{
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    "quadrature-of-the-circle"
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      "target": "0X7CVDE3BG"
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  "body": "\n## Problem\n\nGiven a circle, construct with [[straightedge and compass|0DAECMZVRT]] alone a square with the same area.\n\n## Remarks\n\nFor a circle of radius $1$, the square has side $\\sqrt{\\pi}$.\nSo the problem asks whether $\\sqrt{\\pi}$ is a [[constructible number|0FMN2MN7TM]].\nThe answer is no: [[squaring the circle is impossible|0X7CVDE3BG]].\n\n## History\n\nAnaxagoras is the first known Greek to study the problem.\nHippocrates of Chios squared some figures bounded by circular arcs, the lunes of Hippocrates.\nIn 1882, Ferdinand von Lindemann proved that $\\pi$ is transcendental, and so that the construction is impossible.\n\n## Explanations\n\n### L1 human\n\nThe problem asks for a square with the same area as a given circle, with only an unmarked ruler and a compass.\nThe phrase \"squaring the circle\" now means to attempt something impossible.\n",
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  "markdown": "https://math2.tamnd.com/node/0BSXRER81B.md",
  "msc": [
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  "name": "Squaring the circle",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/0BS/0BSXRER81B.md",
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  "url": "https://math2.tamnd.com/wiki/squaring-the-circle/",
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