# 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 7 subcategories, out of 7 total.

### B

- Bounded Euclidean Spaces (empty)

### E

- Euclidean Metric is Metric (3 P)

### S

- Scaled Euclidean Metric (3 P)

### U

- Unbounded Euclidean Spaces (empty)

## Pages in category "Euclidean Metric"

The following 15 pages are in this category, out of 15 total.

### E

- Euclidean Metric and Chebyshev Distance on Real Metric Space give rise to Same Topological Space
- Euclidean Metric induces Product Topology
- 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