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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12394 |
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| _version_ | 1866929219653599232 |
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| author | Ryabichev, Andrey Shcherbakov, Konstantin |
| author_facet | Ryabichev, Andrey Shcherbakov, Konstantin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Roots of polynomials and tangents of circles Ryabichev, Andrey Shcherbakov, Konstantin Classical Analysis and ODEs 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. |
| title | Roots of polynomials and tangents of circles |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.12394 |