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  "body": "\n## Summary\n\nA configuration is a finite system of points and lines in which two points share at most one line.\nEvery point lies on the same number of lines, and every line contains the same number of points.\nA configuration with $p$ points on $\\gamma$ lines each and $\\ell$ lines with $\\pi$ points each is written $(p_\\gamma\\ \\ell_\\pi)$, and $(p_k)$ when $p = \\ell$ and $\\gamma = \\pi = k$.\nMany classical theorems of projective geometry, such as those of Desargues and Pappus, are statements that certain configurations close up.\n\n## Explanations\n\n### L1 human\n\nDraw some points and some lines so that the picture is completely regular: each point is on $3$ of the lines and each line passes through $3$ of the points.\nSuch a balanced picture is a configuration.\nCounting the pairs (point, line through it) in two ways gives $p \\gamma = \\ell \\pi$.\nThe Fano plane, with $7$ points and $7$ lines, is a $(7_3)$ configuration, but it cannot be drawn with straight lines in the real plane.\n",
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