Cathetus

In a right triangle, a cathetus (originally from the Greek word Κάθετος; plural: catheti), commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called a "side about the right angle". The side opposite the right angle is the hypotenuse. In the context of the hypotenuse, the catheti are sometimes referred to simply as "the other two sides".

If the catheti of a right triangle have equal lengths, the triangle is isosceles. If they have different lengths, a distinction can be made between the minor (shorter) and major (longer) cathetus. The ratio of the lengths of the catheti defines the trigonometric functions tangent and cotangent of the acute angles in the triangle: the ratio is the tangent of the acute angle adjacent to and is also the cotangent of the acute angle adjacent to .

In a right triangle, the length of a cathetus is the geometric mean of the length of the adjacent segment cut by the altitude to the hypotenuse and the length of the whole hypotenuse.

Geometry

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.

Geometry (Ivo Perelman album)

Geometry is an album by Brazilian jazz saxophonist Ivo Perelman featuring American pianist Borah Bergman, which was recorded in 1996 and released on the English Leo label.

Reception

In his review for AllMusic, Alex Henderson says that "this CD doesn't quite fall into the 'essential' category... Nonetheless, Geometry is an enjoyable release that Perelman's more-devoted followers will want."

The Penguin Guide to Jazz notes that "Bergman is wily enough to find ways of both supporting and undercutting the mighty sound of the tenor."

Track listing

Personnel

References

Geometric group action

In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.

Definition

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:

Uniqueness

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.

Examples

Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.

References

Leg

A leg is a weight bearing and locomotive structure, usually having a columnar shape. During locomotion, legs function as "extensible struts". The combination of movements at all joints can be modeled as a single, linear element capable of changing length and rotating about an omnidirectional "hip" joint.

As an anatomical animal structure it is used for locomotion. The distal end is often modified to distribute force (such as a foot). Most animals have an even number of legs.

As a component of furniture it is used for the economy of materials needed to provide the support for the useful surface, the table top or chair seat.

Terminology

Many taxa are characterized by the number of legs:

Legé

Legé is a commune in the Loire-Atlantique department in western France.

See also

Leg (darts)

A leg is a single game in the sport of darts. Most darts matches are played over a number of legs. Alternatively, a match may be divided into sets, with each set being contested often on a first to 3 legs basis.

Start and finish

At the start of each leg, each player or team has a score of 501. A leg is over when either side reaches zero by hitting a double or the bull's eye. If playing several sets, the player throwing first is alternated.

References