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May 2022 A negative answer to Ulam's Problem 19 from the Scottish Book
Dmitry Ryabogin
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Ann. of Math. (2) 195(3): 1111-1150 (May 2022). DOI: 10.4007/annals.2022.195.3.5

Abstract

We give a negative answer to Ulam's Problem 19 from the Scottish Book asking 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 $d\ge 3$.

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Dmitry Ryabogin. "A negative answer to Ulam's Problem 19 from the Scottish Book." Ann. of Math. (2) 195 (3) 1111 - 1150, May 2022. https://doi.org/10.4007/annals.2022.195.3.5

Information

Published: May 2022
First available in Project Euclid: 29 April 2022

Digital Object Identifier: 10.4007/annals.2022.195.3.5

Subjects:
Primary: 52A20 , 52A38
Secondary: 52A10 , 52A15

Keywords: convex body , floating body , Ulam's problem

Rights: Copyright © 2022 Department of Mathematics, Princeton University

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Vol.195 • No. 3 • May 2022
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