By Stephen Barr
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Extra resources for Mathematical Brain Benders: 2nd Miscellany of Puzzles
Parenthetically, such pictures are abstractions-of a three-dimensional reality-whereas so-called abstractions, not being of anything, would be more correctly termed concretes, or Aldens, since they speak for themselves. A perspective representation is the projection by lines converging to a point of a three-dimensional object onto a plane. It differs from orthogonal projection in that the latter uses parallel lines. In both cases a cone, shown at an angle, gives an image which is an ellipse with two lines (see figure).
3). FIGURE l 25 MORE ORIGAMETRY Starting with a square sheet of paper, fold it to produce a square having three-fourths its area. Only five folds are allowed. 26 UNIQUE PARTS OF LETTERS Is there any part of any letter of the alphabet that is unique? That is, a segment of a letter, such as the cross stroke of A, which cannot be found in the corresponding place in any other letter-which of course is not true of the cross stroke of A, because it could be a part of the cross stroke of H. We confine ourselves to block capitals, without serifs or differences of line thickness, or such details, so that the little stroke on a Q can be got from part of the lower right side of A.
What was the exact number of glasses? It is assumed that any number of glasses can be tested simultaneously by taking a small sample of liquid from each, mixing the samples, and making a single test of the mixture. 64 ';'My thanks to Martin Gardner for permission to use his version-much improved-of my puzzle The Poisoned Glass, which appeared in Scientific American. 45 TO COVER A CIRCLE A man wanted to cover the biggest possible circle with a paper rectangle, 1 x 2 in. -diameter circle, but folded as in the figure it covered a slightly larger one, and he was trying to work out the maximum when his Japanese friend Suzi Origami came in.