How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
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A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.
suitable notation.” The student draws the lines of Fig. 4 and chooses, helped more or less by the teacher, the letters as in Fig. 4. “What is the hypothesis? Say it, please, using your notation.” “A, B, C are not in the same plane as A′, B′, C′. And AB || A′B′, AC || A′C′. Also AB has the same direction as A′B′, and AC the same as A′C′.” FIG. 4 “What is the conclusion?” “∠BAC = ∠B′A′C′.” “Look at the conclusion! And try to think of a familiar theorem having the same or a similar
vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or the data, or both if necessary, so that the new unknown and the new data are nearer to each other? Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem? CARRYING OUT THE PLAN Third. Carry out your plan. Carrying out your plan of the solution, check each step.
Can you see clearly that the step is correct? Can you prove that it is correct? LOOKING BACK Fourth. Examine the solution obtained. Can you check the result? Can you check the argument? Can you derive the result differently? Can you see it at a glance? Can you use the result, or the method, for some other problem? Foreword by John H. Conway How to Solve It is a wonderful book! This I realized when I first read right through it as a student many years ago, but it has taken me a long time
compared with his “outstanding” performance in literature, geography, and other subjects. His favorite subject, outside of literature, was biology. He enrolled at the University of Budapest in 1905, initially studying law, which he soon dropped because he found it too boring. He then obtained the certification needed to teach Latin and Hungarian at a gymnasium, a certification that he never used but of which he remained proud. Eventually his professor, Bernát Alexander, advised him that to help
from different sides. Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side. In order to find out which aspect is the right one, which side is accessible, we try various sides and aspects, we vary the problem. 2. Variation of the problem is essential. This fact can be explained in various ways. Thus, from a certain point of view, progress in solving the problem appears as mobilization and organization of formerly acquired