page_title: Equidistant set
section_title: Straight lines
hierarchical_section_title: Equidistant set / Examples / Straight lines
caption_attribution_description: English: Image showing equidistant set of two straight lines in an Euclidean plane.
context_page_description: In mathematics, an equidistant set is a set each of whose elements has the same distance from two or more sets. The equidistant set of two singleton sets in the Euclidean plane is the perpendicular bisector of the segment joining the two sets. The conic sections can also be realized as equidistant sets. This property of conics has been used to generalize the notion of conic sections. The concept of equidistant set is used to define frontiers in territorial domain controversies. For instance, the United Nations Convention on the Law of the Sea establishes that, in absence of any previous agreement, the delimitation of the territorial sea between countries occurs exactly on the median line every point of which is equidistant of the nearest points to each country. Though the usage of the terminology is quite old, the study of the properties of equidistant sets as mathematical objects was initiated only in 1970's.
caption: Image showing equidistant set of two straight lines in a Euclidean plane.
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