Example · High school
Terms
| Term | This example | Why |
|---|
| Euclidean distance |
$d_2(p, q) = \sqrt{100^2 + 100^2} = 100 \sqrt{2} \approx 141.42$
|
|
| Taxicab distance |
$d_1(p, q) = 100 + 100 = 200$
|
|
| Chebyshev distance |
$d_{\infty}(p, q) = \max(100, 100) = 100$
|
The points $(0, 0)$ and $(100, 100)$ are far apart in the Euclidean, taxicab, and Chebyshev distances, which differ by factors of up to $2$.
|
| discrete metric |
$d(p, q) = 1$
|
The discrete distance between $p = (0, 0)$ and $q = (100, 100)$ is $1$, because $p \neq q$.
|
| geodesic distance |
$100 \sqrt{2}$
|
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.
|
Distinctions using this example
- Types of distances: In the discrete metric, they are at distance $1$, the same as every two different points, so the discrete metric does not measure size at all.
All examples · All distinctions · All definitions