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  "body": "\n## Definition\n\nIdentify the plane with $\\mathbb{C}$.\nA complex number $z$ is constructible if the point $z$ can be obtained from $0$ and $1$ by finitely many [[straightedge and compass|0DAECMZVRT]] steps.\nIn each step, one adds an intersection point of two distinct lines or circles drawn through, or centred at, points already obtained.\n\n## Remarks\n\nA real number $x$ is constructible if and only if a segment of length $|x|$ can be constructed from a segment of length $1$.\nA complex number $a + b i$ is constructible if and only if $a$ and $b$ are constructible.\nThe constructible numbers [[form a field closed under square roots|0PN9WMRWT7]].\nThe numbers $\\sqrt{2}$, $\\sqrt{1 + \\sqrt{3}}$ and $\\cos(2\\pi/5)$ are constructible. The numbers $\\sqrt[3]{2}$ and $\\pi$ are not.\n\n## Explanations\n\n### L1 human\n\nStart with two points, $0$ and $1$.\nDraw lines through points you have, and circles centred at points you have, and mark the new intersections.\nThe constructible numbers are all the points you can reach in this way.\n",
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