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  "body": "\n## Problem\n\nGiven the edge of a cube, construct with [[straightedge and compass|0DAECMZVRT]] alone the edge of a cube with twice the volume.\n\n## Remarks\n\nFor an edge of length $1$, the new edge has length $\\sqrt[3]{2}$.\nSo the problem asks whether $\\sqrt[3]{2}$ is a [[constructible number|0FMN2MN7TM]].\nThe answer is no: [[doubling the cube is impossible|0CQ357M0QS]].\nThe problem has solutions with other tools, such as a marked ruler or conic sections.\n\n## History\n\nThe problem is also called the Delian problem, after a legend about an oracle on the island of Delos.\nHippocrates of Chios showed that it is equivalent to finding two mean proportionals between a segment and a segment twice as long.\nPierre Wantzel proved in 1837 that no straightedge and compass solution exists.\n\n## Explanations\n\n### L1 human\n\nThe problem asks to build a cube with twice the volume of a given cube, using only an unmarked ruler and a compass.\nIt is one of the three classical construction problems of Greek geometry.\n",
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