In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle. The word "diameter" derives from Greek διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure).
In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.
For a convex 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 such as the Reuleaux triangle, 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.
The diameter of a connected graph is the distance between the two vertices 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).
Generalisations
The three definitions given above are special cases of a more general definition. The diameter of a subset of a metric space is the least upper bound of the distances between pairs of points in the subset. So, if A is the subset, the diameter is- sup { d(x, y) | x, y ∈ A } .
In differential geometry, the diameter is an important global Riemannian invariant.
In medical parlance the diameter of a lesion is the longest line segment whose endpoints are within the lesion.
Diameter symbol
The symbol or variable for diameter is similar in size and design to ø, the lowercase letter o with stroke. Unicode provides character number 8960 (hexadecimal 2300) for the symbol, which can be encoded in HTML webpages as ⌀ or ⌀. Proper display of this character, however, is unlikely in most situations, as most fonts do not have it included. (Your browser displays ⌀ in the current font.) In most situations the letter ø is acceptable, obtained in Microsoft Windows by holding the [Alt] key down while entering 0 2 4 8 on the numeric keypad.
The diameter symbol, ⌀, is distinct from the empty set symbol, ∅, from an uppercase phi, Φ, 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.
See also
- angular diameter
- hydraulic diameter
- caliper, micrometer, tools for measuring diameters
- Eratosthenes, who calculated the diameter of the Earth around 240 BC.
- Jung's theorem, an inequality relating the diameter to the radius of the smallest enclosing ball
References
External links
- (geometry) Diameter and many other circle properties defined With interactive applets
This article is licensed under the GNU Free Documentation License.
Last updated on Saturday October 11, 2008 at 14:06:00 PDT (GMT -0700)
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Upgrade from RADIUS
The name is a pun on the RADIUS protocol, which is the predecessor (a diameter is twice the radius). Diameter is not directly backwards compatible, but provides an upgrade path for RADIUS. The main differences are as follows:- Reliable transport protocols (TCP or SCTP, not UDP)
- Network or transport level security (IPsec or TLS)
- Transition support for RADIUS, although Diameter is not fully compatible with RADIUS
- Larger address space for attribute-value pairs (AVPs) and identifiers (32 bits instead of 8 bits)
- Client-server protocol, with exception of supporting some server-initiated messages as well
- Both stateful and stateless models can be used
- Dynamic discovery of peers (using DNS SRV and NAPTR)
- Capability negotiation
- Supports application layer acknowledgements, defines failover methods and state machines (RFC 3539)
- Error notification
- Better roaming support
- More easily extended; new commands and attributes can be defined
- Aligned on 32-bit boundaries
- Basic support for user-sessions and accounting
Protocol description
The Diameter base protocol is defined by RFC 3588, and defines the minimum requirements for an AAA protocol. Diameter Applications can extend the base protocol, by adding new commands and/or attributes. An application is not a program, but a protocol based on Diameter. Diameter security is provided by IPSEC or TLS, both well-regarded protocols.Packet format
Commands
Each command is assigned a command code, which is used for both requests and answers.|
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