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By H Dudeney

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Extra info for 536 PUZZLES & CURIOUS PROBLEMS

Sample text

Other configurations of beams and loads can be analyzed in a similar manner. Of interest to do-it-yourself hobbyists is to determine where a bookshelf (effectively, a beam as above) should be supported at two locations along the shelf to minimize the maximum moment M in the shelf uniformly loaded along its length by books. This will minimize the bending of the shelf in the long term, because bending is proportional to the moment M. ) This example illustrates the translation into the Language of Mathematics of an English text accompanied by a diagram.

Such combinations of English text and diagrams arise often in engineering work. This example is typical of topics and problems covered in a course in statics taken by students in all disciplines of engineering early in their studies. Such examples arise so often in engineering studies that students can easily overlook the fact that their mathematical models are really nothing other than translations of English text accompanied by diagrams describing physical mechanisms or systems. 12 FORMING ABBREVIATIONS OF NAMES In this example, a mathematically precise definition is formulated for a dynamic process to form the abbreviation of any given name.

P1: TIX/XYZ JWBS073-02 22 P2: ABC JWBS073-Baber June 27, 2011 10:26 Printer: Markono PREVIEW: SOME STATEMENTS IN ENGLISH AND THE LANGUAGE OF MATHEMATICS Because of the uncertainty of each of the several factors in this problem, one cannot calculate precisely the effort required. One can, however, calculate the range of effort required given the ranges of uncertainty of the several factors involved. One can often draw interesting and useful conclusions from the lower and upper bounds calculated for the values of the quantities in question.

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