Showing papers in "American Mathematical Monthly in 1989"
1,191 citations
155 citations
TL;DR: The year 1987 was the centenary of Ramanujan's birth, which was the first year of modern algebraic manipulation software, such as MACSYMA as discussed by the authors, and it is possible to see how much more spectacular his already astonishing career might have been had he lived to have access to powerful algebraic manipulators.
Abstract: The year 1987 was the centenary of Ramanujan’s birth. He died in 1920 Had he not died so young, his presence in modern mathematics might be more immediately felt. Had he lived to have access to powerful algebraic manipulation software, such as MACSYMA, who knows how much more spectacular his already astonishing career might have been.
127 citations
103 citations
TL;DR: A calisson is a French sweet that looks like two equilateral triangles meeting along an edge as mentioned in this paper, and the long diagonal of each calisson in the box is parallel to one of three different lines, as in the picture.
Abstract: A calisson is a French sweet that looks like two equilateral triangles meeting along an edge. Calissons could come in a box shaped like a regular hexagon, and their packing would suggest an interesting combinatorial problem. Suppose a box with side of length n is filled with sweets of sides of length 1. The long diagonal of each calisson in the box is parallel to one of three different lines, as in the picture.
90 citations
TL;DR: O'Hara as mentioned in this paper gave a constructive proof of the unimodality of the Gaussian polynomials and proved it in the American Mathematical Monthly: Vol. 96, No. 7, 1989.
Abstract: (1989). Kathy O'Hara's Constructive Proof of the Unimodality of the Gaussian Polynomials. The American Mathematical Monthly: Vol. 96, No. 7, pp. 590-602.
80 citations
TL;DR: An Elementary Test for the Galois Group of a Quartic Polynomial is described in this paper, where an elementary test for Galois group of a quartic polynomial.
Abstract: (1989). An Elementary Test for the Galois Group of a Quartic Polynomial. The American Mathematical Monthly: Vol. 96, No. 2, pp. 133-137.
78 citations
68 citations
66 citations
TL;DR: Spencer and Lovasz as discussed by the authors studied combinatorial analysis, particularly Ramsey theory and the probabilistic method, and obtained their degrees from the Eotvos Lorind University in Budapest in 1971.
Abstract: Joel Spencer is Professor of Mathematics and Computer Science at the Courant Institute. His research interests are in combinatorial analysis, particularly Ramsey theory and the probabilistic method. Laszlo Lovasz received his Dr.Rher.Nat. degree from the Eotvos Lorind University in Budapest in 1971. Currently he is Professor of Computer Science at the Eotv6s Lorand University and at Princeton University.
65 citations
TL;DR: Gregory's series for π, truncated at 500,000 terms, gives to forty places in the world where π is truncated as mentioned in this paper, and gives to four places in which π = 3.141590653589793240462643383269502884197.
Abstract: Gregory’s series for π, truncated at 500,000 terms, gives to forty places
$$4\sum\limits_{k = 1}^{500.000} {\frac{{{{\left( { - 1} \right)}^{k - 1}}}}{{2k - 1}}} = 3.141590653589793240462643383269502884197$$
TL;DR: The conjecture of Moser and the problem of Erdos were investigated in this article, where Pach's number was shown to be the same as Moser's number and the conjecture was proved.
Abstract: Keywords: conjecture of Leo Moser ; problem of Erdos Note: Professor Pach's number: [056] Reference DCG-ARTICLE-1989-001doi:10.2307/2325175 Record created on 2008-11-14, modified on 2017-05-12
TL;DR: In this paper, a demonstration de la continuite des racines d'un polynome qui n'utilise pas le theoreme de Rouche is presented, in which the polynomials continuité des racine d'a polynomes.
Abstract: On donne une demonstration de la continuite des racines d'un polynome qui n'utilise pas le theoreme de Rouche
TL;DR: In this article, a Motivated Proof of the Rogers-Ramanujan Identities is presented, which is based on the concept of a "motivated proof" of the identity.
Abstract: (1989). A Motivated Proof of the Rogers-Ramanujan Identities. The American Mathematical Monthly: Vol. 96, No. 5, pp. 401-409.
