ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS

doi:10.1007/s10473-025-0119-5

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 237-256.doi: 10.1007/s10473-025-0119-5

ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS

Chunyan Liu¹, Elisabeth M. Werner², Deping Ye³, Ning Zhang⁴

1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430048, China;
2. Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA;
3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7;
4. School of Mathematics and Statistics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China

收稿日期:2024-09-22 修回日期:2024-10-26 出版日期:2025-02-06 发布日期:2025-02-06
作者简介:Chunyan Liu, E-mail,: chunyanliu@whpu.edu.cn; Elisabeth M. Werner, E-mail,: elisabeth.werner@case.edu; Deping Ye, E-mail,: deping.ye@mun.ca; Ning Zhang, E-mail,: nzhang2@hust.edu.cn
基金资助:
Chunyan Liu's work was supported by the Research Funding of Wuhan Polytechnic University (2024RZ083). Elisabeth M. Werner's work was supported by the NSF grant DMS-2103482. Deping Ye's work was supported by an NSERC grant, Canada. Ning Zhang's work was supported by the NSF of China (11901217, 11971005).

ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS

Chunyan Liu¹, Elisabeth M. Werner², Deping Ye³, Ning Zhang⁴

1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430048, China;
2. Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA;
3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7;
4. School of Mathematics and Statistics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China

Received:2024-09-22 Revised:2024-10-26 Online:2025-02-06 Published:2025-02-06
About author:Chunyan Liu, E-mail,: chunyanliu@whpu.edu.cn; Elisabeth M. Werner, E-mail,: elisabeth.werner@case.edu; Deping Ye, E-mail,: deping.ye@mun.ca; Ning Zhang, E-mail,: nzhang2@hust.edu.cn
Supported by:
Chunyan Liu's work was supported by the Research Funding of Wuhan Polytechnic University (2024RZ083). Elisabeth M. Werner's work was supported by the NSF grant DMS-2103482. Deping Ye's work was supported by an NSERC grant, Canada. Ning Zhang's work was supported by the NSF of China (11901217, 11971005).

摘要/Abstract

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.

关键词: floating body, affine surface area, log-concave functions

Abstract: 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.

Key words: floating body, affine surface area, log-concave functions

中图分类号:

52A20

Chunyan Liu, Elisabeth M. Werner, Deping Ye, Ning Zhang. ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS[J]. 数学物理学报(英文版), 2025, 45(1): 237-256.

Chunyan Liu, Elisabeth M. Werner, Deping Ye, Ning Zhang. ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS[J]. Acta mathematica scientia,Series B, 2025, 45(1): 237-256.

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ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS

ARCHIMEDES' PRINCIPLE OF FLOTATION AND FLOATING BODIES: CONSTRUCTION, EXTENSIONS AND RELATED PROBLEMS

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