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<H1>Euclidean distance</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
The straight line distance between two points.  In a plane with p<sub>1</sub> at (x<sub>1</sub>, y<sub>1</sub>) and p<sub>2</sub> at (x<sub>2</sub>, y<sub>2</sub>), it is  <img src="sqrt.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/sqrt.gif"   border=0 height=15 width=12 alt="square root of">((x<sub>1</sub> - x<sub>2</sub>)<sup>2</sup> + (y<sub>1</sub> - y<sub>2</sub>)<sup>2</sup>).
<P><strong>See also</strong>
<a href="rectilinear.html" tppabs="http://hissa.nist.gov/dads/HTML/rectilinear.html"><em>rectilinear</em></a>, <a href="manhttndstnc.html" tppabs="http://hissa.nist.gov/dads/HTML/manhttndstnc.html"><em>Manhattan distance</em></a>, <a href="lmdistance.html" tppabs="http://hissa.nist.gov/dads/HTML/lmdistance.html"><em>L<sub>m</sub> distance</em></a>.
<P><em>Note:
In N dimensions, the Euclidean distance between two points p and q is  <img src="sqrt.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/sqrt.gif"   border=0 height=15 width=12 alt="square root of">( <img src="Sigma.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Sigma.gif"  border=0 height=10 width=8  alt="summation"><sub>i=1</sub><sup>N</sup> (p<sub>i</sub>-q<sub>i</sub>)<sup>2</sup>) where p<sub>i</sub> (or q<sub>i</sub>) is the coordinate of p (or q) in dimension i.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Fri Oct 15 10:36:40 1999.<BR>
HTML page formatted Wed Dec 22 09:35:15 1999.

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