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  "body": "\n## Summary\n\nThe amoeba of a complex polynomial in $n$ variables is the image of its zero set in $(\\C^\\times)^n$ under a logarithmic map.\nThis map takes the logarithm of the absolute value of each coordinate.\nThe name, given by Gelfand, Kapranov and Zelevinsky, comes from its shape: a body with thin tentacles going off to infinity.\nEach connected component of the complement is convex, and the number of these components is bounded by the [[Newton polytope|CYTTX8KHC8]].\nAmoebas link complex algebraic geometry with convex geometry and degenerate to tropical varieties, see [[tropical geometry|7YTC3BHK60]].\n\n## Explanations\n\n### L1 human\n\nTake the complex solutions of $1 + z + w = 0$ and record only the sizes $\\abs{z}$ and $\\abs{w}$, on a logarithmic scale.\nThe resulting region in the plane looks like a creature with three long arms.\nThe arms reach to infinity in three directions, where one of $z$, $w$ is tiny or both are huge.\nBetween the arms lie three convex holes.\nZooming out, the region shrinks to three rays from a point, the tropical line.\n",
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