How can a folding fan become wide and then fit in a pocket?

A folding fan can hide a broad surface inside a narrow bundle. In a common design, thin ribs meet at a pivot near the handle. A folded leaf of paper or fabric joins the ribs farther out.

When the outer ribs spread apart, the others turn around the same pivot. The leaf opens along alternating folds. Its creases let nearby sections change angle without needing the whole sheet to stretch wider.

Closing reverses the arrangement: the ribs come together and the pleats stack. The thickness of all those layers limits how small the bundle can be. Good joints must let the parts move without tearing their connections.

An open fan pushes air when waved, which can help carry warmth and moisture away from skin. Its special folding trick is separate from that cooling effect. The fan changes its reach through geometry: one connected surface stores itself in a stack.