Example · High school
Terms
| Term | This example | Why |
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| Euclidean distance |
$d_2(p, q) = \sqrt{2^2 + 0^2} = 2$
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| Taxicab distance |
$d_1(p, q) = 2 + 0 = 2$
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| Chebyshev distance |
$d_{\infty}(p, q) = \max(2, 0) = 2$
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The points $(0, 0)$ and $(2, 0)$ lie on a line parallel to an axis, so the Euclidean, taxicab, and Chebyshev distances all equal $2$.
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| discrete metric |
$d(p, q) = 1$
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The discrete distance between $p = (0, 0)$ and $q = (2, 0)$ is $1$, because $p \neq q$.
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| geodesic distance |
$2$
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In the plane, the geodesic distance between $p$ and $q$ equals the Euclidean distance, because the straight segment from $p$ to $q$ stays in the plane.
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