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 119, 219, 319...1819 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. 110 =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 n19 and also for 1 19×2nthough
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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