intersections) and closed and if and all its derivatives agree at and . For any simple closed ribbon the curves given parametrically by are, for all sufficiently small positive , simple closed curves disjoint from .

The ribbon concept plays an important role in the Cǎlugǎreǎnu-White-Fuller formula (Fuller 1971), that states that

where is the asymptotic (Gauss) linking number (a topological quantity), denotes the total writhing number (or simply writhe) and is the total twist number (or simply twist).

Ribbon theory investigates geometric and topological aspects of a mathematical reference ribbon associated with physical and biological properties, such as those arising in topological fluid dynamics, DNA modeling and in material science.

Ribbon (rhythmic gymnastics)

Ribbon is a component of rhythmic gymnastics composed of a handle (called "stick"), a ribbon and attachment.

Stick

This can be of any colour and made of wood, bamboo or plastic with a maximum diameter of 1 cm (²/₅") at its widest, a cylindrical or conical shape and should have a length of 50–60cm (20–24") (including the fastening ring). The bottom end of the stick may be covered by an adhesive, anti-slip tape or may have a rubber handle for a maximum length of 10 cm (4") at the level of the grip. The top of the stick, where the ribbon will be attached, may consist of:

Connective

Connective may refer to:

See also

Logical connective

In logic, a logical connective (also called a logical operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences.

The most common logical connectives are binary connectives (also called dyadic connectives) which join two sentences which can be thought of as the function's operands. Also commonly, negation is considered to be a unary connective.

Logical connectives along with quantifiers are the two main types of logical constants used in formal systems such as propositional logic and predicate logic. Semantics of a logical connective is often, but not always, presented as a truth function.

A logical connective is similar to but not equivalent to a conditional operator.

In language

Natural language

In the grammar of natural languages two sentences may be joined by a grammatical conjunction to form a grammatically compound sentence. Some but not all such grammatical conjunctions are truth functions. For example, consider the following sentences: