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  "body": "\n## Summary\n\nA Steiner conic is a conic built synthetically from two pencils of lines.\nTake two points $U$ and $V$ and a projective map from the lines through $U$ to the lines through $V$.\nThe points where each line meets its image form the Steiner conic.\nIn a projective plane over a field, Steiner conics are exactly the non-degenerate [[projective conics|R3TMVHTP3A]], so this gives a definition of conics with no equations.\nThe construction goes back to Jakob Steiner.\n\n## Explanations\n\n### L1 human\n\nPin one ruler at a point $U$ and another at a point $V$.\nTurn them together by a fixed rule, so that each position of the first ruler decides the position of the second.\nMark where the two rulers cross.\nWhen the rule is a projective map, and the line $UV$ is not sent to itself, the marks trace out a conic through $U$ and $V$.\n",
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