A zoetrope is a device that produces an illusion of action from a rapid succession of static pictures. The term means 'wheel of life'.
A zoetrope is usually a cylinder with slits cut in the sides. Beneath the slits on the inner surface of the cylinder is a band which has either individual frames from a video/film or images from a set of sequenced drawings or photographs. As the cylinder spins the user looks through the slits at the pictures on the opposite side of the cylinder's interior. The scanning of the slits keeps the pictures from simply blurring together so that the user sees a rapid succession of images producing the illusion of motion, the equivalent of a motion picture. Cylindrical zoetropes have the property of causing the images to appear thinner than their actual sizes when viewed in motion through the slits.
Read more: Build your own zoetrope
Ting Huan created the earliest zoetrope in China around 180 AD. Driven by convection, this device hung over a lamp and was called 'The Pipe Which Makes Fantasies Appear'. The rising air turned vanes at the top from which were hung translucent paper or mica panels. Pictures painted on the panels would appear to move if the device is spun at the right speed.
The modern zoetrope was invented in 1834 by British mathematician William George Horner. He called it the 'Daedalum' popularly translated as 'the wheel of the devil' though there is no evidence of this etymology. More likely it is a reference to the Greek myth of Daedalus. It didn't become popular until the 1860s, when it was patented by makers in both England and America. The American developer, William F. Lincoln, named his toy the 'zoetrope', which means 'wheel of life.'
Almost simultaneously similar inventions were made independently in Belgium by Joseph Antoine Ferdinand Plateau (Phenakistoscope) and Austria by Simon von Stampfer (Stroboscope).
The zoetrope worked on the same principles as the phenakistiscope, but the pictures were drawn on a strip which could be set around the bottom third of a metal drum, with the slits now cut in the upper section of the drum. The drum was mounted on a spindle so that it could be spun, and viewers looking through the slits would see the cartoon strip form a moving image. The faster the drum is spun, the smoother the image that is produced.
Other names and devices: zoetrope, zootrope (France), wundertrommel (Germany), praxinoscope, phenakistoscope. Here's a link to a large collection.
What's it worth? Take a look at this Zoetrope price guide: sold listings for a value indication.