# Category:Euclidean Metric

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This category contains results about the Euclidean metric.

Definitions specific to this category can be found in Definitions/Euclidean Metric.

The **Euclidean metric** on $A_{1'} \times A_{2'}$ is defined as:

- $\map {d_2} {x, y} := \paren {\paren {\map {d_{1'} } {x_1, y_1} }^2 + \paren {\map {d_{2'} } {x_2, y_2} }^2}^{1/2}$

where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in A_{1'} \times A_{2'}$.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Euclidean Metric"

The following 14 pages are in this category, out of 14 total.

### E

- Euclidean Metric and Chebyshev Distance on Real Metric Space give rise to Same Topological Space
- Euclidean Metric is Metric
- Euclidean Metric on Real Number Line is Metric
- Euclidean Metric on Real Number Plane is Rotation Invariant
- Euclidean Metric on Real Number Space is Translation Invariant
- Euclidean Metric on Real Vector Space is Metric
- Existence of Translation between Each Pair of Points in Euclidean Space