MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Mathematical Recreations 107
(a) (b) (c)
Figure 4.7: Polygon-to-Triangle Dissections; (a) Pentagon. (b) Hexagon. (c)
Nonagon (Enneagon). [109]
Witness Figure 4.7: (a) displays Goldberg’s six piece dissection of a regular
pentagon; (b) displays Lindgren’s five piece dissection of a regular hexagon; (c)
displays Theobald’s eight piece dissection of a regular nonagon (enneagon). All
three have been reassembled to form an equilateral triangle and all are believed
to be minimal dissections [109].
Figure 4.8: Dissections into Five Isosceles Triangles [135]
Recreation 8 (Dissection into Five Isosceles Triangles [135]). Figure
4.8 shows four ways to cut an equilateral triangle into five isosceles triangles
[135].
The four patterns, devised by R. S. Johnson, include one example of no
equilateral triangles among the five, two examples of one equilateral triangle
and one example of two equilateral triangles. H. L. Nelson has shown that
there cannot be more than two equilateral triangles.