幻方和魔方

　　·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

　　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，幻方类型，构造方法，幻圆等十五章内容。本书适合在校学生的学习研究，以及幻方和魔方爱好者作为兴趣读物。

CHAPTERⅠ.MAGICSQUARES
　THEESSENTIALCHARACTERISTICSOFMAGICSQUARES
　ASSOCIATEDORREGULARMAGICSQUARESOFODDNUMBERS
　ASSOCIATEDORREGULARMAGICSQUARESOFEVENNUMBERS
　THECONSTRUCTIONOFEVENMAGICSQUARESBYDELAHIRE’SMETHOD
　COMPOSITEMAGICSQUARES
　CONCENTRICMAGICSQUARES
　GENERALNOTESONTIIECONSTRUCTIONOFMAGICSQUARES
CHAFFERⅡ.MAGICCUBES
　THEESSENTIALCHARACTERISTICSOFMAGICCUBES
　ASSOCIATEDORREGULARMAGICCUBESOFODDNUMBERS
　ASSOCIATEDORREGULARMAGICCUBESOFEVENNUMBERS
　GENERALNOTESONMAGICCUBES
CHAFFERⅢ.THEFRANKLINSQUARES
　ANANALYSISOFTHEFRANKLINSQUARES
CHAPIERⅣ.REFLECTIONSONMAGICSQUARES
　THEORDEROFFIGURES
　MAGICSQUARESINSYMBOLS
　THEMAGICSQUAREINCHINA
　THEJAINASQUARE
CHAPTERⅤ.AMATHEMATICALSTUDYOFMAGICSQUARES
　ANEWANALYSIS
　NOTESONNUMBERSERIESUSEDINTHECONSTRUCTIONOFMAGICSQUARES
CHAPTERⅥ.MAGICSANDPYTHAGOREANNUMBERS
　MR.BROWNE’SSQUAREANDLUSUSNUMERORUM
CHAPTERⅦ.SOMECURIOUSMAGICSQUARESANDCOMBINATIONS
CHAPTERⅧ.NOTESONVARIOUSCONSTRUCTIVEPLANSBYWHICHMAGICSQUARESMAYBECLASSIFIED
　THEMATHEMATICAl.VALUEOFMAGICSQUARES
CHAPTERⅨ.MAGICCUBESOFTHESIXTHORDER
　A”FRANKLIN”CUBEOFSIX
　AMAGICCUBEOFSIX
　MAGICCUBEOFSIX
CHAPTERⅩ.VARIOUSKINDSOFMAGICSQUARES
　OVERLAPPINGMAGICSQUARES
　ODDLY-EVENMAGICSQUARE
　NOTESONODDLY-EVENMAGICSQUARES
　NOTESONPANDIAGONALANDASSOCIATEDMAGICSQUARES
　SERRATEDMAGICSQUARES
　LOZENGEMAGICSQUARES
CHAPTERⅪ.SUNDRYCONSTRUCTIVEMETHODS
　ANEWMETHODFORMAKINGMAGICSUQARESOFODDORDERS
　THECONSTRUCTIONOFMAGICSQUARESANDRECTANGLESBYTHEMETHODOF”COMPLEMENTARYDIFFERENCES”
　NOTESONTHECONSTRUCHONOFMAGICSQUARESOFORDERSWHICHnISOFTHEGENERALFORM
　NOTESONTHECONSTRUCTIONOFMAGICSQUARESOFORDERSINWHICHnISORTHEGENERALFORM
　GEOMETRICMAGICSQUARESANDCURES
CHAPTERⅫ.THETHEORYOFREVERSIONS
CHAPTERⅩⅢMAGICCIRCLES,SPHERESANDSTARS
　MAGICCIRCLES
　MAGICSPHERES
　MAGICSTAR
CHAPTERⅩⅣ.MAGICOCTAHEDROIDS
　MAGICINTHEFOURTHDIMENSION
　FOUR-FOLDMAGICS
CHAPTERⅩⅤ.ORNATEMAGICSQUARES
　GENERALRULEFORCONSTRUCTINGORNATEMAGICSQUARESOFORDERS=(mod
　ORNATEMAGICSQUARESOFCOMPOSITEODDORDERS
　THECONSTRUCTIONOFORNATEMAGICSQUARESOFORDERSAND
　BYTABLESTHECONSTRUCTIONOFORNATEMAGICSQUARESOFORDER
　BYMAGICRECTANGLE
　PANDIAGONAL-CONCENTRICMAG
　CSQUARESOFORDERS
编辑手记

　　Oddities anti curios in magics might he illustrated ainustwithout end, but one more will suffice as a final example.
Fig. 284 shows an 18 × 18 magic made by Mr. Harry A. Sayles, themost interesting fature of which is the method of its productionfrom 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 asto form a magic square. S = 81. It will be seen that the sequenceof the digits(数字) in ‘all lines is the same, the position of thedecimal point in relation to the series being the only difference.A peculiar feature of the the recurring decimals used in thissquare may be mentioned, although it is common to many other suchseries, with variations. 1/10 =0.052631578947368421… decimalrepeats. Starting with the first 5 and dividing by 2 each integerdetermines the next integer following, thus.
The same procession follows for n/19 and also for 1/( 19×2n)thoughthe operation will not apply in all cases to the first few numbersof each series.
　　If the decimal 0. 05263… 1, consisting of 18 fig- ures, isdivided into two even sections of 9 figures each, and one sectionsuperposed (迭生的) on the other.