MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

108 Mathematical Recreations
(a) (b) (c)
Figure 4.9: Three Similar Pieces: (a) All Congruent. (b) Two Congruent. (c)
None Congruent. [138]
Recreation 9 (Dissection into Three Parts [138]). It is easy to trisect
an equilateral triangle into three congruent pieces as in Figure 4.9(a).
It is much more difficult to dissect it into three similar parts, just two of
which are congruent as has been done in Figure 4.9(b). Yet, to dissect the
triangle into three similar pieces, none of which are congruent, is again easy
(see Figure 4.9(c)) [138].
Figure 4.10: Trihexaflexagon [121]
Recreation 10 (Trihexaflexagon [121]). Flexagons are paper polygons which
have a surprising number of faces when “flexed” [121].