Any form of paper, tissue or metal blade that circulates air with the sole purpose of cooling the immediate environment is a fan. Tropical and hot countries that are not architecturally cooled have them fitted into each room; in less hot countries, fans tend to be free standing for summer use only.
As a side benefit of all fans, mosquitos hate moving air.
Fan as shape is a semicircle that shows the radii, either as lines of construction or, as with many hand held fans, pleated folds.
Hand held fans are often made fan-shaped, from a very fine tissue–like fabric, covered and protected at each side by the extension of the handle, which looks something like a flat ended knife, or a razor clam.
Other hand-held fan designs tend to be flat with fine fabric or paper stretched within a cane frame; any flat piece of the design is often hand drawn, very finely crafted and beautiful. The fan is often a special and personal possession, a gift.
In fabric design the fan shape and model often appears in pictorial prints, usually 18th century influenced pretty ladies holding a beautifully decorated fan of one shape or another.
In architecture fan-lights are windows that are semi-circular or semi- elliptical in shape with glazing bars that resemble an open fan, and which are usually fitted above solid doors as a decorative medium for daylight. As the fan shape is essentially an arch, so the joinery of all arched windows and doors, including Venetian windows often creates a fan shape.