A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
More precisely, it is the solid figure bounded by a base in a plane and by a surface (called the lateral surface) formed by the locus of all straight line segments joining the apex to the perimeter of the base. The term "cone" sometimes refers just to the surface of this solid figure, or just to the lateral surface.
The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a circular symmetry.
In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. Contrasted with right cones are oblique cones, in which the axis does not pass perpendicularly through the centre of the base. In general, however, the base may be any shape and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base).
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.
In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.
In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions:
If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.
Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.
Geometry is the second album by electronic musician Jega, released in 2000 on the Planet Mu label.
A conical hill (also cone or conical mountain) is a landform with a distinctly conical shape. It is usually isolated or rises above other surrounding foothills, and is often, but not always, of volcanic origin.
Conical hills or mountains occur in different shapes and are not necessarily geometrically-shaped cones; some are more tower-shaped or have an asymmetric curve on one side. Typically, however, they have a circular base and smooth sides with a gradient of up to 30°. Such conical mountains are found in all volcanically-formed areas of the world such as the Bohemian Central Uplands in the Czech Republic, the Rhön in Germany or the Massif Central in France.
Cone cells, or cones, are one of two types of photoreceptor cells in the retina of the eye. They are responsible for color vision and function best in relatively bright light, as opposed to rod cells, which work better in dim light. Cone cells are densely packed in the fovea centralis, a 0.3 mm diameter rod-free area with very thin, densely packed cones which quickly reduce in number towards the periphery of the retina. There are about six to seven million cones in a human eye and are most concentrated towards the macula.
A commonly cited figure of six million in the human eye was found by Osterberg in 1935. Oyster's textbook (1999) cites work by Curcio et al. (1990) indicating an average close to 4.5 million cone cells and 90 million rod cells in the human retina.
Cones are less sensitive to light than the rod cells in the retina (which support vision at low light levels), but allow the perception of colour. They are also able to perceive finer detail and more rapid changes in images, because their response times to stimuli are faster than those of rods. Cones are normally one of the three types, each with different pigment, namely: S-cones, M-cones and L-cones. Each cone is therefore sensitive to visible wavelengths of light that correspond to short-wavelength, medium-wavelength and long-wavelength light. Because humans usually have three kinds of cones with different photopsins, which have different response curves and thus respond to variation in colour in different ways, we have trichromatic vision. Being colour blind can change this, and there have been some verified reports of people with four or more types of cones, giving them tetrachromatic vision. The three pigments responsible for detecting light have been shown to vary in their exact chemical composition due to genetic mutation; different individuals will have cones with different color sensitivity. Destruction of the cone cells from disease would result in blindness.
In linear algebra, a (linear) cone is a subset of a vector space that is closed under multiplication by positive scalars. In other words, a subset C of a real vector space V is a cone if and only if λx belongs to C for any x in C and any positive scalar λ of V (or, more succinctly, if and only if λC = C for any positive scalar λ).
A cone is said to be pointed if it includes the null vector (origin) 0; otherwise it is said to be blunt. Some authors use "non-negative" instead of "positive" in this definition of "cone", which restricts the term to the pointed cones only. In other contexts, a cone is pointed if the only linear subspace contained in it is {0}.
The definition makes sense for any vector space V which allows the notion of "positive scalar" (i.e., where the ground field is an ordered field), such as spaces over the rational, real algebraic, or (most commonly) real numbers.
The concept can also be extended for any vector space V whose scalar field is a superset of those fields (such as the complex numbers, quaternions, etc.), to the extent that such a space can be viewed as a real vector space of higher dimension.