Hexagon in the context of "Hexagonal window"

In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass.

The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so it may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, the only permissible constructions are those granted by the first three postulates of Euclid's Elements.

A coffin or casket is a funerary box used for viewing or keeping a corpse, for burial, entombment or cremation. Coffins are sometimes referred to as caskets, particularly in American English.

A distinction is commonly drawn between "coffins" and "caskets", using "coffin" to refer to a tapered hexagonal or octagonal (also considered to be anthropoidal in shape) box and "casket" to refer to a rectangular box, often with a split lid used for viewing the deceased as seen in the picture. Receptacles for cremated and cremulated human ashes (sometimes called cremains) are called urns.

Honey is a sweet and viscous substance made by several species of bees, the best-known of which are honey bees. Honey is made and stored to nourish bee colonies. Bees produce honey by gathering and then refining the sugary secretions of plants (primarily floral nectar) or the secretions of other insects, like the honeydew of aphids. This refinement takes place both within individual bees, through regurgitation and enzymatic activity, and during storage in the hive, through water evaporation that concentrates the honey's sugars until it is thick and viscous.

Honey bees stockpile honey in the hive. Within the hive is a structure made from wax called honeycomb. The honeycomb is made up of hundreds or thousands of hexagonal cells, into which the bees regurgitate honey for storage. Other honey-producing species of bee store the substance in different structures, such as the pots made of wax and resin used by the stingless bee.

The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word "apothem" can also refer to the length of that line segment and comes from the ancient Greek ἀπόθεμα ("put away, put aside"), made of ἀπό ("off, away") and θέμα ("that which is laid down"), indicating a generic line written down. Regular polygons are the only polygons that have apothems. Because of this, all the apothems in a polygon will be congruent.

A Klemperer rosette is a gravitational system of (optionally) alternating heavier and lighter bodies orbiting in a symmetrical pattern around a common barycenter. It was first described by W.B. Klemperer in 1962, and is a special case of a central configuration.

Klemperer described rosette systems as follows:

Two mathematical objects a and b are called "equal up to an equivalence relation R"

• if a and b are related by R, that is,
• if aRb holds, that is,
• if the equivalence classes of a and b with respect to R are equal.

This figure of speech is mostly used in connection with expressions derived from equality, such as uniqueness or count.For example, "x is unique up to R" means that all objects x under consideration are in the same equivalence class with respect to the relation R.

Bar stock, also (colloquially) known as blank, slug or billet, is a common form of raw purified metal, used by industry to manufacture metal parts and products. Bar stock is available in a variety of extrusion shapes and lengths. The most common shapes are round (circular cross-section), rectangular, square and hexagonal. A bar is characterised by an "enclosed invariant convex cross-section", meaning that pipes, angle stock and objects with varying diameter are not considered bar stock.

Bar stock is commonly processed by a sequence of sawing, turning, milling, drilling and grinding to produce a final product, often vastly different from the original stock. In some cases, the process is partially automated by specialized equipment which feeds the stock into the appropriate processing machine.