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"^{[1]}).
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.
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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
Some people prefer to treat the empty set () as a special case.^{[2]}
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.
The symbol or variable for diameter is similar in size and design to ø, the Latin small letter o with stroke. Unicode provides character number 8960 (hexadecimal 2300) for the symbol, which can be encoded in HTML webpages as ⌀ or ⌀. The character can be obtained in Microsoft Windows by holding the [Alt] key down while entering 8 9 6 0 on the numeric keypad. On an Apple Inc. Macintosh, the diameter symbol can be entered via the character palette (this is opened by pressing ⌥⌘T in most applications), where it can be found in the Technical Symbols category.
The character often will not display correctly, however, since most fonts do not include it. (Your browser displays "⌀" in the current font.) In most situations the letter ø is acceptable, which is unicode 0248 (hexadecimal 00F8). It can be obtained in UNIXlike operating systems using a Compose key by pressing, in sequence, Compose / o and on a Macintosh by pressing ⌥O (in both cases, that is the letter o, not the number 0).
In LaTeX the symbol is achieved with the command \diameter which is part of the wasysym package.
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.
DIAMETER (from the Gr. Sca, through, ,u rpov, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the "principal diameters of the ellipse and hyperbola coincide with the "axes" and are at right angles; " conjugate diameters " are such that each bisects chords parallel to the other. The diameter of a quadric surface is a line at the extremities of which the tangent planes are parallel. Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line. The word is also used as a unit of linear measurement of the magnifying power of a lens or microscope.
In architecture, the term is used to express the measure of the lower part of the shaft of a column. It is employed by Vitruvius (iii. 2) to determine the height of a column, which should vary from eight to ten diameters according to the intercolumniation: and it is generally the custom to fix the lower diameter of the shaft by the height required and the Order employed. Thus the diameter of the Roman Doric should be about oneeighth of the height, that of the Ionic oneninth, and of the Corinthian onetenth (see Order).
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Categories: DERDIF  Mathematics
