内容摘要 Oddities anti curios in magics might he illustrated ainust without end, but one more will suffice as a final example. Fig. 284 shows an 18 × 18 magic made by Mr. Harry A. Sayles, the most interesting fature of which is the method of its production from the values of rill9. The lines of recurring decimals (循环小数) for 1/19, 2/19, 3/19...18/19 are arranged one below the other so as to form a magic square. S = 81. It will be seen that the sequence of the digits(数字) in all lines is the same, the position of the decimal point in relation to the series being the only difference. A peculiar feature of the the recurring decimals used in this square may be mentioned, although it is common to many other such series, with variations. 1/10 =0.052631578947368421... decimal repeats. Starting with the first 5 and dividing by 2 each integer determines the next integer following, thus. The same procession follows for n/19 and also for 1/( 19×2n)though the operation will not apply in all cases to the first few numbers of each series. If the decimal 0. 05263... 1, consisting of 18 fig- ures, is divided into two even sections of 9 figures each, and one section superposed (迭生的) on the other.
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