A negative answer to Ulam's Problem 19 from the Scottish Book
| Autor: | Ryabogin, Dmitry |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give a negative answer to Ulam's Problem 19 from the Scottish Book asking {\it is a solid of uniform density which will float in water in every position a sphere?} Assuming that the density of water is $1$, we show that there exists a strictly convex body of revolution $K\subset {\mathbb R^3}$ of uniform density $\frac{1}{2}$, which is not a Euclidean ball, yet floats in equilibrium in every orientation. We prove an analogous result in all dimensions $d\ge 3$. Comment: 7 figures. arXiv admin note: text overlap with arXiv:1201.0393 |
| Databáze: | arXiv |
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