Henry Ernest Dudeney/Modern Puzzles/121 - Paper Folding/Solution

Modern Puzzles by Henry Ernest Dudeney: $121$

Suppose you are given a perfectly square piece of paper,

how are you going to fold it so as to indicate by creases a regular hexagon,

as shown in the illustration, all ready to be cut out?

Fold the square through the midpoints of opposite sides to get the folds $AOB$ and $COD$.

Fold $EH$ and $FG$ so as to bisect $AO$ and $OB$.

Make the fold $AJ$ through $A$ so that the vertex $K$ lies on $EH$ at $H$.

$H$ is one of the vertices of the hexagon.

Fold $HG$ to make that side.

Make the other vertices of the hexagon similarly.

The rest follows.