Packing a cake into a box

Handle URI:
http://hdl.handle.net/10754/561765
Title:
Packing a cake into a box
Authors:
Skopenkov, Mikhail
Abstract:
Given a triangular cake and a box in the shape of its mirror image, how can the cake be cut into a minimal number of pieces so that it can be put into the box? The cake has icing, so we are not allowed to put it into the box upside down. V. G. Boltyansky asked this question in 1977 and showed that three pieces always suffice. In this paper we provide examples of cakes that cannot be cut into two pieces to be put into the box. This shows that three is the answer to Boltyansky's question. We also give examples of cakes which can be cut into two pieces. © THE MATHEMATICAL ASSOCIATION OF AMERICA.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Mathematical Association of America
Journal:
American Mathematical Monthly
Issue Date:
May-2011
DOI:
10.4169/amer.math.monthly.118.05.424
ARXIV:
arXiv:1003.2101
Type:
Article
ISSN:
00029890
Sponsors:
The author is grateful to R. Clawson, B. R. Frenkin, A. A. Glazyrin, I. V. Izmestiev, and M. V. Prasolov for useful discussions. The author is also grateful to his wife Anastasia for some figures and cakes. The author was supported in part by the Moebius Contest Foundation for Young Scientists and the Euler Foundation.
Additional Links:
http://arxiv.org/abs/arXiv:1003.2101v1
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorSkopenkov, Mikhailen
dc.date.accessioned2015-08-03T09:04:06Zen
dc.date.available2015-08-03T09:04:06Zen
dc.date.issued2011-05en
dc.identifier.issn00029890en
dc.identifier.doi10.4169/amer.math.monthly.118.05.424en
dc.identifier.urihttp://hdl.handle.net/10754/561765en
dc.description.abstractGiven a triangular cake and a box in the shape of its mirror image, how can the cake be cut into a minimal number of pieces so that it can be put into the box? The cake has icing, so we are not allowed to put it into the box upside down. V. G. Boltyansky asked this question in 1977 and showed that three pieces always suffice. In this paper we provide examples of cakes that cannot be cut into two pieces to be put into the box. This shows that three is the answer to Boltyansky's question. We also give examples of cakes which can be cut into two pieces. © THE MATHEMATICAL ASSOCIATION OF AMERICA.en
dc.description.sponsorshipThe author is grateful to R. Clawson, B. R. Frenkin, A. A. Glazyrin, I. V. Izmestiev, and M. V. Prasolov for useful discussions. The author is also grateful to his wife Anastasia for some figures and cakes. The author was supported in part by the Moebius Contest Foundation for Young Scientists and the Euler Foundation.en
dc.publisherMathematical Association of Americaen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1003.2101v1en
dc.titlePacking a cake into a boxen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalAmerican Mathematical Monthlyen
dc.identifier.arxividarXiv:1003.2101en
kaust.authorSkopenkov, Mikhailen
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