Showing papers in "Mathematics Magazine in 1968"
TL;DR: An Explicit Expression for Binary Digital Sums as mentioned in this paper is an explicit expression for binary digital sum, which can be used to express binary digital sums in the form of binary digital numbers.
Abstract: (1968). An Explicit Expression for Binary Digital Sums. Mathematics Magazine: Vol. 41, No. 1, pp. 21-25.
77 citations
TL;DR: In this paper, Sylvester's Problem on Collinear Points (SSPP) is considered and the authors present a solution to the Sylvesters' problem on points.
Abstract: (1968). Sylvester's Problem on Collinear Points. Mathematics Magazine: Vol. 41, No. 1, pp. 30-34.
38 citations
TL;DR: In this paper, the critical graph of Diameter has been studied in the context of graph of diameter and critical graphs of dimension 2.5.1.2.3.4.
Abstract: (1968). On Critical Graphs of Diameter 2. Mathematics Magazine: Vol. 41, No. 3, pp. 138-140.
29 citations
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28 citations
TL;DR: In this article, the Recurrent Sequences and Pascal's Triangle are discussed. But they do not discuss the Pascal's triangle. And they do so in a very abstract manner.
Abstract: (1968). Recurrent Sequences and Pascal's Triangle. Mathematics Magazine: Vol. 41, No. 1, pp. 13-21.
24 citations
12 citations
TL;DR: Some generalizations of Wythoff's game and other related games are discussed in this article, where the authors present a game theoretic analysis of the generalization of the game.
Abstract: (1968). Some Generalizations of Wythoff's Game and Other Related Games. Mathematics Magazine: Vol. 41, No. 1, pp. 7-13.
11 citations
TL;DR: A combinatorial interpretation of a numerical quantity is defined as a set of objects that are counted by the quantity as mentioned in this paper, which is a subset of the combinatorials that are considered in this paper.
Abstract: Definition: A combinatorial interpretation of a numerical quantity is a set of combinatorial objects that is counted by the quantity.
8 citations
8 citations
TL;DR: Weak sufficient conditions for Fatou's Lemma and Lebesgue's Dominated Convergence Theorem were given in this paper, where they were shown to be sufficient for both conditions.
Abstract: (1968). Weak Sufficient Conditions for Fatou's Lemma and Lebesgue's Dominated Convergence Theorem. Mathematics Magazine: Vol. 41, No. 3, pp. 109-117.
8 citations
TL;DR: Sutcliffe as mentioned in this paper discusses the problem of finding a solution to the Problem of Note on a Problem of Alan Sutcliffe in Mathematics Magazine: Vol. 41, No. 2, pp. 84-86.
Abstract: (1968). Note on a Problem of Alan Sutcliffe. Mathematics Magazine: Vol. 41, No. 2, pp. 84-86.
TL;DR: The Group of the Composition of two Tournaments (GCT) as discussed by the authors was the first group of two-tournament tournament organizers to formally define the notion of a tournament.
Abstract: (1968). The Group of the Composition of two Tournaments. Mathematics Magazine: Vol. 41, No. 2, pp. 77-80.
TL;DR: A Note on One-Sided Directional Derivatives as discussed by the authors is an example of one-sided directional derivatives, which are derived from one-side directional derivatives.
Abstract: (1968). A Note on One-Sided Directional Derivatives. Mathematics Magazine: Vol. 41, No. 3, pp. 147-150.
TL;DR: In this article, a note on complex polynomials having Rolle's property and the Mean Value Property for Derivatives is given, along with a comparison of the two properties.
Abstract: (1968). A Note on Complex Polynomials Having Rolle's Property and the Mean Value Property for Derivatives. Mathematics Magazine: Vol. 41, No. 3, pp. 140-144.
TL;DR: In this article, the vector representation of rigid body rotation is used to represent the body rotation of a rigid body, and it is shown that the representation can be expressed as a vector.
