Editing Distance (section)

===Straight-line or Euclidean distance===
{{main|Euclidean distance}}

The distance between two points in physical [[space]] is the [[length]] of a [[line segment|straight line]] between them, which is the shortest possible path.  This is the usual meaning of distance in [[classical physics]], including [[Newtonian mechanics]]. 

Straight-line distance is formalized mathematically as the [[Euclidean distance]] in [[two-dimensional Euclidean space|two-]] and [[three-dimensional space]].  In [[Euclidean geometry]], the distance between two points {{mvar|A}} and {{mvar|B}} is often denoted <math>|AB|</math>.  In [[Cartesian coordinate system|coordinate geometry]], Euclidean distance is computed using the [[Pythagorean theorem]]. The distance between points {{math|(''x''<sub>1</sub>, ''y''<sub>1</sub>)}} and {{math|(''x''<sub>2</sub>, ''y''<sub>2</sub>)}} in the plane is given by:<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Distance|url=https://mathworld.wolfram.com/Distance.html|access-date=2020-09-01|website=mathworld.wolfram.com|language=en}}</ref><ref>{{Cite web|title=Distance Between 2 Points|url=https://www.mathsisfun.com/algebra/distance-2-points.html|access-date=2020-09-01|website=www.mathsisfun.com}}</ref>
<math display="block">d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.</math>
Similarly, given points (''x''<sub>1</sub>, ''y''<sub>1</sub>, ''z''<sub>1</sub>) and (''x''<sub>2</sub>, ''y''<sub>2</sub>, ''z''<sub>2</sub>) in three-dimensional space, the distance between them is:<ref name=":0" />
<math display="block">d=\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}.</math>
This idea generalizes to higher-dimensional [[Euclidean space]]s.

==== Measurement ====
{{main|Distance measurement}}
There are many ways of [[measuring]] straight-line distances. For example, it can be done directly using a [[ruler]], or indirectly with a [[radar]] (for long distances) or [[interferometry]] (for very short distances).  The [[cosmic distance ladder]] is a set of ways of measuring extremely long distances.