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  "body": "\n## Summary\n\nA Schwarz–Christoffel mapping is a conformal map from the upper half-plane onto the interior of a polygon.\nSuch maps have an explicit integral form, in which the derivative is a product of powers of linear factors, one for each vertex.\nThe exponents come from the angles of the polygon, while the positions of the preimages of the vertices must usually be found numerically.\nThe formula is one of the few cases where the Riemann mapping theorem comes with a concrete map.\nIt is much used in engineering and in numerical conformal mapping.\n\n## Explanations\n\n### L1 human\n\nA conformal map from the half-plane must bend the straight boundary line into the edges of a polygon.\nAlong the real axis, the direction of the image changes only at a few points, where it turns by the exterior angle of a corner.\nA factor $(z - x_k)^{\\alpha_k - 1}$ in the derivative does exactly this: it turns the direction by a fixed angle when $z$ passes $x_k$.\nFor instance, $z \\mapsto z^{1/2}$ maps the upper half-plane onto the quarter-plane, a polygon with one corner of angle $\\pi/2$ at $0$ and one at infinity.\n",
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