Example · High school
Terms
| Term | This example | Why |
|---|
| Euclidean distance |
$d_2(p, q) = \sqrt{1^2 + 0^2 + 1^2} = \sqrt{2} \approx 1.41$
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The Euclidean distance $\sqrt{2} \approx 1.41$ is shorter, because the straight segment cuts through the inside of the sphere.
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| Taxicab distance |
$d_1(p, q) = 1 + 0 + 1 = 2$
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| Chebyshev distance |
$d_{\infty}(p, q) = \max(1, 0, 1) = 1$
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| discrete metric |
$d(p, q) = 1$
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The discrete distance between $p = (0, 0, 1)$ and $q = (1, 0, 0)$ is $1$, because $p \neq q$.
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| geodesic distance |
$\frac{\pi}{2} \approx 1.57$
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The geodesic distance on the unit sphere from the north pole to a point on the equator is the length of a quarter of a great circle, $\frac{2 \pi}{4} = \frac{\pi}{2}$.
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