Mathematical entertainments

@article{Reingold2000MathematicalE,
  title={Mathematical entertainments},
  author={E. Reingold},
  journal={The Mathematical Intelligencer},
  year={2000},
  volume={22},
  pages={14-15}
}
  • E. Reingold
  • Published 2000
  • Mathematics
  • The Mathematical Intelligencer
Cutting a Pie Is Not a Piece of Cake
TLDR
This work provides complete answers for both cakes and pies and gives some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. Expand
Ground and Explanation in Mathematics
© 2019 Marc Lange This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. I ncreased attention has recently been paid to the fact that in mathematicalExpand
Towards a philosophical account of explanation in mathematics
All proofs show that their conclusions are true; some also explain why they are true. But what makes a proof (or argument) explanatory, if it is? That is the central question of my thesis. I begin byExpand
3 Persons, 2 Cuts: A Maximin Envy-Free and a Maximally Equitable Cake-Cutting Algorithm
We describe a 3-person, 2-cut envy-free cake-cutting algorithm, inspired by a continuous moving-knife procedure, that does not require that the players continuously move knifes across the cake. ByExpand
Explanatory Proofs and Beautiful Proofs
This paper concerns the relation between a proof’s beauty and its explanatory power — that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. ExplanatoryExpand
The Laurent Phenomenon and Discrete Integrable Systems
The Laurent phenomenon is the property that the solution to an initial value problem of a discrete equation is expressed as a Laurent polynomial of the initial values. This concept has arisen fromExpand
The Efficiency of Fair Division with Connected Pieces
TLDR
This work focuses on divisions that give each agent a single (contiguous) piece of the cake and provides tight bounds on the possible degradation in utilitarian and egalitarian welfare resulting from meeting the fairness requirements. Expand
N-Person Cake-Cutting: There May Be No Perfect Division
TLDR
It is proved that no perfect division exists for more than 4 cuts and for an extension of this example to more than three players. Expand
The Laurent Phenomenon and Discrete Integrable Systems (The breadth and depth of nonlinear discrete integrable systems)
The Laurent phenomenon is the property that the solution to an initial value problem of a discrete equation is expressed as a Laurent polynomial of the initial values. This concept has arisen fromExpand
The Solitaire Memory Game
Memory is a popular card game played by people of all ages around the world. Given a set of n pairs of cards laid out face down, a player may in one move turn over two cards one after another. If theExpand
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References

SHOWING 1-4 OF 4 REFERENCES
Reingold Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801-2987 USA e-mail: reingold@cs.uiuc
  • Reingold Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801-2987 USA e-mail: reingold@cs.uiuc
  • 2000
The Average-Case Complexity of Determining the Majority
TLDR
It is proved that pairwise equal/not equal color comparisons are necessary and sufficient to determine the majority color in the average case. Expand
Determining the Majority
TLDR
A new, simple proof of this lower bound that pairwise equal/not equal colour comparisons are necessary and sufficient to determine the majority color is presented. Expand
Both papers deal with (exact, achievable) lower bounds
  • Both papers deal with (exact, achievable) lower bounds