{
  "id": "2401.12394",
  "version": "v1",
  "published": "2024-01-22T22:55:54.000Z",
  "updated": "2024-01-22T22:55:54.000Z",
  "title": "Roots of polynomials and tangents of circles",
  "authors": [
    "Andrey Ryabichev",
    "Konstantin Shcherbakov"
  ],
  "comment": "7 pages, in Russian, 3 figures. Comments are welcome!",
  "categories": [
    "math.CA"
  ],
  "abstract": "Given a real cubic function $f(x)$ with three roots, take an equilateral triangle $ABC$, the projections of which vertices are the roots of $f(x)$. There is a folklore fact that the vertical lines through the extrema of $f(x)$ are tangent to the inscribed circle of $ABC$. We generalise this fact to a regular $n$-gon and the corresponding degree $n$ polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-22T22:55:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial",
      "real cubic function",
      "folklore fact",
      "equilateral triangle",
      "projections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}