Fold

A fold is a reflection across a crease. One half of the sheet lands on the other, and the mark flips because the determinant is −1.

The line passes through the origin. The determinant is −1. The mark flips.

Angle θ 22° Offset −0.32

The red mark turns the crease. The ink mark slides it. A fold always flips handedness, as on the determinant page.

Where this is used

A mechanical designer often models half of a symmetric part, then mirrors that half to finish it.
Pattern designers repeat a motif by reflection. A kaleidoscope does the same thing with mirrors.
In optics, a mirror sends a point or a light ray to its reflection across a line or a plane.
Engineers study flat folds so a solar panel or a stent can pack into a small space and then open. A flat fold reflects part of the sheet across a crease.

Common mistakes

A fold is not a turn of 180°. A fold flips the mark. A rotation does not.
An offset crease is a slide, a reflection, and a slide back. The offset is not a second fold.
Only one half of the sheet moves. The other half stays put.
The determinant stays −1. A fold always flips handedness.