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  "body": "\n## Summary\n\nPoints of an [[affine space|09XNAPTJQ7]] are affinely independent if none of them is an [[affine combination|0KJH6SRFZK]] of the others.\nEquivalently, the vectors from one of the points to the others are [[linearly independent|0CRMGPAH83]].\nAffinely independent points are the vertices of a simplex.\nIn an $n$-dimensional space, $n + 1$ of them form an affine frame, in which barycentric coordinates are defined.\n\n## Explanations\n\n### L1 human\n\nTwo points are affinely independent when they are different.\nThree points are affinely independent when they do not lie on one line, so they span a triangle.\nFour points are affinely independent when they do not lie in one plane, so they span a tetrahedron.\nIn general, affinely independent points are in \"general position\": no one of them lies in the flat spanned by the others.\n",
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