TL;DR: In this article, a nouvelle approche de l'inegalite isoperimetrique par la formule de Stokes complexe and la theorie of l'approximation rationnelle is presented.
Abstract: Etude d'une nouvelle approche de l'inegalite isoperimetrique par la formule de Stokes complexe et la theorie de l'approximation rationnelle
TL;DR: In this article, normalized symmetric functions, Newton's Inequalities, and a new set of Stronger inequalities are discussed. But they do not consider the relation between normalized Symmetric Functions and Stronger Inequality.
Abstract: (1989). Normalized Symmetric Functions, Newton's Inequalities, and a New Set of Stronger Inequalities. The American Mathematical Monthly: Vol. 96, No. 9, pp. 815-819.
TL;DR: Arakelian's Approximation Theorem has been studied extensively in the literature, see as mentioned in this paper for an overview. But this paper is not an extended version of the article presented here.
Abstract: (1989). Arakelian's Approximation Theorem. The American Mathematical Monthly: Vol. 96, No. 5, pp. 432-434.
TL;DR: In this article, Minimal Periods of Discrete and Smooth Orbits (MDSO) are studied. But they do not consider smooth ornaments, and they are not considered in this paper.
Abstract: (1989). Minimal Periods of Discrete and Smooth Orbits. The American Mathematical Monthly: Vol. 96, No. 1, pp. 5-17.
TL;DR: In this paper, a very short proof of Stirling's formula is presented, and the proof is used to prove the existence of the Stirling formula. The American Mathematical Monthly: Vol. 96, No. 1, pp. 41-42.
Abstract: (1989). A Very Short Proof of Stirling's Formula. The American Mathematical Monthly: Vol. 96, No. 1, pp. 41-42.
TL;DR: I bought my first home computer about nine years ago, and after opening the carton, following the setup instructions minutely, and finally getting the thing working on my dining room table, I wrote a little Basic* program that kept the computer working for a very long time and made a rather pretty, or anyway interesting, pattern on the screen, for the price of just a few program instructions.
Abstract: (1989). The Editor's Corner: The White Screen Problem. The American Mathematical Monthly: Vol. 96, No. 8, pp. 704-707.
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TL;DR: The Butterfly Curve as discussed by the authors is a well-known example of the butterfly curve and it has been studied extensively in the mathematical community, e.g., in the American Mathematical Monthly: Vol. 96, No. 5, pp. 442-443
Abstract: (1989). The Butterfly Curve. The American Mathematical Monthly: Vol. 96, No. 5, pp. 442-443.
TL;DR: In this paper, the authors present a group in which every element has finite order and show that every element in the group has a finite order in the set of elements in which each element has finite order.
Abstract: (1989). On Groups in Which Every Element Has Finite Order. The American Mathematical Monthly: Vol. 96, No. 4, pp. 297-308.
TL;DR: The goal is to derive properties of the Vandermonde matrix not in a faster manner, but in a more integrated and straightforward one, and to offer a bridge between two disciplines of thought: on the one hand that of the engineer, speaking of transforms, and on the other that the algebraist,speaking of homomorphisms.
Abstract: (1989). On the Vandermonde Matrix. The American Mathematical Monthly: Vol. 96, No. 10, pp. 921-924.
TL;DR: The Shortest Planar Arc of Width 1 as mentioned in this paper 1 is the shortest planar arc of width 1 in the planar plane and has been shown to be the shortest one in the plane.
Abstract: (1989). The Shortest Planar Arc of Width 1. The American Mathematical Monthly: Vol. 96, No. 4, pp. 309-327.
TL;DR: In this paper, the effect of prior calculus experience on introductory college calculus was studied and the effects of prior Calculus experience on the performance of introductory calculus were discussed. The American Mathematical Monthly: Vol. 96, No. 4, pp. 350-354.
Abstract: (1989). The Effect of Prior Calculus Experience on “Introductory” College Calculus. The American Mathematical Monthly: Vol. 96, No. 4, pp. 350-354.