Henry Ernest Dudeney/Puzzles and Curious Problems/201 - Square and Triangle/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $201$
- Square and Triangle
- Take a perfectly square piece of paper,
- and fold it as to form the largest possible equilateral triangle.
- A triangle in which the sides are the same length as those of the square, as shown in our diagram,
- will not be the largest possible.
- Of course, no markings or measurements may be made except by the creases themselves.
Solution
Fold the square in half to get the crease $EF$.
Fold along $AH$ to get $B$ to lie on $EF$ at $G$.
With that fold in place, fold $HGJ$.
While $B$ is on $G$, fold $AB$ back on $AH$ to get the line $AK$.
You can now fold the triangle $AJK$, which is the largest possible equilateral triangle that can be obtained.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $201$. -- Square and Triangle
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $364$. Square and Triangle