MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

72 Mathematical Properties
The best known such tiling with 15 equilateral triangles is shown in Figure
2.63 and has an area of 4,782 etus which is a considerable improvement over
the minimum order perfect triangulation with area of 1,374 etus.
Figure 2.64: Partridge Tiling [162]
Property 79 (Partridge Tiling). A partridge tiling of order n of an equilateral
triangle is composed of 1 equilateral triangle of side 1, 2 equilateral
triangles of side 2, and so on, up to n equilateral triangles of side n [162].
The partridge number of the equilateral triangle is defined to be the smallest
value of n for which such a tiling is possible. W. Marshall discovered the
partridge tiling of Figure 2.64 and P. Hamlyn showed that this is indeed the
smallest possible, and so the equilateral triangle has a partridge number of 9
[162].
Figure 2.65: Partition of an Equilateral Triangle [149]