POPULAR SCIENCE 



THE 34 SUPERMAGIC SQUARE 



By BRIGADIER-GENERAL F. J. ANDERSON, C.B. 



In the progress report of the Superintendent of Hindu and 

 Buddhist Monuments for 191 5-16 was reproduced a Hindu 

 magic square, found inscribed on a hidden portion of a lintel, 

 brought to light by a fall of masonry, in the Chota Surang 

 shrine at Dudhai in the Jhansi District, India. 



This square, which is said to date from the first half of the 

 eleventh century, is as follows : 



In addition to the usual claim for such squares that the 

 rows, columns, and diagonals each total 34, the discoverer in 

 this case points out that the sub-squares (i.e. the numbers in 

 the four cells clustered around any point where two lines 

 intersect) each give a similar total, but we shall see presently 

 that this enumeration by no means exhausts the supermagic 

 properties of the square. 



The following general definition of the term " Magic Square " 

 is given by Hutton (Recreations in Mathematics, 1803), and 

 seems to be generally accepted : 



11 The name magic square, is given to a square divided into 

 several other small equal squares or cells, filled with the terms 

 of any progression of numbers, but generally an arithmetical 

 one, in such a manner, that those in each band, whether hori- 

 zontal, or vertical, or diagonal, shall always form the same 



sum. 



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