Abstract: (1968). On Vector Representation of Rigid Body Rotation. Mathematics Magazine: Vol. 41, No. 1, pp. 28-29.
TL;DR: In this paper, the problem of the shortest network joining n points is considered and the authors propose a solution to the problem: the Shortest Network Joining n Points Problem (SNTJPP).
Abstract: (1968). The Problem of the Shortest Network Joining n Points. Mathematics Magazine: Vol. 41, No. 5, pp. 225-231.
TL;DR: The Tristam Shandy paradox as discussed by the authors states that every second a genie throws ten balls into an urn and at every throw he adds the next ten numbers to the urn so that at the nth throw the balls numbered lOn-9, l On-8, 10n(n_ 1) are added.
Abstract: Introduction. A simple "paradox" relating to the enumeration of the elements in a countable set may be described in the following way. Every second a genie throws ten balls into an urn. The balls are numbered 1, 2, * * * and at every throw he adds the next ten numbers to the urn so that at the nth throw the balls numbered lOn-9, lOn-8, 10n(n_ 1) are added. This goes on forever. Another genie removes one ball from the urn after each addition, but he must guarantee that every ball will eventually be thrown out. If he can see the balls, there is of course no problem. He can remove the balls 1, 2, 3, * successively and for any natural number k, he knows when it enters the urn and when it is removed. It enters the urn at the [k/10] + 1st throw and is removed after the kth throw. Though the number of balls in the urn tends to infinity, any given ball is eventually thrown out. No ball stays in the urn forever. This is one of the paradoxes of infinity, stated by Georg Cantor and discussed as the "Tristam Shandy paradox" by Russell [7]. For every k, the length of time Tk spent in the urn by the ball k is given by
TL;DR: In this article, it was shown that the row rank and column rank are equal in the subspace of Fin spanned by the rows of A and column space of F71 spanned the columns of A. The row rank is the dimension of the row space of A, and the column rank of A is the dimensions of the column space.
Abstract: Let A = (aij) be an n X m matrix with entries in a field F. Each of the n rows -of A can be regarded as a vector in coordinate m-space, Fm, and each of the m columns of A can be regarded as a vector in Fn. The row space of A is the subspace of Fin spanned by the rows of A and column space of A is the subspace of F71 spanned by the columns of A. The row rank of A is the dimension of the row space of A and the column rank of A is the dimension of the column space of A. It is proved in most undergraduate courses in linear algebra that the row rank and column rank are equal. This can be done by resorting to the determinants of square minors of A [3, pp. 22-24], or by computing the dimension of the solution space of a certain system of linear equations [2, pp. 47-51]. Products of linear transformations and the matrices associated with them can also be employed [1, pp. 234-235; 5, pp. 35, 42, 48-50; and 6, pp. 100-108]. In [4] Liebeck gives a short proof valid only for complex scalars. The purpose of this note is to present two very simple proofs that row rank and column rank are equal without resorting to any of these notions. Undergraduates should easily follow our arguments which the authors have not seen in any of the standard texts on linear algebra.
TL;DR: The relation between the Beta and the Gamma functions was studied in this article, where the relation between Beta and Gamma functions is discussed. But the relationship between the two functions is not discussed.
Abstract: (1968). Relation Between the Beta and the Gamma Functions. Mathematics Magazine: Vol. 41, No. 1, pp. 37-39.
TL;DR: In this paper, extra dividends from a Calculus Problem are given for solving the extra-dividends from a calculus problem, and the authors propose a solution to the problem.
Abstract: (1968). Extra Dividends from a Calculus Problem. Mathematics Magazine: Vol. 41, No. 5, pp. 280-281.
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TL;DR: In this paper, the authors discuss the problems in Gravitational attraction, and propose a solution to the problem of finding the minimum number of vertices in a graph of a graph.
Abstract: (1968). On Some Problems in Gravitational Attraction. Mathematics Magazine: Vol. 41, No. 3, pp. 130-132.