Showing papers in "American Mathematical Monthly in 1952"
11,456 citations
TL;DR: The Problem of Simplifying Truth Functions is concerned with the problem of reducing the number of operations on a graph to a simple number.
Abstract: (1952). The Problem of Simplifying Truth Functions. The American Mathematical Monthly: Vol. 59, No. 8, pp. 521-531.
885 citations
TL;DR: In this paper, unique arrangements of points on a sphere are presented. But the arrangement is not a unique arrangement of points in a sphere, it is a set of points arranged on a circle.
Abstract: (1952). Unique Arrangements of Points on a Sphere. The American Mathematical Monthly: Vol. 59, No. 9, pp. 606-611.
105 citations
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84 citations
TL;DR: In this paper, the different distances determined by n points were investigated and the distance between n points was defined by n-points in terms of the distance of n points to n points.
Abstract: (1952). On The Different Distances Determined By n Points. The American Mathematical Monthly: Vol. 59, No. 2, pp. 85-91.
68 citations
TL;DR: The General Chinese Remainder Theorem as mentioned in this paper is a generalization of the General Chinese Remender Theorem (GCHT) and it has been studied extensively in the literature.
Abstract: (1952). The General Chinese Remainder Theorem. The American Mathematical Monthly: Vol. 59, No. 6, pp. 365-370.
67 citations
TL;DR: The Finite Difference Analogue of Rodrigues' Formula has been studied in this paper, where it is shown that it is possible to construct a finite difference analogue of the Rodrigues formula.
Abstract: (1952). On the Finite Difference Analogue of Rodrigues' Formula. The American Mathematical Monthly: Vol. 59, No. 3, pp. 163-168.
48 citations
43 citations
TL;DR: In this article, a continuous function without derivatives is defined, and continuous functions without derivatives can be found in the form of continuous functions, without derivatives, in the continuous function. The American Mathematical Monthly.
Abstract: (1952). Continuous Functions Without Derivatives. The American Mathematical Monthly: Vol. 59, No. 4, pp. 222-225.
38 citations
35 citations
TL;DR: In this paper, partial ordering and Moore-Smith limits are discussed in the context of partial orderings and partial ordering in the setting of partial ordering problems, and the American Mathematical Monthly: Vol. 59, No. 1, pp. 1-11
Abstract: (1952). Partial Orderings and Moore-Smith Limits. The American Mathematical Monthly: Vol. 59, No. 1, pp. 1-11.
TL;DR: The Unsatisfactory Story of Curvature as mentioned in this paper is a collection of essays about curvature in the context of mathematical logic, with a focus on non-convexity.
Abstract: (1952). The Unsatisfactory Story of Curvature. The American Mathematical Monthly: Vol. 59, No. 6, pp. 375-379.
TL;DR: The Sums of the Dihedral and Trihedral Angles in a Tetrahedron were first presented in this article, where they were shown to be the sum of the dihedral and trihedral angles.
Abstract: (1952). The Sums of the Dihedral and Trihedral Angles in a Tetrahedron. The American Mathematical Monthly: Vol. 59, No. 6, pp. 370-371.
TL;DR: The Origin of Polar Coordinates as mentioned in this paper is a well-known topic in physics and astronomy, and it has been extensively studied in the literature. But it is not suitable for astronomy applications.
Abstract: (1952). The Origin of Polar Coordinates. The American Mathematical Monthly: Vol. 59, No. 2, pp. 78-85.
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TL;DR: In this paper, the Radon inequality is shown to be a generalization of an inequality due to Beckenbach, and it is shown that Dresher's inequality is a melange of the Holder and Minkowski inequalities.
Abstract: : This note gives an elementary proof of the Dresher inequality, based on the Minkowski inequality and an inequality due to Radon. The Radon inequality is gotten easily by transforming the Holder inequality; thus Dresher's inequality is seen to be a melange of the Holder and Minkowski inequalities. It is appropriate to note here that Dresher's inequality is a generalization of an inequality due to Beckenbach.
TL;DR: A note on Gambling systems and birth statistics is given in this article, where the authors propose a method to estimate the probability that a person will be born in a given year.
Abstract: (1952). A Note on Gambling Systems and Birth Statistics. The American Mathematical Monthly: Vol. 59, No. 10, pp. 685-686.
TL;DR: In this paper, the authors give a derivation of the properties of the elementary transcendentals from a more unified point of view than is customary, assuming that the general properties of analytic functions are established.
Abstract: The purpose of the present paper is to give a derivation of the properties of the elementary transcendentals from a more unified point of view than is customary. It will be assumed that the general properties of analytic functions are established. In particular we shall use the theorem that the real (or imaginary) part of an analytic function cannot assume its maximum value in the inside of a closed domain in which it is regular. Similarly, use will be made of Weierstrass’s theorem about a set of uniformly converging analytic functions, of Liouville’s and Rolle’s theorems.§ All of these theorems can be established without the use of the properties of the transcendental functions, using only elementary calculations and the concept of convergence. The present paper shows how the properties of the elementary transcendentals can then be derived from the aforementioned theorems by means of the methods of the theory of complex functions. From the point of view of this theory, this appears to be more appropriate than taking over the results concerning the properties of these functions, at least for real arguments, from other parts of analysis. An outline of our procedure follows.