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  "body": "\n## Summary\n\nA triangle center is a point attached to every [[triangle|0CTNFGYMM2]] by a fixed rule.\nThe rule must not depend on the labelling of the vertices, and it must commute with similarities.\nClassical examples are the [[centroid|0X7EEWES5G]], the [[incentre|0M9MX8YW0A]], the [[circumcentre|0F98FZK14A]] and the [[orthocentre|0WB619CA0V]].\nThe notion is made precise with trilinear coordinates, and Clark Kimberling's Encyclopedia of Triangle Centers catalogues many thousands of them.\n\n## Explanations\n\n### L1 human\n\nEvery triangle has several natural \"middle points\": the balance point, the centre of the inscribed circle, the centre of the circle through the corners, and so on.\nA triangle center is any such point given by a fixed recipe.\nThe recipe must treat the three corners in the same way, so renaming the corners gives the same point.\nIt must also behave well under scaling: enlarge the triangle and the point moves with it.\n",
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