JF Ptak Science Books   Post 1987

I found these extraordinary magic squares lurking in the September 1915 issue of Himmel und Erde–seeing them was a shock to me, especially since I was expecting articles dealing with more technical and also astronomy-related issues, though treated as a history of astrology/astronomy aspect I guess that I should’ve have been too surprised.  The author, W. Ahrens (of  Rostock) had written on different aspects of the magic square in the South Pacific (“Etwas von magischen Quadraten in Sumatra und Celebes”) and more extensively on the Kabalah and magic squares (in “Hebraeische Amulette mit Magischen Zahlenquadraten” for example), and in general in his Mathematische Unterhaltungen und Spiele (1901). 

(An interesting example of a “Venus” magic square, with seven cells).

(This magic square, a “Moon” or “Lunar” square, has nine cells, and also has a form of a “T” world map.  The names of the magic squares were adopted by Cornelius Agrippa (1486-1535) who constructed squares of 3,4,5,6,7,8 and 9 cells, naming them for the seven “planetary” astrological symbols, Saturn, Jupiter, Mars, the Sun, Venus, Mercury and the Moon.  The magic square as an idea seems to have been introduced in the west by Moschopulus of Constantinople in the earlier 15th century–the magic square itself though is ancient, alive and well in India more than 1500 years before its arrival in Europe). 

A magic square amulette from East India.

Another 9-cell magic square, indentifying itself with “Lunae” and “Luna”. 

They’re all quite beautiful.