The ham sandwich theorem and some related results
نویسندگان
چکیده
منابع مشابه
Leftovers from the Ham Sandwich Theorem
The traditional proofisa clev eruseoftheBorsuk-Ulamtheorem;see[1,p.120] . As Munkresremarks[5,p.405] ,theham sandwic h theoremisnotelemen tary ,evenindimension2,whereitisknown asthebabyham sandwichtheorem. But isitreally sohard? Consider thefollo wing:\aplanethroughthecentresofgravit y ofeach ofthebodieswill dothetric k" [3,p.57].Unfortunately ,thiseductiv eargumentjustdoesn’t work:a plane thro...
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The ham-sandwich theorem states that, given d ≥ 2 measures in R, it is possible to divide all of them in half with a single (d − 1)-dimensional hyperplane. We study an orthogonal version of the ham-sandwich theorem and define an orthogonal cut using at most d hyperplanes orthogonal to coordinate axes. For example, a hyperplane orthogonal to a coordinate axis and the boundary of an orthant are o...
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The conclusion of the classical ham sandwich theorem of Banach and Steinhaus may be strengthened: there always exists a common bisecting hyperplane that touches each of the sets, that is, intersects the closure of each set. Hence, if the knife is smeared with mayonnaise, a cut can always be made so that it will not only simultaneously bisect each of the ingredients, but it will also spread mayo...
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متن کاملA stronger conclusion to the classical ham sandwich theorem
The conclusion of the classical ham sandwich theorem for bounded Borel sets may be strengthened, without additional hypotheses – there always exists a common bisecting hyperplane that touches each of the sets, that is, that intersects the closure of each set. In the discrete setting, where the sets are finite (and the measures are counting measures), there always exists a bisecting hyperplane t...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1981
ISSN: 0035-7596
DOI: 10.1216/rmj-1981-11-3-473