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Floating Bodies

Caglar, Umut
http://rave.ohiolink.edu/etdc/view?acc_num=case1274467259

Abstract Details

2010, Master of Sciences, Case Western Reserve University, Mathematics.
We introduce various concepts of floating bodies, namely Ulam's floating body, Dupin's floating body, and the convex floating body and we give examples for the different concepts. In particular, we investigate if counterexamples to certain long standing open problems for the one type of bodies can be used for the other. One of the problems is Ulam's problem asking whether spheres are the only solids that can float in equilibrium in every direction. The other one is the homothety problem which asks if a body must be an ellipsoid if it is homothetic to its floating body. While there are partial solutions to these problems, complete solutions still need to be found.
Elisabeth Werner, PhD (Committee Chair)
Erkki Somersalo, PhD (Committee Member)
Mark Meckes, PhD (Committee Member)
50 p.
Mathematics
convex floating bodies; Ulam's problem; Homothety conjecture;

Recommended Citations

Citations

  • Caglar, U. (2010). Floating Bodies [Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1274467259

    APA Style (7th edition)

  • Caglar, Umut. Floating Bodies. 2010. Case Western Reserve University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1274467259.

    MLA Style (8th edition)

  • Caglar, Umut. "Floating Bodies." Master's thesis, Case Western Reserve University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=case1274467259

    Chicago Manual of Style (17th edition)

case1274467259
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This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.