Packing a cake into a box

Mikhail Skopenkov

doi:10.4169/amer.math.monthly.118.05.424

Packing a cake into a box

Mikhail Skopenkov

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Pages (from-to)	424
Journal	The American Mathematical Monthly
Volume	118
Issue number	5
DOIs	https://doi.org/10.4169/amer.math.monthly.118.05.424
State	Published - Jun 13 2011

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

ASJC Scopus subject areas

General Mathematics

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10.4169/amer.math.monthly.118.05.424

Cite this

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title = "Packing a cake into a box",

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. {\textcopyright} THE MATHEMATICAL ASSOCIATION OF AMERICA.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.",

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N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/561765

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JO - The American Mathematical Monthly

JF - The American Mathematical Monthly

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Packing a cake into a box

Abstract

Bibliographical note

ASJC Scopus subject areas

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