Diameter

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Diameter

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 diameter of 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....
is any straight line segment

Line segment

In geometry, a line segment is a part of a line that is bounded by two end Point , and contains every point on the line between its end points....
that passes through the center of the circle and whose endpoint

Endpoint

An endpoint or end point is a mark of termination or completion.* Endpoint , the conclusion of a chemical reaction, particularly for titration...
s are on the circle. The diameters are the longest chords

Chord (geometry)

A chord of a curve is a geometry line segment whose endpoints both lie on the curve.A secant or a secant line is the line extension of a chord....
of the circle. The word "diameter" derives from Greek

Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
d??µet??? (diametros), "diagonal of a circle", from d?a- (dia-), "across, through" + µ?t??? (metron), "a measure").

In more modern usage, the length of a diameter is also called the diameter.

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Encyclopedia

In geometry

Geometry

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....
is any straight line segment

Line segment

Endpoint

Chord (geometry)

Greek language

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....
have the same length, this being twice the radius

RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
.

For a convex

Convex

The word convex means curving out or bulging outward.Convex or convexity may refer to:Mathematics:* Convex set, a set of points containing all line segments between each pair of its points...
shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance. For a curve of constant width

Curve of constant width

In geometry, a curve of constant width is a Convex set planar shape whose width, measured by the distance between two opposite parallellines touching its boundary, is the same regardless of the direction of those two parallel lines....
such as the Reuleaux triangle

Reuleaux triangle

A Reuleaux polygon is a curve of constant width - that is, a curve such that, if two parallel lines are drawn tangent to the curve in any orientation, the distance between them is fixed....
, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. See also Tangent lines to circles

Tangent lines to circles

In Euclidean geometry, tangent lines to circles form the subject of several theorems, and play an important role in many geometrical Compass and straightedge constructionss and Mathematical proof....
.

The diameter of a connected graph is the distance between the two vertices

Vertex (graph theory)

In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs ....
which are furthest from each other. The distance between two vertices a and b is the length of the shortest path connecting them (for the length of a path, see Graph theory

Graph theory

In mathematics and computer science, graph theory is the study of graph : mathematical structures used to model pairwise relations between objects from a certain collection....
).

Generalisations

The three definitions given above are special cases of a more general definition. The diameter of a subset

Subset

In mathematics, especially in set theory, a Set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide....
of a metric space

Metric space

In mathematics, a metric space is a Set where a notion of distance between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space....
is the least upper bound

Supremum

In mathematics, given a subset S of a partially ordered set T, the supremum of S, if it exists, is the greatest element of T that is greater than or equal to each element of S....
of the distances between pairs of points in the subset. So, if A is the subset, the diameter is

sup

Supremum

In mathematics, given a subset S of a partially ordered set T, the supremum of S, if it exists, is the greatest element of T that is greater than or equal to each element of S....
.

In differential geometry, the diameter is an important global Riemannian

Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, manifold with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smooth function from point to point....
invariant

Invariant

Invariant and invariance may have several meanings, among which are:* Invariant , an expression whose value doesn't change during execution ...
.

In medical parlance

Idiom

An idiom is a phrase whose meaning cannot be determined by the literal definition of the phrase itself, but refers instead to a figurative language meaning that is known only through common use....
the diameter of a lesion

Lesion

A lesion is any abnormal tissue found on or in an organism, usually damaged by disease or trauma. Lesion is derived from the Latin word laesio which means injury....
is the longest line segment whose endpoints are within the lesion.

Diameter symbol

The symbol

Symbol

A symbol is something such as an entity, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention....
or variable

Variable

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e....
for diameter is similar in size and design to ø

? , is a vowel and a Letter used in the Danish and Norwegian alphabet, Faroese language#Alphabet and Danish and Norwegian alphabet languages....
, the lowercase letter o with pooy poo poop. Unicode

Unicode

Unicode is a computing industry standard allowing computers to consistently represent and manipulate Character expressed in most of the world's writing systems....
provides character number 8960 (hexadecimal

Hexadecimal

In mathematics and computer science, hexadecimal is a numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen....
2300) for the symbol, which can be encoded in HTML

HTML

HTML, an Acronym and initialism of HyperText Markup Language, is the predominant markup language for Web pages. It provides a means to describe the structure of text-based information in a document?by denoting certain text as links, headings, paragraphs, lists, and so on?and to supplement that text with interactive forms, embedded '...
webpages as ⌀ or ⌀. Proper display of this character, however, is unlikely in most situations, as most font

Typeface

In typography, a typeface is a set of one or more fonts, in one or more sizes, designed with stylistic unity, each comprising a coordinated set of glyphs....
s do not have it included. (Your browser displays ? in the current font.) In most situations the letter ø is acceptable, obtained in Microsoft Windows

Microsoft Windows

Microsoft Windows is a series of software operating systems and graphical user interfaces produced by Microsoft. Microsoft first introduced an operating environment named Windows in November 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces ....
by holding the [Alt] key down while entering 0 2 4 8 on the numeric keypad

Numeric keypad

A numeric keypad, or numpad for short, is the small, palm-sized, seventeen key section of a computer keyboard, usually on the very far right....
, or in UNIX-like operating systems using a Compose key

Compose key

On some computer systems, a compose key is a key which is designated to signal the software to interpret the next keystrokes as a combination in order to produce a character not found on the keyboard....
by pressing, in sequence, Compose / o.

The diameter symbol, , is distinct from the empty set

Empty set

In mathematics, and more specifically set theory, the empty set is the unique Set having no members. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced....
symbol, Ø, from an uppercase phi

Phi (letter)

Phi , pronounced [] in Modern Greek language and as [] in English, is the 21st letter of the Greek alphabet. In modern Greek, it represents [], a voiceless labiodental fricative....
, F, and the Nordic vowel, Ø.

The diameter also refers to the approximate size of the corner of a frame of any given object to the nearest flat surface it represents.

Graph theory

To find diameter of a graph

Graph (mathematics)

In mathematics a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges....
, first find the shortest path

Path (graph theory)

In graph theory, a path in a graph is a sequence of vertex such that from each of its vertices there is an edge to the next vertex in the sequence....
between each pair of vertices

Vertex

Vertex may refer to:...
. The longest of these paths is the diameter of the graph.

Inside diameter

Inside diameter is the diameter of the addendum circle of an internal gear, or of tubing or pipe.

External links

(geometry) With interactive applets