MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

106 Mathematical Recreations
Figure 4.5: Square and Triangle Puzzle [87]
With reference to Figure 4.5, fold the square in half and make the crease
FE. Fold the side AB so that the point B lies on FE, and you will get the
points F an H from which you can fold HGJ. While B is on G, fold AB back
on AH, and you will have the line AK. You can now fold the triangle AJK,
which is the largest possible equilateral triangle obtainable.
Figure 4.6: Triangle-to-Triangle Dissection [214]
Recreation 6 (Triangle-to-Triangle Dissection [214]). A given equilateral
triangle can be dissected into noncongruent pieces that can be rearranged
to produce the original triangle in two different ways.
Such a dissection of an equilateral triangle into eight pieces is shown in
Figure 4.6 [214]. This interesting dissection was found by superimposing two
different strips of triangular elements. Incidentally, this is not a minimal-piece
dissection.
Recreation 7 (Polygonal Dissections [109]). Mathematicians’ appetite for
polygonal dissections never seems to be sated [109].