The American Mathematical Monthly; The Official Journal of the Mathematical Association of America Volume 12

The American Mathematical Monthly; The Official Journal of the Mathematical Association of America Volume 12

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 edition. Excerpt: ... not occur again until the year 2015. Solution by WILLIAM HOOVES. Ph. D., Athens, Ohio. The Dominical Letter for Sunday when on January 1 is A, and also when on December 31, the year being common. Those common years in the present century fulfilling the required conditions must have A for their Dominical Letter; such years are 1905, 1911, 1922, 1933, 1939, 1950, 1961, 1967, 1978, 1989, 1995, sufficient to show that the statement in the problem is not true. Rkmark By Proposer. The year 2015 will begin on a Thursday. Also solved by A. H. Holmes, Henry Heaton, G. B. M Zerr, and G. W. Greenwood. 147. Proposed by F. P. MATZ. Sc. D.. Ph. D.. Reading. Pa. If an unknown curve be described under a constant acceleration not tending to the center and the hodograph is a cardioid, what is the unknown curve? I. Solution by WILLIAM HOOTER. Ph. D. Athens, Ohio. Let r and p be the radius vector and perpendicular upon the tangent to the curve at, the outer extremity of r and r'; p' the analogous lines in the hodograph, and k the double area generated by r in a unit of time. Then by the theory of the hodograph, r'= (1'"T-(2)' Also, from the theory of central forces, h_Vdp Then (5) in (3), gives krdr=iapdp (6), the differential equation to the required orbit. Integrating (6), and supposing r andj to vanish together, -j-r=ap (7), the required orbit. II. Solution by 0. W. GREENWOOD, M. A., Froiessor oi Mathematics, McKendree College. Lebanon, 111. Let the equation to the hodograph be r=2acos2 0. Since the acceleration in the original curve is constant the velocity of the point in the hodograph is constant, and s--iakt, where k is some constant; that is ft=sin 0. From the equation to the hodograph we have =2acos ifi, where v is the velocity more

Product details

  • Paperback | 74 pages
  • 189 x 246 x 4mm | 150g
  • United States
  • English
  • black & white illustrations
  • 1236781376
  • 9781236781376