MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

104 Mathematical Recreations
Figure 4.2: Dissected Triangle [86]
Recreation 2 (H. E. Dudeney’s Dissected Triangle [86]). Cut a paper
equilateral triangle into five pieces in such a way that they will fit together and
form either two or three smaller equilateral triangles, using all the material in
each case.
In Figure 4.2, diagram A is the original triangle, which for the sake of
definiteness is assumed to have an edge of 5 units in length, dissected as shown.
For the two-triangle solution, we have region 1 together with regions 2, 3, 4 and
5 assembled as in diagram B. For the three-triangle solution, we have region
1 together with regions 4 and 5 assembled as in diagram C and regions 2 and
3 assembled as in diagram D. Observe that in diagrams B and C, piece 5 has
been turned over which was not prohibited by the statement of the problem.
(a) (b)
Figure 4.3: (a) Triangle Dissection. (b) Triangle Hinged Dissection. [85]
Recreation 3 (H. E. Dudeney’s Haberdasher’s Puzzle [85]). The Haberdasher’s
Puzzle [85] concerns cutting an equilateral triangular piece of cloth
into four pieces that can be rearranged to make a square.