Dissection of 2 Regular Hexagons into One
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Problem
Dissect $2$ regular hexagons, and use the pieces to make $1$ larger regular hexagon.
Solution
Dissect one of the regular hexagons into $6$ equal triangles as shown on the left.
Arrange these triangles around the outside of the other regular hexagon as shown on the right.
Join the $6$ obtuse angles of those $6$ triangles to make a larger regular hexagon.
The overlapping bits are then cut off and are fitted into the gaps.
$\blacksquare$
Sources
- June 1975: David Wells: On Gems and Generalisations (Games and Puzzles no. 37)
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Abul Wafa ($\text {940}$ – $\text {998}$): $41$