Henry Ernest Dudeney/Puzzles and Curious Problems/186 - Triangle and Square/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $186$
- Triangle and Square
- Can you cut each of two equilateral triangles into three pieces,
- so that the six pieces will fit together and form a perfect square?
Solution
Cut one triangle in half, and place the pieces together as in Figure $1$.
Now cut along the dotted lines, making $ab$ and $cd$ each equal to the side of the square we are making.
Then fit together the pieces as in Figure $2$, sliding the pieces $F$ and $C$ upwards to the left, bringing down $D$ to fill that gap in the corner.
Historical Note
Martin Gardner reports that Harry Lindgren has discovered a $5$-piece dissection.
This appears in his $1964$ work Geometric Dissections.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $186$. -- Triangle and Square
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $350$. Triangle and Square