Henry Ernest Dudeney/Modern Puzzles/123 - Making an Octagon/Solution

Modern Puzzles by Henry Ernest Dudeney: $123$

Can you cut the regular octagon from a square piece of paper without using compasses or ruler,

or anything but scissors?

You can fold the paper to make creases.

Let the square be $\Box ABCD$.

Fold $AD$ to $BC$ and $AB$ to $DC$ to obtain the midpoints $E$, $F$, $G$ and $H$ of $AD$, $BC$, $AB$ and $DC$ respectively.

Fold $EG$, $FG$, $EH$ and $FH$.

Fold at $H$ to place $DH$ against $EH$, then at $E$ to place $ED$ against $EH$.

Where those folds cross at $I$ is one of the vertices of the regular octagon we are seeking.

The other three vertices are obtained similarly.