Example · High school
Terms
| Term | This example | Why |
|---|
| Euclidean distance |
$d_2(p, q) = \sqrt{3^2 + 4^2} = 5$
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The straight-line distance is $5$, the distance along the axes is $3 + 4 = 7$, and the larger difference is $4$. Every pair of different points is at discrete distance $1$.
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| Taxicab distance |
$d_1(p, q) = 3 + 4 = 7$
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| Chebyshev distance |
$d_{\infty}(p, q) = \max(3, 4) = 4$
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| geodesic distance |
$5$
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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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| discrete metric |
$d(p, q) = 1$
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The discrete distance between $p = (1, 1)$ and $q = (4, 5)$ is $1$, because $p \neq q$.
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Distinctions using this example
- Types of distances: The points $(1, 1)$ and $(4, 5)$ differ by $3$ in the first coordinate and $4$ in the second.
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