幻方和魔方 （簡體書）

《歐美初等數學經典系列（第1輯）：幻方和魔方》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。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。．

《幻方和魔方》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。

CHAPTER Ⅰ．MAGIC SQUARES
THE ESSENTIAL CHARACTERISTICS OF MAGIC SQUARE
ASSOCIATED OR REGULAR MAGIC SQUARES OF ODD NUMBERS
ASSOCIATED OR REGULAR MAGIC SQUARES OF EVEN NUMBERS
THE CONSTRUCTION OF EVEN MAGIC SQUARES BY DE LA HIRE'S METHOD
COMPOSITE MACIC SQUARES
CONCENTRIC MAGIC SQUARES
GENERAL NOTES ON THE CONSTRUCTION OF MAGIC SQUARES

CHAPTER Ⅱ．MAGIC CUBES
THE ESSENTIAL CHARACTERISIICS OF MAGIC CUBES
ASSOCIATED OR RECUJAR MAGIC CUBES OF ODD NUMBERS
ASSOCIATED OR REGUlAR MAGIC CUBES OF EVEN NUMBERS
GENERAL NUrES ON MAGIC CUBES

CHAPTER Ⅲ．THE FRANKLIN SQUARES
AN ANALYSIS OF THE FRANK-UN SQUARES

CHAPTER Ⅳ．REFIECTIONS ON MAGIC SQUARES
THE ORDER OF FIGURES
MAGIC SQUARESIN SYMBOLS
THE MACIC SQUAREIN CHINA
THE JAINA SQUARE

CHAPTERⅤ．A MATHEMATICAL STUDY OF MAGIC SQUARES
A NEW ANALYSIS
NOTES ON NUMBER SERIES USED IN THE CONSTRUCTION OF MAGIC SQUARES

CHAPTER Ⅵ．MAGICS AND PYTHAGOREAN NUMBERS
MR．BROWI\WS SQUAF：E AND LUSUS NUMERORUM

CHAPTER Ⅶ．SOME CURIOUS MAGIC SQUARES AND COMBINATIONS

CHAPTER Ⅷ．NOTES ON VARIOUS CONSTRUCTIVE PLANS BY WHICH MAGIC SQUARES MAY BE CLASSIFIED
THE MATHEMATICAL VALUE OF MACIC SQUARES

CHAPTER Ⅸ．MAGIC CUBES OF THE SIXTH ORDER
A "FRANKLIN" CUBE OF SIX
A MAGIC CUBE OF SIX
MAGIC CUBE OF SIX

CHAPTER Ⅹ．VARIOUS KINDS OF MAGIC SQUARES
OVERLAPPING MAGIC SQUARES
ODDLY-EVEN MAGIC SQUARES
NOTES ON ODDLY-EVEN MAGIC SQUARES
NOTES ON PANDIAGONAL AND ASSOCIATED MAGIC SQUARES
SERRATED MAGIC SQUARES
LOZENGE MAGIC SQUARES

CHAPTER Ⅺ．SUNDRY CONSTRUCTIVE
……

CHAPTER Ⅻ．THE THEORY OF REVERSIONS
CHAPTER XIII．MAGIC CIRCLES, SPHERES AND STARS
CHAPTER XIV．MAGIC OCTAHEDROIDS
CHAPTER XV．ORNATE MAGIC SQUARES
編輯手記．

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 (循環小數) 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(數字) 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.