"വ്യാസം" എന്ന താളിന്റെ പതിപ്പുകൾ തമ്മിലുള്ള വ്യത്യാസം
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വരി 22:
== സാമാന്യവത്കരണം ==
The definitions given above are only valid for circles, spheres and convex shapes. However, they are special cases of a more general definition which is valid for any kind of ''n''-dimensional convex or non-convex object, such as a [[hypercube]] or a set of scattered points. 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.
For any solid object or set of scattered points in n-dimensional [[Euclidean space]], the diameter of the object or set is the same as the diameter of its [[convex hull]].
In [[differential geometry]], the diameter is an important global [[Riemannian geometry|Riemannian]] [[invariant (mathematics)|invariant]].
In plane geometry, a diameter of a [[conic section]] is typically defined as 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.
== വ്യാസം: ചിഹ്നന സമ്പ്രദായം ==
[[Image:Technical Drawing Hole 01.png|thumb|122px|Sign {{Unicode|⌀}} in a technical drawing]]
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