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  "body": "\n## Definition\n\nLet $c \\in \\mathbb{C}$ and let $R \u003e 0$ be a real number.\nLet $f$ be a complex function that is continuous on the circle $\\{z : |z - c| = R\\}$.\nThe circle integral of $f$ over this circle is the [[contour integral|00FWNP9TXY]] along the path $\\gamma(\\theta) = c + R e^{i\\theta}$, $\\theta \\in [0, 2\\pi]$:\n$$\\oint_{|z - c| = R} f(z) \\, dz = \\int_0^{2\\pi} f(c + R e^{i\\theta}) \\, i R e^{i\\theta} \\, d\\theta.$$\n\n## Remarks\n\nThe path goes once around the circle, in the positive (counterclockwise) direction.\nThe length of the path is $2 \\pi R$.\nThe basic example is the [[integral of 1/z|0SXZ68HV6F]]: $\\oint_{|z| = 1} \\frac{dz}{z} = 2 \\pi i$.\n\n## Explanations\n\n### L1 human\n\nA circle integral is a contour integral where the path is a circle, traveled once counterclockwise.\nCircles are the paths that appear most in complex analysis, for example in [[Cauchy's integral formula|0DG10TVYPN]].\n",
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