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Disk (mathematics)

 

 
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Disk (mathematics)
 
 
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In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a disk (also spelled disc) is the region in a plane
Plane (mathematics)

In mathematics, a plane is a curvature surface. Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry....
 bounded by a circle
Circle

A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
.

A disk is said to be closed or open according to whether or not it contains the circle that constitutes its boundary. In Cartesian coordinates, the open disk of center and radius R is given by the formula while the closed disk of the same center and radius is given by

The area of a closed or open disk of radius R is pR2 (see p
Pi

Pi or p is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean geometry; this is the same value as the ratio of a circle's area to the square of its radius....
).

The ball
Ball (mathematics)

In mathematics, a ball is the inside of a sphere; both concepts apply not only in the three-dimensional space but also for lower and higher dimensions, and for metric spaces in general....
 is the disk generalised to metric spaces.






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Circle 1
In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a disk (also spelled disc) is the region in a plane
Plane (mathematics)

In mathematics, a plane is a curvature surface. Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry....
 bounded by a circle
Circle

A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
.

A disk is said to be closed or open according to whether or not it contains the circle that constitutes its boundary. In Cartesian coordinates, the open disk of center and radius R is given by the formula while the closed disk of the same center and radius is given by

The area of a closed or open disk of radius R is pR2 (see p
Pi

Pi or p is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean geometry; this is the same value as the ratio of a circle's area to the square of its radius....
).

The ball
Ball (mathematics)

In mathematics, a ball is the inside of a sphere; both concepts apply not only in the three-dimensional space but also for lower and higher dimensions, and for metric spaces in general....
 is the disk generalised to metric spaces. However, sometimes "disk" is used to mean "ball".

In theoretical physics a disk is a rigid body which is capable of participating in collisions in a two-dimensional gas
Two-dimensional gas

A two-dimensional gas is a collection of N objects which are constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be: ideal gas elements such as rigid Disk undergoing elastic collisions; elementary particles, or any object in physics which obeys laws of motion....
. Usually the disk is considered rigid so that collisions are deemed elastic
Elastic collision

An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision....
.

See also


  • Unit disk
    Unit disk

    In mathematics, the open unit disk around P , is the set of points whose distance from P is less than 1:The closed unit disk around P is the set of points whose distance from P is less than or equal to one:...
    , a disk with radius one
  • annulus (mathematics)
    Annulus (mathematics)

    In mathematics, an annulus is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. Or, it is the area between two concentric circles....
  • Disk algebra
    Disk algebra

    In function theory, the disk algebra is the set of continuous functionswhere D is the closed unit disk in the complex plane C, such that the restriction of f to the interior of D is an analytic function....
  • Lentoid
    Lentoid

    Lentoid is a geometric shape of a three dimensional body, best described as a circle viewed from one direction and a convex lens viewed from an orthogonal direction....
  • Moment of inertia of a uniform disc