Mathematical questions with their solutions, from the "Educational times" Volume 38
W. J. C. Miller
Paperback
(RareBooksClub.com, May 21, 2012)
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...mathematical and nonmathematical, may obtain approximate solutions to some of the probability questions which appear in it from time to time, and so test the correctness of the more scientific solutions supplied by the mathematical contributors. As an example of the class of problems to which I refer, I would here propose for solution the following question:--"A point is taken at random on a window consisting of nine equal square panes, and through this point a line is drawn in a random direction. What are the respective chances of the line so drawn cutting one, two, three, four, or five panes?" Experimentally this may be solved as follows. Take a circular piece of white card-board; draw a straight line across the centre on one side, and through the centre on the opposite side insert a pin. Move the cardboard round this pin as a pivot till the stiffness is so far gone that when the pin is held by the point head downwards, a slight jerk of the finger will make the card-board revolve easily and rapidly. This may be a rude contrivance, but it will answer the purpose. Now draw a figure on paper representing the window; twirl the card-board, and while it is spinning mark with a pencil a point anywhere on the figure. If the rotatory motion of the card-board still continues, arrest it suddenly, so as to economize time; then place the card-board on the paper so that the pin's head shall fall on the pencil mark, or near it, extreme accuracy upon this point not being at all necessary. Observe now how many panes the line drawn across the centre of the card-board would cut through if produced; and register accordingly. Mark another point with the pencil, and proceed as before; and so on as long as you please; taking care, however, to distribute the points as ...