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<p>In this article, we explain how the famous Archimedes’ principle of flotation can be used to construct various floating bodies. We survey some of the most important results regarding the floating bodies, including their relations with affine surface area and projection body, their extensions in different settings such as space forms and log-concave functions, and mention some associated open problems.</p>

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Archimedes’ principle of flotation and floating bodies: construction, extensions and related problems

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Chunyan Liu,
  • Elisabeth M. Werner,
  • Deping Ye,
  • Ning Zhang

摘要

In this article, we explain how the famous Archimedes’ principle of flotation can be used to construct various floating bodies. We survey some of the most important results regarding the floating bodies, including their relations with affine surface area and projection body, their extensions in different settings such as space forms and log-concave functions, and mention some associated open problems.