Si tratta di un importante risultato topologico noto anche come corollario al sandwich theorem proof pdf di Borsuk-Ulam. Il teorema del panino al prosciutto non va confuso con il teorema del sandwich, in Italia noto come teorema dei due carabinieri, che riguarda lo studio dei limiti di funzioni. 3, ossia in tre dimensioni, e abbiamo esattamente tre oggetti, ossia due fette di pane e una fetta di prosciutto: è possibile dividere un panino al prosciutto con un solo taglio netto in modo che la fetta di pane inferiore, la fetta di prosciutto e la fetta di pane superiore siano simultaneamente tagliate esattamente a metà? Il teorema dimostra che ciò è possibile.
An optimal time algorithm for ham-sandwich cuts in the plane”. In Proceedings of the Second Canadian Conference on Computational Geometry, pp.
A note on the ham sandwich theorem”. Left-overs from the Ham-Sandwich Theorem Amer. Questa pagina è stata modificata per l’ultima volta il 16 gen 2017 alle 16:24.
Vedi le condizioni d’uso per i dettagli. Tukey theorem after Arthur H. Beyer and Zardecki’s paper includes a translation of the 1938 paper.
The paper poses the problem in two ways: first, formally, as “Is it always possible to bisect three solids, arbitrarily located, with the aid of an appropriate plane? Can we place a piece of ham under a meat cutter so that meat, bone, and fat are cut in halves? Later, the paper offers a proof of the theorem. 2 at the positive side of the knife.
Cutting at that angle bisects both pancakes simultaneously. The proof is again a reduction to the Borsuk-Ulam theorem. A ham-sandwich cut of eight red points and seven blue points in the plane. In discrete geometry and computational geometry, the ham sandwich theorem usually refers to the special case in which each of the sets being divided is a finite set of points.
Here the relevant measure is the counting measure, which simply counts the number of points on either side of the hyperplane. For a finite set of points in the plane, each colored “red” or “blue”, there is a line that simultaneously bisects the red points and bisects the blue points, that is, the number of red points on either side of the line is equal and the number of blue points on either side of the line is equal.
There is an exceptional case when points lie on the line. A situation where the numbers of points on each side cannot match each other is provided by adding an extra point out of the line in the previous configuration. In computational geometry, this ham sandwich theorem leads to a computational problem, the ham sandwich problem.
Here all red points are on one side of some line and all blue points are on the other side, a situation where there is a unique ham sandwich cut, which Megiddo could find in linear time. Computing a ham sandwich cut in two dimensions”, J. An optimal time algorithm for ham-sandwich cuts in the plane”, Proceedings of the Second Canadian Conference on Computational Geometry, pp. This page was last edited on 10 October 2017, at 14:07.
Any help would be greatly appreciated. Can you take it from here? And as another tiny hint, there’s a metric space axiom you use over and over again that you will want to use here. Yeah, I’ve been taking that inequality over and over.