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  "body": "\n## Example\n\nLet $n \\ge 1$ be an integer.\nFor points $x = (x_1, \\ldots, x_n)$ and $y = (y_1, \\ldots, y_n)$ in $\\mathbb{R}^n$, let\n$$d_2(x, y) = \\sqrt{\\sum_{i=1}^{n} (x_i - y_i)^2}.$$\nThen $d_2$ is a [[metric|063W5JMY85]] on $\\mathbb{R}^n$, the Euclidean metric.\n\n## Remarks\n\nFor $n = 1$, $d_2(x, y) = |x - y|$, the [[usual metric on the real line|0KXJTZSW9B]].\nFor $n = 2$, the formula is the theorem of Pythagoras for the segment from $x$ to $y$.\nThe triangle inequality for $d_2$ follows from the Cauchy–Schwarz inequality.\n\n## Explanations\n\n### L1 human\n\nThe Euclidean metric is the length of the straight segment between two points.\nIn the plane, the distance from $(0, 0)$ to $(3, 4)$ is $\\sqrt{9 + 16} = 5$.\n",
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