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  "body": "\n## Description\n\nThe cosine function has exactly one zero in the interval $[0, 2]$. The number $\\pi$ is twice this zero.\nSo $\\cos(\\pi/2) = 0$, and\n$$\\pi \\approx 3.14159265.$$\n\n## Remarks\n\nA zero exists by the [[intermediate value theorem|00KAFBR32E]], since $\\cos 0 = 1$ and $\\cos 2 \u003c 0$. It is unique because $\\cos$ is strictly decreasing on $[0, 2]$, by [[its derivative|0V2DV29EGT]] $-\\sin$.\nWith this definition, $\\pi$ is the ratio of the circumference of a circle to its diameter, and the area of the unit disc.\nMathlib defines `Real.pi` in the same way, as twice the zero of $\\cos$ in $[1, 2]$.\nWilliam Jones first used the letter $\\pi$ for this ratio, in 1706. Around 250 BC, Archimedes approximated $\\pi$ with regular polygons.\n\n## Explanations\n\n### L1 human\n\nThe number $\\pi$ is the length of half of the unit circle.\nIn analysis, we find it through the first positive zero of cosine, which is $\\pi/2$.\n",
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