Editing Euclidean distance (section)

=== Objects other than points ===
For pairs of objects that are not both points, the distance can most simply be defined as the smallest distance between any two points from the two objects, although more complicated generalizations from points to sets such as [[Hausdorff distance]] are also commonly used.<ref>{{citation|title=Metric Spaces|series=Springer Undergraduate Mathematics Series|first=Mícheál|last=Ó Searcóid|publisher=Springer|year=2006|isbn=978-1-84628-627-8|contribution=2.7 Distances from Sets to Sets|pages=29–30|url=https://books.google.com/books?id=aP37I4QWFRcC&pg=PA29}}</ref> Formulas for computing distances between different types of objects include:
*The [[distance from a point to a line]], in the Euclidean plane<ref name=baljer>{{citation|last1=Ballantine|first1=J. P.|last2=Jerbert|first2=A. R.|date=April 1952|department=Classroom notes|doi=10.2307/2306514|issue=4|journal=[[American Mathematical Monthly]]|jstor=2306514|pages=242–243|title=Distance from a line, or plane, to a point|volume=59}}</ref>
*The [[distance from a point to a plane]] in three-dimensional Euclidean space<ref name=baljer />
*The [[Skew lines#Distance|distance between two lines]] in three-dimensional Euclidean space<ref>{{citation|last=Bell|first=Robert J. T.|author-link=Robert J. T. Bell|edition=2nd|contribution=49. The shortest distance between two lines|contribution-url=https://archive.org/details/elementarytreati00bell/page/56/mode/2up|pages=57–61|publisher=Macmillan|title=An Elementary Treatise on Coordinate Geometry of Three Dimensions|year=1914}}</ref>
The distance from a point to a [[curve]] can be used to define its [[parallel curve]], another curve all of whose points have the same distance to the given curve.<ref>{{citation | last = Maekawa | first = Takashi | date = March 1999 | doi = 10.1016/s0010-4485(99)00013-5 | issue = 3 | journal = Computer-Aided Design | pages = 165–173 | title = An overview of offset curves and surfaces | volume = 31}}</ref>