MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

16 History
(a) (b) (c)
Figure 1.31: Hexagram: (a) Magic Hexagram. (b) Star of David. (c) Chinese
Checkers
A hexagram is a six-pointed star, with a regular hexagon at its center,
formed by combining two equilateral triangles (Figure 1.31). Throughout the
ages and across cultures, it has been one of the most potent symbols used in
magic [49]. The yantra of Vishnu, the Supreme God of the Vishnavite tradition
of Hinduism, contains such a hexagram [193]. Mathematically, a normal magic
hexgram (Figure 1.31(a)) arranges the first 12 positive integers at the vertices
and intersections in such a way that the four numbers on each line sum to the
magic constant M = 26 [87, p. 145]. This can be generalized to a normal
magic star which is an n-pointed star with an arrangement of the consecutive
integers 1 thru 2n summing to a magic number of M = 4n + 2 [308].
The Star of David (Figure 1.31(b)) is today generally recognized as a symbol
of Jewish identity. It is identified with the Shield of David in Kabbalah,
the school of thought associated with the mystical aspect of Rabbinic Judaism.
Named after King David of ancient Israel, it first became associated with the
Jews in the 17th Century when the Jewish quarter of Vienna was formally
distinguished from the rest of the city by a boundary stone having a hexagram
on one side and a cross on the other. After the Dreyfus affair in 19th Century
France, it became internationally associated with the Zionist movement. With
the establishment of the State of Israel in 1948, the Star of David became
emblazoned on the Flag of Israel [278].
Figure 1.31(c) contains the playing board for the inappropriately named
Chinese Checkers. The game was invented not in ancient China but in Germany
by Ravensburger in 1893 under the name “Stern-Halma” as a variation
of the older American game of Halma. “Stern” is German for star and refers
to the star-shaped board in contrast to the square board of Halma. In the
United States, J. Pressman & Co. marketed the game as “Hop Ching Checkers”
in 1928 but quickly changed the name to “Chinese Checkers” as it gained
popularity. This was subsequently introduced to China by the Japanese [236].