Centre (geometry)

In geometry, a centre (or center) (from Greek κέντρον) of an object is a point in some sense in the middle of the object. According to the specific definition of center taken into consideration, an object might have no center. If geometry is regarded as the study of isometry groups then a centre is a fixed point of all the isometries which move the object onto itself.

Circles, spheres, and segments

The centre of a circle is the point equidistant from the points on the edge. Similarly the centre of a sphere is the point equidistant from the points on the surface, and the centre of a line segment is the midpoint of the two ends.

Symmetric objects

For objects with several symmetries, the centre of symmetry is the point left unchanged by the symmetric actions. So the centre of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this being (amongst other properties) the fixed point of rotational symmetries. Similarly the centre of an ellipse or a hyperbola is where the axes intersect.

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

Geometry (disambiguation)

Geometry is a branch of mathematics dealing with spatial relationships.

Geometry or geometric may also refer to:

Pseudoscientific metrology

Some approaches in the branch of historic metrology are highly speculative and can be qualified as pseudoscience.

Origins

In 1637 John Greaves, professor of geometry at Gresham College, made his first of several studies in Egypt and Italy, making numerous measurements of buildings and monuments, including the Great Pyramid. These activities fuelled many centuries of interest in metrology of the ancient cultures by the likes of Isaac Newton and the French Academy.

The pendulum

The first known description and practical use of a physical pendulum is by Galileo Galilei, however, Flinders Petrie, a disciple of Charles Piazzi Smyth, is of the opinion that it was used earlier by the ancient Egyptians. In a 1933 letter to Nature, Petrie wrote:

If we take the natural standard of one day divided by 10⁵, the pendulum would be 29.157 inches at lat 30 degrees. Now this is exactly the basis of Egyptian land measures, most precisely known through the diagonal of that squared, being the Egyptian double cubit. The value for this cubit is 20.617 inches, while the best examples in stone are 20.620±0.005inches.

Centre-Val de Loire

Centre-Val de Loire (French pronunciation: ​[sɑ̃tʁ val də lwaʁ]), French for Centre-Loire valley, is one of the 18 regions of France. It straddles the middle Loire Valley and in the interior of the country. The administrative capital is Orléans, but the largest city is Tours.

Naming and etymology

Like many contemporary regions of France, the Region of Centre was created from parts of several historical provinces. The name "Centre" was chosen by the French government purely on the basis of geography, in reference to its location in north-central France (the central part of the original French language area),

However, Centre is not situated in the geographical centre of France, and the name was criticized as being too dull and nondescript. Proposed names for the region included Val de Loire after the Loire Valley (the main feature of the region) or "Cœur de Loire" (i.e. "Heart of Loire"). On 17 January 2015, in the wake of the proposed reorganization of French regions, the region's official name was changed to "Centre-Val de Loire".Val de Loire is associated with positive images of the Loire Valley, such as the châteaux, the gentle and refined lifestyle, wine, and the mild and temperate climate, all of which attract many tourists to the region. A new logo was also created.

Rugby league positions

A rugby league football team consists of thirteen players on the field, with four substitutes on the bench. Players are divided into two general categories, forwards and backs.

Forwards are generally chosen for their size and strength. They are expected to run with the ball, to attack, and to make tackles. Forwards are required to improve the team's field position thus creating space and time for the backs. Backs are usually smaller and faster, though a big, fast player can be of advantage in the backs. Their roles require speed and ball-playing skills, rather than just strength, to take advantage of the field position gained by the forwards.

Names and numbering

The laws of the game recognise standardised numbering of positions. The starting side normally wear the numbers corresponding to their positions, only changing in the case of substitutions and position shifts during the game. In some competitions, such as Super League, players receive a squad number to use all season, no matter what positions they play in.

Center (basketball)

The center (C), also known as the five or the big man, is one of the five positions in a regulation basketball game. The center is normally the tallest player on the team, and often has a great deal of strength and body mass as well.

The tallest player to ever be drafted in the NBA or the WNBA was the 7'8" (2.33 m) Yasutaka Okayama from Japan, though he never played in the NBA. The tallest players to ever play in the NBA, at 7'7" (2.31 m), are centers Gheorghe Mureșan, and Manute Bol. Standing at 7'2" (2.18 m), Margo Dydek is the tallest player to have ever played in the WNBA.

History of the center position

Emergence of the center and the era of George Mikan

The center is considered a necessary component for a successful team, especially in professional leagues such as the NBA. Great centers have been the foundation for most of the dynasties in both the NBA and NCAA. The 6’10" (2.08 m) George Mikan pioneered the Center position, shattering the widely held perception that tall players could not develop the agility and coordination to play basketball well, and ushering in the role of the dominant big man. He led DePaul University to the NIT title, then, after turning professional, won seven National Basketball League, Basketball Association of America and NBA Championships in his ten-year career (1946–56), nine of them with the Minneapolis Lakers. Using his height to dominate opposing players, Mikan invented the hook shot and the shot block; as a consequence, the NCAA, and later NBA, adopted the goaltending rule, and, in 1951, the NBA widened the foul lane, a decision known as the 'Mikan rule'.