The American Mathematical Monthly: The Official Journal of the Mathematical Association of America, Volume 17Mathematical Association of America, 1910 - Electronic journals Registers of officers and members were issued as supplements to some vols. |
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Algorismus AMERICAN MATHEMATICAL MONTHLY analytic function analytic geometry arithmetic augmented matrix C. N. SCHMALL calculus Cauchy circle coefficients conic coordinate coordinate axis curve differential equation DRURY COLLEGE edition elementary elements ellipse ETH and ETH Euclid foci follows G. B. M. ZERR given group theory Hence integral interest Jordanus Jordanus Nemorarius Klein L. E. DICKSON linear equations logarithms major axis mathe mathematician matics matrix method minor axis parallel Patents perfect numbers Petrus de Dacia Philadelphia plane geometry potential function Professor of Mathematics Projective Geometry Proposed by C. N. published rank S. G. Barton Scheffer School Solution by G. B. M. solved Springfield student tangents teachers teaching theorem tion triangle trigonometry University of Chicago University of Illinois unknowns V. M. Spunar vertex
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Page 4 - This report was prepared under the joint auspices of the American Federation of Teachers of the Mathematical and Natural Sciences and the National Education Association.
Page 3 - The Congress, recognizing the importance of a comparative examination of the methods and plans of study of the instruction in mathematics in the secondary schools of the different nations, empowers Messrs. Klein, Greenhill, and Fehr to form an International Commission, to study these questions and present a general report to the next Congress.
Page 190 - About 1570 Sir Henry Savile began to lecture at Oxford on Greek geometry, and in 1619 Briggs at Cambridge on Euclid. In 1665 Isaac Barrow at Cambridge prepared a complete edition of Euclid, which was the standard for fifty years. Gow says that " the seventy years or so, from 1660 to 1730, when Wallis and Halley were professors at Oxford, Barrow and Newton at Cambridge, were the period during which the study of Greek geometry was at its height in England."5 In 1703, William Whiston became the successor...
Page 189 - Geometry, brought out in 1899 by Professor Hilbert of Gottingen.27 Though widely read by mathematicians. it has exerted no direct influence upon elementary teaching in Germany. It has been felt that this mode of treatment is not suitable for pupils first entering upon demonstrative geometry. ITALY. Since the unification of Italy, great mathematical activity has existed in that country. Before that event, very different practices in geometrical teaching existed in different parts of the...
Page 198 - It has been said of American writers, that while they have given up Euclid, they have modified Legendre's Geometry so as to make it resemble Euclid as much as possible. This applies to Loomis with greater force perhaps than to any other author. In 1871 Professor Olney, of the University of Michigan, published a Geometry under two main heads: I. Special or Elementary Geometry, comprising ( i ) Empirical Geometry, (2) Demonstrative Geometry, (3) Original Exercises in the Application of Algebra to Geometry,...
Page 180 - Elements of geometry carefully weeded of every proposition tending to demonstrate another ; all lying so handy that you may pick and choose without ceremony. This is useful in fortification ; you cannot play at billiards without this. You only look through a telescope like a Hottentot until this proposition is read, with many such powerful strokes of rhetoric to the same purpose. And upon such terms, and with such inducements, who would not be a mathematician ? Who would go to work with all that...
Page 198 - Empirical Geometry, (2) Demonstrative Geometry, (3) Original Exercises in the Application of Algebra to Geometry, (4) Trigonometry. II. General Geometry (Plane Loci). Olney was a self-educated man. He was a great teacher and had original ideas about teaching. It is said that he was prevented by his publishers from departing very far from the traditional classification. His ideas were novel and forecasted in many ways the present tendencies in mathematical teaching. His geometry shows that he attempted...
Page 185 - ... axiom; he formulates a complete list of axioms, but introduces each only when it is needed; nor does he aim to limit their number to a minimum. Characteristic of Meray is the complete fusion of plane and solid geometry, and the use of motion, not only as a means of proof, but also to define parallels. Recently there has been considerable discussion in France on the question whether in laying the foundations to geometry, motion should be used or not. The defenders of a static theory of parallels...
Page 199 - ... self-evident truth," but as a synonym for "postulate." In conclusion, we note that, with the beginning of the twentieth century, England began once more to influence the teaching of geometry in the United States, through the so-called "Perry movement," and that Germany, which at no time during the nineteenth century affected geometrical teaching in America, makes itself felt at the present time through the pupils of Klein and Hilbert and through the international movement towards reform in the...
Page 192 - A question has been sometimes agitated whether it is most advantageous, for the study of geometry, to possess a number of elementary treatises, or to have one standard work, like that of Euclid . . . the same lessons are not suited to every intellect, and on these accounts it may be of advantage that different elementary texts should exist. We are very much inclined to the latter opinion.