Henry Ernest Dudeney/Puzzles and Curious Problems/222 - Folding a Pentagon/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $222$
- Folding a Pentagon
- Given a ribbon of paper, as in the diagram, of any length -- say more than $4$ times as long as broad --
- it can all be folded into a perfect pentagon,
- with every part lying within the boundaries of the figure.
- The only condition is that the angle $ABC$ must be the correct angle of two contiguous sides of a regular pentagon.
- How are you to fold it?
Solution
By folding $A$ over, find $C$, so that $BC = AB$.
Then fold as in Figure $1$ across the point $A$.
This will give point $D$.
Fold as in Figure $2$, making the edge of the ribbon lie along $AB$.
This will give point $E$.
Continue the fold as in Figure $3$, and so on, until all the ribbon lies in the pentagon.
Also see
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $222$. -- Folding a Pentagon
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $365$. Strip to Pentagon