MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

126 Mathematical Recreations
Figure 4.31: Nonattacking Rooks on a Triangular Honeycomb [136]
Recreation 26 (Nonattacking Rooks on a Triangular Honeycomb
[136]). The maximum number of nonattacking rooks that can be placed on
a triangular honeycomb of order n in known for 1 ≤ n ≤ 13: 1, 1, 2, 3, 3, 4,
5, 5, 6, 7, 7, 8, 9. Figure 4.31 shows such a configuration of 5 rooks on an
order-8 board [136].
Figure 4.32: Sangaku Geometry [112]
Recreation 27 (Sangaku Geometry [112]). Figure 4.32 portrays a Sangaku
Geometry (“Japanese Temple Geometry”) problem: Express the radius,
c, of the small white circles in terms of the radius, r, of the dashed circle. The
solution is c = r/10 [112, p. 124].
During Japan’s period of isolation from the West (roughly mid-Seventeenth
to mid-Nineteenth Centuries A.D.) imposed by decree of the shogun [242],
Sangaku arose which were colored puzzles in Euclidean geometry on wooden
tablets that were hung under the roofs of Shinto temples and shrines.