Showing papers in "American Mathematical Monthly in 1999"
TL;DR: In this article, Sperner's Lemma in Fair Division in Rental Harmony has been studied in the context of the fair division problem, and the American Mathematical Monthly: Vol. 106, No. 10, pp. 930-942.
Abstract: (1999). Rental Harmony: Sperner's Lemma in Fair Division. The American Mathematical Monthly: Vol. 106, No. 10, pp. 930-942.
323 citations
268 citations
TL;DR: An elementary view of Euler's Summation Formula is presented in this paper, where an elementary view is used to define the Euler summation formula and the elementary version of the SumMation Formula.
Abstract: (1999). An Elementary View of Euler's Summation Formula. The American Mathematical Monthly: Vol. 106, No. 5, pp. 409-418.
158 citations
TL;DR: The American Mathematical Monthly (AMM) Vol. 106, No. 2, pp. 99-111 as discussed by the authors discusses the question "Do Mathematics Need New Axioms?"
Abstract: (1999). Does Mathematics Need New Axioms? The American Mathematical Monthly: Vol. 106, No. 2, pp. 99-111.
99 citations
TL;DR: In this paper, the authors introduce the concept of metric-preserving functions, and present an introduction to metric preserving functions in the context of metric preservation functions, including the following:
Abstract: (1999). Introduction to Metric-Preserving Functions. The American Mathematical Monthly: Vol. 106, No. 4, pp. 309-323.
90 citations
TL;DR: The Isoperimetric Problem on Surfaces as discussed by the authors has been studied extensively in the literature, see, e.g., the American Mathematical Monthly: Vol. 106, No. 5, pp. 430-439.
Abstract: (1999). The Isoperimetric Problem on Surfaces. The American Mathematical Monthly: Vol. 106, No. 5, pp. 430-439.
89 citations
TL;DR: In this article, the determinants of Commuting Block Matrices are discussed. But they do not consider the relation between Commuting-Block Matrices and Commuting block matrices.
Abstract: (1999). Determinants of Commuting-Block Matrices. The American Mathematical Monthly: Vol. 106, No. 10, pp. 950-952.
79 citations
TL;DR: In this paper, the Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence are discussed and discussed in the context of the FIFO sequence and its relation to the FCA.
Abstract: (1999). The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence. The American Mathematical Monthly: Vol. 106, No. 4, pp. 289-302.
79 citations
TL;DR: In this article, Descartes' Rule of Signs: Another Construction is constructed by adding another construction to the first construction of the Rule of Signals, and it is shown that the construction can be seen as a construction.
Abstract: (1999). Descartes' Rule of Signs: Another Construction. The American Mathematical Monthly: Vol. 106, No. 9, pp. 854-856.
73 citations
TL;DR: In this paper, it was shown that an equation for a nonlinearly supported beam with this type of nonlinearity could explain both large amplitude vertical periodic oscillations and the travelling wave behaviour.
Abstract: Good historical sources for these behaviours are [2] and [5]. Of course, these behaviours strongly suggest nonlinearity, and in the late eighties, following recent and rapid progress in nonlinear analysis of boundary value problems that had just been taking place, I and co-workers attempted to give a mathematical explanation for these phenomena [13], [16-19]. Our starting point was that an unloaded cable cannot be described by the usual Hooke's law, since it resists expansion but not compression. Thus if an unloaded cable is expanded downward by a distance u from the unloaded state, the cable should have a resisting force ku+, in other words, ku if u is positive, and 0 if u is negative. When the cable is loaded, it stretches to a new equilibrium, around which it obeys the linear Hooke's law until deviations from equilibrium become large enough to result in loss of tension when the cable approaches the unloaded state. Using the tools of nonlinear analysis and numerical investigations, we showed that an equation for a nonlinearly supported beam with this type of nonlinearity could explain both large amplitude vertical periodic oscillations and the travelling wave behaviour. With the usual fervor of the newly converted, I suggested that the
72 citations
TL;DR: The object of the puzzle is to use a sequence of legal moves to switch the positions of blocks 14 and 15 while returning all other blocks to their original positions.
Abstract: (1999). A Modern Treatment of the 15 Puzzle. The American Mathematical Monthly: Vol. 106, No. 9, pp. 793-799.
[...]
TL;DR: Paperfolding as mentioned in this paper is a popular technique for paperfolding and paper-folding has been widely used in the literature, e.g., the American Mathematical Monthly: Vol. 106, No. 1, pp. 27-35.
Abstract: (1999). More on Paperfolding. The American Mathematical Monthly: Vol. 106, No. 1, pp. 27-35.
[...]
TL;DR: Conway's ZIP Proof as discussed by the authors is an example of a ZIP proof algorithm for deterministic deterministic linear programming (DDP) with respect to deterministic polynomials.
Abstract: (1999). Conway's ZIP Proof. The American Mathematical Monthly: Vol. 106, No. 5, pp. 393-399.
TL;DR: The Emerging Tools for Experimental Mathematics (ETME) as discussed by the authors is a collection of tools for experimental mathematics that can be used in a variety of applications, e.g. in computer science.
Abstract: (1999). Emerging Tools for Experimental Mathematics. The American Mathematical Monthly: Vol. 106, No. 10, pp. 889-909.
