By George Pólya
ISBN-10: 1400828678
ISBN-13: 9781400828678
Contributor note: With a brand new ahead through John Conway
Publish 12 months note: First released in 1945, and second printing in 2004
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A perennial bestseller through eminent mathematician G. Polya, How to unravel It will convey a person in any box how one can imagine immediately. In lucid and attractive prose, Polya unearths how the mathematical approach to demonstrating an explanation or discovering an unknown could be of assist in attacking any challenge that may be "reasoned" out--from construction a bridge to profitable a online game of anagrams.
Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going immediately to the guts of the matter.
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Extra resources for How to Solve It: A New Aspect of Mathematical Method (2nd Edition) (Princeton Science Library)
Sample text
Let us illustrate some of the points explained in the foregoing section. We take the following simple problem: Find the diagonal of a rectangular parallelepiped of which the length> the width> and the height are known. In order to discuss this problem profitably, the students must be familiar with the theorem of Pythagoras, and with some of its applications in plane geometry, but they may have very little systematic knowledge in solid geometry. The teacher may rely here upon the student's unsophisticated familiarity with spatial relations.
And how could he, the student, find such a question by himself? It appears as an unnatural surprise, as a rabbit pulled out of a hat; it is really not instructive. I8. A Problem of Construction None of these objections can be raised against the procedure described in section 10, or against that in section 15. MORE EXAMPLES 18. A problem of construction. Inscribe a square in a given triangle. Two vertices of the square should be on the base of the triangle, the two other vertices of the square on the two other sides of the triangle, one on each.
By such a success, he discovers the right way of using the question, and then he has really assimilated it. The student may absorb a few questions of our list so well that he is finally able to put to himself the right question in the right moment and to perform the corresponding mental operation naturally and vigorously. Such a student has certainly derived the greatest possible profit from our list. What can the teacher do in order to obtain this best possible result? Solving problems is a practical skill like, let us say, swimming.
How to Solve It: A New Aspect of Mathematical Method (2nd Edition) (Princeton Science Library) by George Pólya
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