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  "body": "\n## Summary\n\nThe Radon transform sends a function $f$ on $\\R^n$ to the function that gives the integral of $f$ over each hyperplane.\nIn the plane the hyperplanes are lines.\nThere the Radon transform records what an X-ray scanner measures: the total absorption along each line through a body.\nThe [[projection-slice theorem|J7VA040MC3]] links it to the [[Fourier transform|DPVM34ADZV]], and the [[Radon inversion formula|HN93ST5CBT]] recovers $f$ from its Radon transform.\nIt is the mathematical basis of computed tomography and a central object of integral geometry.\n\n## Explanations\n\n### L1 human\n\nShine parallel X-rays through a body and measure how much each ray is weakened.\nEach measurement is the integral of the density of the body along one line.\nDoing this for every direction and every offset gives the Radon transform of the density.\nFor example, the indicator of the unit disk has the integral $2\\sqrt{1 - s^2}$ over each line at distance $s \u003c 1$ from the center, the length of the chord.\nThe surprising fact is that these line integrals determine the density completely.\n",
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