TL;DR: The American Mathematical Monthly: Vol. 106, No. 5, No 4, pp. 440-448 as discussed by the authors discusses the concept of closed-form numbers and its application to the problem of counting.
Abstract: (1999). What Is a Closed-Form Number? The American Mathematical Monthly: Vol. 106, No. 5, pp. 440-448.
TL;DR: The Cayley Addition Table of Zn as mentioned in this paper is the Cayley addition table for Zn and Zn is a Cayley table for the Zn. The American Mathematical Monthly: Vol 106, No. 6, pp. 584-585.
Abstract: (1999). The Cayley Addition Table of Zn. The American Mathematical Monthly: Vol. 106, No. 6, pp. 584-585.
TL;DR: In this paper, the Weyr Characteristic was used to define the Wey Characteristic of a Weyr, which is a special case of the standard Weyr-characteristic.
Abstract: (1999). The Weyr Characteristic. The American Mathematical Monthly: Vol. 106, No. 10, pp. 919-929.
TL;DR: In this article, Chaos, Cantor Sets, and Hyperbolicity for Logistic Maps are discussed in the context of the Logistic Map Problem, and the authors propose a solution to the problem.
Abstract: (1999). Chaos, Cantor Sets, and Hyperbolicity for the Logistic Maps. The American Mathematical Monthly: Vol. 106, No. 5, pp. 400-408.
TL;DR: In this paper, the authors show that a simple differential equation modeling a damped forced pendulum can exhibit extraordinarily complicated and unstable behavior, and they use the pendulum's instability to control it.
Abstract: We show that a "simple" differential equation modeling a garden-variety damped forced pendulum can exhibit extraordinarily complicated and unstable behavior. While instability and control might at first glance appear contradictory, we can use the pendulum's instability to control it. Such results are vital in robotics: the forced pendulum is a basic subsystem of any robot. Most of the mathematical methods used in this paper were initially developed in celestial mechanics, largely by Poincare. The literature of the field tends to be quite advanced indeed (see [1] and [11]); one object of this paper is to show that computer programs, properly used, can make these advanced topics transparent. All the computer-generated pictures in this paper were produced by the programs Planar Systems and Planar Iterations [6], both written by Ben Hinkle (now at Maple). 1. SOME PARALLELS IN CELESTIAL MECHANICS. When I was a graduate
TL;DR: In this article, the change of Variables in Multiple Integrals II is discussed. But they focus on the change in the number of variables and not on the order of the variables.
Abstract: (2001). Change of Variables in Multiple Integrals II. The American Mathematical Monthly: Vol. 108, No. 2, pp. 115-119.
TL;DR: The Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians as discussed by the authors is a seminal work in the field of aerodynamic drag analysis and its application to physics.
Abstract: (1999). The Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians. The American Mathematical Monthly: Vol. 106, No. 2, pp. 127-135.
TL;DR: In this paper, an elegant continued fraction for π was proposed, which is an extension of the continued fraction of π for the π-approximation problem, where π is a constant.
Abstract: (1999). An Elegant Continued Fraction for π. The American Mathematical Monthly: Vol. 106, No. 5, pp. 456-458.
TL;DR: The Hyperbolic Pythagorean theorem in the Poincare disc model of hyperbolic geometry has been studied in this article, where it is shown to be a theorem of the form
Abstract: (1999). The Hyperbolic Pythagorean Theorem in the Poincare Disc Model of Hyperbolic Geometry. The American Mathematical Monthly: Vol. 106, No. 8, pp. 759-763.
TL;DR: The Union of Vieta's and Wallis's Products for Pi as discussed by the authors has published a collection of products for Pi for the first time in 1999, with the title "Product for Pi".
Abstract: (1999). The Union of Vieta's and Wallis's Products for Pi. The American Mathematical Monthly: Vol. 106, No. 8, pp. 774-776.
TL;DR: In this article, the n-Ellipses and the minimum distance sum problem were studied and a solution was given for the problem of finding the minimum number of n-ellipses.
Abstract: (1999). n-Ellipses and the Minimum Distance Sum Problem. The American Mathematical Monthly: Vol. 106, No. 3, pp. 193-202.
TL;DR: In this article, Random Walk and Plane Arrangements in Three-dimensional (W3D) are presented for the first time in the context of three-dimensional plane arrangement.
Abstract: (1999). Random Walks and Plane Arrangements in Three Dimensions. The American Mathematical Monthly: Vol. 106, No. 6, pp. 502-524.
TL;DR: In this article, H. J. Smith and the Fermat Two Squares Theorem are discussed. But they do not discuss the relation between Smith's theorem and the two-squares theorem.
Abstract: (1999). H. J. S. Smith and the Fermat Two Squares Theorem. The American Mathematical Monthly: Vol. 106, No. 7, pp. 652-665.
[...]
TL;DR: In this article, a stability theorem is defined and a stable theorem is proved. But this theorem is not applicable to the stability theorem of the stable theorem of Pareto-Szegedy.
Abstract: (1999). A Stability Theorem. The American Mathematical Monthly: Vol. 106, No. 8, pp. 768-770.
TL;DR: An elementary proof of Binet's formula for the Gamma function is given in this article, where it is shown that the Gamma Function can be expressed in terms of a binary function.
Abstract: (1999). An Elementary Proof of Binet's Formula for the Gamma Function. The American Mathematical Monthly: Vol. 106, No. 2, pp. 156-158.