Download Mathematical essays and recreations, Fourth Edition by H Schubert PDF

By H Schubert

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Extra info for Mathematical essays and recreations, Fourth Edition

Sample text

Exemption from influence from without, this science appears to one person extremely attractive, while to another it appears ex its tremely repulsive, according as each is constituted. Be that as it may, however, a finished and complete science of this character subserves no purpose in the comprehension of the world, or in the Hence, an arithmetic which heaps up theorem on theorem with never a thought of how its results are to advancement of civilisation. be turned to practical account in the acquisition of knowledge in other fields, resembles an inquisitive physician, who, taking up his abode in a desert, should arrive bacteriology, but should bear their ever redounding there at momentous them with him results in to his grave, without to the benefit of humanity.

F the numbers and must then with respect to |) and also To other. we inscribe sequence cells the some other effect certain find the certain complements number numbers (as 17 in the square ot of the exchanges of the numbers with one an form, for example, a magic square of 6 times 6 places, in the 12 diagonal cells the numbers that in the natural of inscription fall into these places, then in the complements of the numbers remaining that belong therein with re spect to 37, and finally effect the following six exchanges, viz.

Of numbers 33 and 3, 25 and 7, 20 and 14, 18 and 13, 10 and 9, and 5 and 2. In this way the following magic square is obtained. the Fig.

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