本书列举诸多幻方和魔方的例子，研究幻方和魔方所具备的特性及构筑方法，生动地展示幻方和魔方的神奇之处，主要包括幻方的数学研究，六阶幻方，构造方法，幻圆等等十五章内容。
·富兰克林幻方
·幻方的数学研究
·六阶幻方
·诸多幻方类型
·多种构造方法
·幻圆
CHAPTERⅠ.MAGICSQUARES
THEESSENTIALCHARACTERISTICSOFMAGICSQUARES
ASSOCIATEDORREGULARMAGICSQUARESOFODDNUMBERS
ASSOCIATEDORREGULARMAGICSQUARESOFEVENNUMBERS
THECONSTRUCTIONOFEVENMAGICSQUARESBYDELAHIRE'SMETHOD
COMPOSITEMAGICSQUARES
CONCENTRICMAGICSQUARES
GENERALNOTESONTIIECONSTRUCTIONOFMAGICSQUARES
CHAFFERⅡ.MAGICCUBES
THEESSENTIALCHARACTERISTICSOFMAGICCUBES
ASSOCIATEDORREGULARMAGICCUBESOFODDNUMBERS
ASSOCIATEDORREGULARMAGICCUBESOFEVENNUMBERS
GENERALNOTESONMAGICCUBES
CHAFFERⅢ.THEFRANKLINSQUARES
ANANALYSISOFTHEFRANKLINSQUARES
CHAPTERⅠ.MAGICSQUARES
THEESSENTIALCHARACTERISTICSOFMAGICSQUARES
ASSOCIATEDORREGULARMAGICSQUARESOFODDNUMBERS
ASSOCIATEDORREGULARMAGICSQUARESOFEVENNUMBERS
THECONSTRUCTIONOFEVENMAGICSQUARESBYDELAHIRE'SMETHOD
COMPOSITEMAGICSQUARES
CONCENTRICMAGICSQUARES
GENERALNOTESONTIIECONSTRUCTIONOFMAGICSQ
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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