What is "incidence"

Angle \An"gle\ ([a^][ng]"g'l), n. [F. angle, L. angulus angle, corner; akin to uncus hook, Gr. 'agky`los bent, crooked, angular, 'a`gkos a bend or hollow, AS. angel hook, fish-hook, G. angel, and F. anchor.]

1. The inclosed space near the point where two lines meet; a corner; a nook.

   Into the utmost angle of the world.
   --Spenser.

   To search the tenderest angles of the heart.
   --Milton.

2. (Geom.)

   1. The figure made by. two lines which meet.

   2. The difference of direction of two lines. In the lines meet, the point of meeting is the vertex of the angle.

3. A projecting or sharp corner; an angular fragment.

   Though but an angle reached him of the stone.
   --Dryden.

4. (Astrol.) A name given to four of the twelve astrological ``houses.'' [Obs.]
   --Chaucer.

5. [AS. angel.] A fishhook; tackle for catching fish, consisting of a line, hook, and bait, with or without a rod. Give me mine angle: we 'll to the river there. --Shak. A fisher next his trembling angle bears. --Pope. Acute angle, one less than a right angle, or less than 90[deg]. Adjacent or Contiguous angles, such as have one leg common to both angles. Alternate angles. See Alternate. Angle bar.

   1. (Carp.) An upright bar at the angle where two faces of a polygonal or bay window meet.
      --Knight.

   2. (Mach.) Same as Angle iron.

      Angle bead (Arch.), a bead worked on or fixed to the angle of any architectural work, esp. for protecting an angle of a wall.

      Angle brace, Angle tie (Carp.), a brace across an interior angle of a wooden frame, forming the hypothenuse and securing the two side pieces together.
      --Knight.

      Angle iron (Mach.), a rolled bar or plate of iron having one or more angles, used for forming the corners, or connecting or sustaining the sides of an iron structure to which it is riveted.

      Angle leaf (Arch.), a detail in the form of a leaf, more or less conventionalized, used to decorate and sometimes to strengthen an angle.

      Angle meter, an instrument for measuring angles, esp. for ascertaining the dip of strata.

      Angle shaft (Arch.), an enriched angle bead, often having a capital or base, or both.

      Curvilineal angle, one formed by two curved lines.

      External angles, angles formed by the sides of any right-lined figure, when the sides are produced or lengthened.

      Facial angle. See under Facial.

      Internal angles, those which are within any right-lined figure.

      Mixtilineal angle, one formed by a right line with a curved line.

      Oblique angle, one acute or obtuse, in opposition to a right angle.

      Obtuse angle, one greater than a right angle, or more than 90[deg].

      Optic angle. See under Optic.

      Rectilineal or Right-lined angle, one formed by two right lines.

      Right angle, one formed by a right line falling on another perpendicularly, or an angle of 90[deg] (measured by a quarter circle).

      Solid angle, the figure formed by the meeting of three or more plane angles at one point.

      Spherical angle, one made by the meeting of two arcs of great circles, which mutually cut one another on the surface of a globe or sphere.

      Visual angle, the angle formed by two rays of light, or two straight lines drawn from the extreme points of an object to the center of the eye.

      For Angles of commutation, draught, incidence, reflection, refraction, position, repose, fraction, see Commutation, Draught, Incidence, Reflection, Refraction, etc.

early 15c., "incidental matter," from Middle French incidence (15c.), from Late Latin incidentia (see incident (n.)). Meaning "act of coming into contact with" is from 1650s; sense in physics is from 1620s.

n. 1 The act of something happening; occurrence 2 The extent, or the relative frequency of something happening 3 (context physics English) The striking of radiation or a projectile upon a surface 4 (context epidemiology English) A measure of the risk that a person develops a new condition within a specified period of time, usually a year.

1. n. the relative frequency of occurrence of something [syn: relative incidence]

2. the striking of a light beam on a surface; "he measured the angle of incidence of the reflected light"

Incidence may refer to:

Incidence in epidemiology is a measure of the probability of occurrence of a given medical condition in a population within a specified period of time. Although sometimes loosely expressed simply as the number of new cases during some time period, it is better expressed as a proportion or a rate with a denominator.

Incidence proportion (also known as cumulative incidence) is the number of new cases within a specified time period divided by the size of the population initially at risk. For example, if a population initially contains 1,000 non-diseased persons and 28 develop a condition over two years of observation, the incidence proportion is 28 cases per 1,000 persons per two years, i.e. 2.8%.

In geometry, an incidence relation is a binary relation between different types of objects that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, , and a line, , sometimes denoted . If the pair is called a flag. There are many expressions used in common language to describe incidence (for example, a line passes through a point, a point lies in a plane, etc.) but the term "incidence" is preferred because it does not have the additional connotations that these other terms have, and it can be used in a symmetric manner, reflecting this property of the relation. Statements such as "line intersects line " are also statements about incidence relations, but in this case, it is because this is a shorthand way of saying that "there exists a point that is incident with both line and line ". When one type of object can be thought of as a set of the other type of object (viz., a plane is a set of points) then an incidence relation may be viewed as containment.

Statements such as "any two lines in a plane meet" are called incidence propositions. This particular statement is true in a projective plane, though not true in the Euclidean plane where lines may be parallel. Historically, projective geometry was developed in order to make the propositions of incidence true without exceptions, such as those caused by the existence of parallels. From the point of view of synthetic geometry, projective geometry should be developed using such propositions as axioms. This is most significant for projective planes due to the universal validity of Desargues' theorem in higher dimensions.

In contrast, the analytic approach is to define projective space based on linear algebra and utilizing homogeneous co-ordinates. The propositions of incidence are derived from the following basic result on vector spaces: given subspaces and of a (finite dimensional) vector space , the dimension of their intersection is . Bearing in mind that the geometric dimension of the projective space associated to is and that the geometric dimension of any subspace is positive, the basic proposition of incidence in this setting can take the form: linear subspaces and of projective space meet provided .

The following sections are limited to projective planes defined over fields, often denoted by , where is a field, or . However these computations can be naturally extended to higher dimensional projective spaces and the field may be replaced by a division ring (or skewfield) provided that one pays attention to the fact that multiplication is not commutative in that case.

In graph theory, an incidence is a pair (u, e) where u is a vertex and e is an edge incident to u.

Two distinct incidences (u, e) and (v, f) are adjacent if and only if u = v, e = f or uv = e or f.

An incidence coloring of a graph G is an assignment of a color to each incidence of G in such a way that adjacent incidences get distinct colors. It is equivalent to a strong edge coloring of the graph obtained by subdivising once each edge of G.