Showing papers in "American Mathematical Monthly in 1920"
TL;DR: In this article, a theory of strict implication based on criticism of Russell and Whitebread's concept of implication is presented, as well as historical information on the history and application of algebra to developments in symbolic logic.
Abstract: Modern interest in modal logic began with this seminal work by the American C.I. Lewis. As well as developing a theory of strict implication based on criticism of Russell and Whitebread's concept of implication, it contains historical information on the history and application of algebra to developments in symbolic logic.
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TL;DR: Euclidean's postulate concerning parallels is a thought that links the ages as discussed by the authors, and its history is a long story with a dramatic climax and farreaching in?uence on modern mathematical and general scientific thought.
Abstract: Like the famous problems of construction, Euclid's postulate concerning parallels is a thought that links the ages. Its history is a long story with a dramatic climax and far-reaching in?uence on modern mathematical and general scientific thought. I wish to recall briefly the salient features of the story, and to state what seem to me its suggestions in regard to the teaching of elementary geometry. Euclid's fifth postulate (called also the eleventh or twelfth axiom) states: “If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines if produced indefinitely meet on that side on which are the angles less than two right angles” [2]. The earliest commentators found fault with this statement as being not self-evident. Concerning the meaning of axiom , Aristotle says: “That which it is necessary for anyone to hold who is to learn anything at all is an axiom”; and “It is ignorance alone that could lead anyone to try to prove the axiom.” Without going into the difficult question of the precise distinction to the Greek mind between axiom and postulate, we may take it that the character of being indisputable pertained to each. Postulates stating that a straight line joining any two points can be drawn, that a circle can be drawn with given center and radius, or that all right angles are equal, were accepted, while the postulate of parallels was scrutinized and admitted at best with reluctance.
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TL;DR: In this article, the roots of the derivative of a polynomial are discussed and discussed in the context of a Polynomial Derivative of Polynomials (PDO).
Abstract: (1920). Note on the Roots of the Derivative of a Polynomial. The American Mathematical Monthly: Vol. 27, No. 7-9, pp. 299-300.
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TL;DR: In this article, the danger area curve is defined as follows the curve of the graph of the "Danger Area" curve, and the authors propose a solution to the problem.
Abstract: (1920). The “Danger Area” Curve. The American Mathematical Monthly: Vol. 27, No. 11, pp. 398-401.
TL;DR: In this article, the continuuity in synthetic geometry was discussed and a Continuity Continuity in Synthetic Geometry (CIG) model was proposed for the first time.
Abstract: (1920). Continuity in Synthetic Geometry. The American Mathematical Monthly: Vol. 27, No. 2, pp. 47-53.
TL;DR: In this paper, the Orthocentric Quadrilateral has been studied in terms of the orthocentric quadrilateral, and the authors show that it can be computed in a linear fashion.
Abstract: (1920). On the Orthocentric Quadrilateral. The American Mathematical Monthly: Vol. 27, No. 5, pp. 199-202.