English: A rectangular sheet of paper may be folded in half several times. The drawing shows two possible ways to fold. The operation superimposes two halves of the rectangle, the crease lies on one or the other axis of symmetry of the rectangle. The dashed lines depict the axes of symmetry d and Δ of the original grey sheet. A single or double folding results in a rectangle drawn with an empty surface.

A single folding in one direction or the other results in the rectangle with red sides or that with blue sides. Red and blue are similar to each other if and only if the original sheet is square. In this case they have also the same size, they are congruent to each other.

The rectangle drawn in green comes out of two successive foldings of the grey sheet in either direction. This is a contraction of the gray one on a scale of 1:2, whatever the original rectangular shape.

Folding in half divides the area of a rectangle by two, so if this single folding transforms a rectangle into a similar one, it necessarily duplicates the rectangle with the scale factor √0.5. This condition of similarity is satisfied if and only if the original sheet has the shape of the standard paper ISO 216, and if the fold parallel to the short sides halves the wide sides of the sheet.