| 1. |
- Abramson, Nils, et al.
(författare)
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Plane intersections of rotational ellipsoids
- 2006
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Ingår i: The American mathematical monthly. - : JSTOR. - 0002-9890 .- 1930-0972. ; 113:4, s. 336-339
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Tidskriftsartikel (refereegranskat)
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| 2. |
- Bostan, Alin, et al.
(författare)
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On an Integral Identity
- 2021
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Ingår i: American Mathematical Monthly. - : Informa UK Limited. - 0002-9890 .- 1930-0972. ; 128:8, s. 737-743
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Tidskriftsartikel (refereegranskat)abstract
- We give three elementary proofs of a nice equality of definite integrals, recently proven by Ekhad, Zeilberger, and Zudilin. The equality arises in the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a generalization together with an equally elementary proof and discuss some consequences.
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| 3. |
- Deijfen, Maria, et al.
(författare)
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Friendly Frogs, Stable Marriage, and the Magic of Invariance
- 2017
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Ingår i: The American mathematical monthly. - : Informa UK Limited. - 0002-9890 .- 1930-0972. ; 124:5, s. 387-402
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a two-player game involving two tokens located at points of a fixed set. The players take turns moving a token to an unoccupied point in such a way that the distance between the two tokens is decreased. Optimal strategies for this game and its variants are intimately tied to Gale-Shapley stable marriage. We focus particularly on the case of random infinite sets, where we use invariance, ergodicity, mass transport, and deletion-tolerance to determine game outcomes.
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| 4. |
- Eriksen, Niklas, 1974
(författare)
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The freshman's approach to Conway's napkin problem
- 2008
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Ingår i: The American mathematical monthly. - Washington, USA : Mathematical Association of America. - 0002-9890 .- 1930-0972. ; 115:6, s. 492-498
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Tidskriftsartikel (refereegranskat)abstract
- In the March 2006 issue of the MONTHLY, Claesson and Petersen gave a thorough solution to Conway's napkin problem. The problem is the following: Assume that n mathematicians arrive in random order at a conference dinner with a circular table, and that the napkins are placed exactly halfway between the plates so that the guests do not know whether they are supposed to use the right or the left napkin. Each guest prefers these napkins with probabilities p and 1-p, respectively, and tries her preferred alternative before trying the other, if the preferred napkin has been taken. Which proportion of guests is expected to sit down at a place where both adjacent napkins have been taken and thus be without a napkin? Claesson and Petersen use a system of generating functions to compute both the expectation and the variance of this proportion and to address similar questions, for instance regarding the number of guests who get a napkin though not the preferred one. However, these expectations can also be computed using purely elementary methods, such as the binomial theorem. We present the freshman's approach to the napkin problem and related problems, for instance the one with French diners mentioned, but not solved, by Claesson and Petersen.
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| 5. |
- Holst, Lars
(författare)
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A proof of Euler's infinite product for the sine
- 2012
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Ingår i: The American mathematical monthly. - : Informa UK Limited. - 0002-9890 .- 1930-0972. ; 119:6, s. 518-521
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Tidskriftsartikel (refereegranskat)abstract
- The product formula for the sine function is proved using the Gamma function and elementary probability theory. Some corollaries of the sine formula are also pointed out.
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| 6. |
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| 7. |
- Kufner, Alois, et al.
(författare)
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The prehistory of the Hardy inequality
- 2006
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Ingår i: The American mathematical monthly. - : Informa UK Limited. - 0002-9890 .- 1930-0972. ; 113:8, s. 715-732
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Tidskriftsartikel (refereegranskat)
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| 8. |
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| 9. |
- Lu, Zhiqin, et al.
(författare)
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The Sound of Symmetry
- 2015
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Ingår i: The American mathematical monthly. - : Informa UK Limited. - 0002-9890 .- 1930-0972. ; 122:9, s. 815-835
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Tidskriftsartikel (refereegranskat)abstract
- The inverse spectral problem was popularized by M. Kac's 1966 article in THIS MONTHLY “Can one hear the shape of a drum?” Although the answer has been known for over twenty years, many open problems remain. Intended for general audiences, readers are challenged to complete exercises throughout this interactive introduction to inverse spectral theory. The main techniques used in inverse spectral problems are collected and discussed, then used to prove that one canhear the shape of: parallelograms, acute trapezoids, and the regular n-gon. Finally, we show that one can realistically hear the shape of the regular n-gon amongst all convex n-gons because it is uniquely determined by a finite number of eigenvalues; the sound of symmetry can really be heard!
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| 10. |
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