Editing Euclidean distance (section)

=== One dimension ===
The distance between any two points on the [[real line]] is the [[absolute value]] of the numerical difference of their coordinates, their [[absolute difference]]. Thus if <math>p</math> and <math>q</math> are two points on the real line, then the distance between them is given by:<ref name=smith>{{citation|title=Precalculus: A Functional Approach to Graphing and Problem Solving|first=Karl|last=Smith|publisher=Jones & Bartlett Publishers|year=2013|isbn=978-0-7637-5177-7|page=8|url=https://books.google.com/books?id=ZUJbVQN37bIC&pg=PA8}}</ref>

<math display=block>d(p,q) = |p-q|.</math>

A more complicated formula, giving the same value, but generalizing more readily to higher dimensions, is:<ref name=smith />

<math display=block>d(p,q) = \sqrt{(p-q)^2}.</math>

In this formula, [[square (algebra)|squaring]] and then taking the [[square root]] leaves any positive number unchanged, but replaces any negative number by its absolute value.<ref name=smith />