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ఒక వృత్తం యొక్క చుట్టుకొలతను పరిధి అంటారు. ఆ వృత్తం యొక్క పరిధి లోపల ఒక అంచు నుంచి మరొక అంచుకు కేంద్ర బిందువు గుండా వెళ్ళే సరళ రేఖను అడ్డుకొలత అంటారు. అడ్డుకొలతను వ్యాసం అని కూడా అంటారు. అడ్డుకొలతను ఆంగ్లంలో డయామీటర్ అంటారు. వృత్తం యొక్క పొడవైన చోర్డ్స్ (తీగలు) గా అడ్డుకొలతలు ఉంటాయి. డయామీటర్ అనే ఆంగ్ల పదం వృత్తం లోపల అడ్డు కొలతలు అనే అర్థాల నిచ్చే డయా మరియు మెట్రాన్ అనే గ్రీకు భాష పదాల నుండి ఉద్భవించింది. ఆధునిక వాడుకలో డయామీటర్ యొక్క పొడవును డయామీటర్ (వ్యాసం యొక్క పొడవును వ్యాసం) అని పిలుస్తున్నారు.
==డయామీటర్ చిహ్నం==
In [[geometry]], the '''diameter''' of a [[circle]] is any straight [[line segment]] that passes through the center of the circle and whose endpoints are on the boundary of the circle. The diameters are the longest [[chord (geometry)|chords]] of the circle. The word "diameter" is derived from [[Greek language|Greek]] ''διάμετρος'' (''diametros''), "diagonal of a circle", from ''δια-'' (''dia-''), "across, through" + ''μέτρον'' (''metron''), "a measure"<ref>[http://www.etymonline.com/index.php?term=diameter Online Etymology Dictionary]</ref>).
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 set|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. Both quantities can be calculated efficiently using [[rotating calipers]].<ref>{{cite journal
| author = Toussaint, Godfried T.
| title = Solving geometric problems with the rotating calipers
| publisher=Proc. MELECON '83, Athens
|url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.155.5671
|year = 1983
}}</ref> 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]]. For a set of scattered points in the plane, the diameter of the points is the same as the diameter of their [[convex hull]].
==Generalizations==
The four definitions given above are special cases of a more general definition. The '''diameter''' of a [[subset]] of a [[metric space]] is the [[supremum|least upper bound]] of the distances between pairs of points in the subset. So, if ''A'' is the subset, the diameter is
:[[supremum|sup]] { d(''x'', ''y'') | ''x'', ''y'' ∈ ''A'' } .
If the [[distance function]] d is viewed here as having [[codomain]] '''R''' (the set of all [[real number]]s), this implies that the diameter of the [[empty set]] (the case {{nowrap|1=''A'' = ∅}}) equals −∞ ([[negative infinity]]). Some authors prefer to treat the empty set as a special case, assigning it a diameter equal to 0,<ref>[http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2004;task=show_msg;msg=0860.0002 Re: diameter of an empty set]</ref> which corresponds to taking the codomain of d to be the set of nonnegative reals.
In [[differential geometry]], the diameter is an important global [[Riemannian geometry|Riemannian]] [[invariant (mathematics)|invariant]]. In plane and coordinate geometry, a diameter of a [[conic section]] is any chord which passes through the conic's centre; such diameters are not necessarily of uniform length, except in the case of the circle, which has [[eccentricity (mathematics)|eccentricity]] ''e'' = 0.
In medical [[Idiom#Parlance|parlance]] the diameter of a [[lesion]] is the longest line segment whose endpoints are within the lesion.
==Diameter symbol==
[[Image:Technical Drawing Hole 01.png|thumb|122px|Sign {{Unicode|⌀}} in a technical drawing]]
[[Image:Sign diameter.png|thumb|150px|Sign {{Unicode|⌀}} from [[Autocad]] drawing]]
{{distinguish2|the Scandinavian letter "[[Ø]]" or the [[Empty set]] symbol {{italics correction|"}}''{{Unicode|∅}}''"}}
The [[symbol]] or [[variable (mathematics)|variable]] for diameter, {{Unicode|⌀}}, is [[Homoglyph|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 <tt>&#8960;</tt> or <tt>&#x2300;</tt>. The character can be obtained in [[Microsoft Windows]] by holding the {{key press|[[Alt key|Alt]]}} key down while entering {{key press|8}}{{key press|9}}{{key press|6}}{{key press|0}} on the [[numeric keypad]]. On an [[Apple, Inc.|Apple]] [[Macintosh]], the diameter symbol can be entered via the character palette (this is opened by pressing {{key press|Opt}}{{key press|Cmd}}{{key press|T}} in most applications), where it can be found in the Technical Symbols category.
The character often will not display correctly, however, since most [[Typeface|font]]s do not include it. In most situations the letter ø is acceptable, which is unicode 0248 (hexadecimal 00F8). It can be obtained in UNIX-like operating systems using a [[Compose key]] by pressing, in sequence, {{key press|[[Compose key|Compose]]}}{{key press|/}}{{key press|o}} and on a Macintosh by pressing {{key press|Opt}} {{key press|O}} (in both cases, that is the letter [[o]], not the number [[0 (number)|0]]).
In [[LaTeX]] the symbol is achieved with the command \diameter which is part of the wasysym package.
The diameter symbol {{Unicode|⌀}} is distinct from the [[empty set]] symbol {{Unicode|∅}}, from an ([[italic script|italic]]) uppercase [[Phi (letter)|phi]] ''Φ'', and from the Nordic vowel [[Ø]].<ref>{{citation|title=Unicode Explained|first=Jukka K.|last=Korpela|publisher=O'Reilly Media, Inc.|year=2006|isbn=978-0-596-10121-3|pages=23–24|url=http://books.google.com/books?id=lxndiWaFMvMC&pg=PA23}}.</ref>
==See also==
* [[Distance (graph theory)|Graph or network diameter]]
* [[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 [[circumradius|smallest enclosing ball]]
* [[Sauter mean diameter]]
* [[List_of_gear_nomenclature#Inside diameter|Inside diameter]]
==Notes==
{{reflist}}
[[Category:Elementary geometry]]
[[Category:Length]]
[[Category:Greek loanwords]]
==ఇవి కూడా చూడండి==
[[వర్గం:గణిత శాస్త్రము]]
[[వర్గం:పొడవు]]
[[en:Diameter]]
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