了得網自然科學_幻方和魔方

編輯推薦

·富蘭克林幻方
·幻方的數學研究
·六階幻方
·諸多幻方類型
·多種構造方法
·幻圓

內容簡介

本書列舉諸多幻方和魔方的例子，研究幻方和魔方所具備的特性及構築方法，生動地展示幻方和魔方的神奇之處。主要包括幻方的數學研究，六階幻方，幻方類型，構造方法，幻圓等十五章內容。本書適合在校學生的學習研究，以及幻方和魔方愛好者作為興趣讀物。

CHAPTERⅠ.MAGICSQUARES
THEESSENTIALCHARACTERISTICSOFMAGICSQUARES
ASSOCIATEDORREGULARMAGICSQUARESOFODDNUMBERS
ASSOCIATEDORREGULARMAGICSQUARESOFEVENNUMBERS
THECONSTRUCTIONOFEVENMAGICSQUARESBYDELAHIRE'SMETHOD
COMPOSITEMAGICSQUARES
CONCENTRICMAGICSQUARES
GENERALNOTESONTIIECONSTRUCTIONOFMAGICSQUARES
CHAFFERⅡ.MAGICCUBES
THEESSENTIALCHARACTERISTICSOFMAGICCUBES
ASSOCIATEDORREGULARMAGICCUBESOFODDNUMBERS
ASSOCIATEDORREGULARMAGICCUBESOFEVENNUMBERS
GENERALNOTESONMAGICCUBES
CHAFFERⅢ.THEFRANKLINSQUARES

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
編輯手記

在線試讀

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 (循環小數)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(數字) 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.

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