A zoetrope is a device that produces the illusion of motion from a rapid succession of static pictures. The term zoetrope is from the Greek words ζωή (zoē), meaning "alive, active", and τροπή (tropē), meaning "turn", with "zoetrope" taken to mean "active turn" or "wheel of life".

The zoetrope consists of a cylinder with slits cut vertically in the sides. On the inner surface of the cylinder is a band with images from a set of sequenced pictures. As the cylinder spins, the user looks through the slits at the pictures across. The scanning of the slits keeps the pictures from simply blurring together, and the user sees a rapid succession of images, producing the illusion of motion.

The earliest known zoetrope was created in China around 180 AD by the inventor Ting Huan (丁緩). Ting Huan's device, driven by convection, hung over a lamp and was called chao hua chich kuan (the pipe which makes fantasies appear). The rising air turned vanes at the top, from which translucent paper or mica panels hung. When the device was spun at the right speed, pictures painted on the panels would appear to move.

A zoetrope is a device that produces the illusion of motion from a rapid succession of static pictures. The term zoetrope is from the Greek words ζωή (zoē), meaning "alive, active", and τροπή (tropē), meaning "turn", with "zoetrope" taken to mean "active turn" or "wheel of life".

The zoetrope consists of a cylinder with slits cut vertically in the sides. On the inner surface of the cylinder is a band with images from a set of sequenced pictures. As the cylinder spins, the user looks through the slits at the pictures across. The scanning of the slits keeps the pictures from simply blurring together, and the user sees a rapid succession of images, producing the illusion of motion.

The earliest known zoetrope was created in China around 180 AD by the inventor Ting Huan (丁緩). Ting Huan's device, driven by convection, hung over a lamp and was called chao hua chich kuan (the pipe which makes fantasies appear). The rising air turned vanes at the top, from which translucent paper or mica panels hung. When the device was spun at the right speed, pictures painted on the panels would appear to move.

The modern zoetrope was invented in 1833 by British mathematician William George Horner. He called it the "daedalum", most likely as a reference to the Greek myth of Daedalus, though it was popularly referred to as "the wheel of the devil". The daedalum failed to become popular until the 1860s, when it was patented by both English and American makers, including Milton Bradley. The American developer William F. Lincoln named his toy the "zoetrope", meaning "wheel of life". Almost simultaneously, similar inventions were made independently in Belgium by Joseph Antoine Ferdinand Plateau (the phenakistoscope) and in Austria by Simon von Stampfer (the stroboscope).

The zoetrope worked on the same principles as the phenakistoscope, 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 and spun; viewers looking through the slits would see the cartoon strip form a moving image. The faster the drum was spun, the smoother the animation appeared.

The praxinoscope was an improvement on the zoetrope that became popular toward the end of the 19th century. The earliest projected moving images were displayed using a magic lantern zoetrope. This crude projection of moving images occurred as early as the 1860s. A magic lantern praxinoscope was later demonstrated in the 1880s.

Zoetrope development continues into the 21st century, primarily with the "linear zoetrope". A linear zoetrope consists of an opaque linear screen with thin vertical slits in it. Behind each slit is an image, often illuminated. A motion picture is seen by moving past the display.

Linear zoetropes have several differences compared to cylindrical zoetropes due to their different geometries. Linear zoetropes can have arbitrarily long animations and can cause images to appear wider than their actual sizes. Via Zoetrope

The Monty Hall problem is a probability puzzle loosely based on the American television game show Let's Make a Deal and named after the show's original host, Monty Hall. The problem, also called the Monty Hall paradox, is a veridical paradox because the result appears odd but is demonstrably true. The Monty Hall problem, in its usual interpretation, is mathematically equivalent to the earlier Three Prisoners problem, and both bear some similarity to the much older Bertrand's box paradox.

The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. A well-known statement of the problem was published in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:

• Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
  

Vos Savant's response was that the contestant should always switch to the other door. If the car is initially equally likely to be behind each door, a player who picks Door 1 and doesn't switch has a 1 in 3 chance of winning the car while a player who picks Door 1 and does switch has a 2 in 3 chance. Consequently, contestants who switch double their chances of winning the car.

Troxler’s fading or Troxler’s effect is a phenomenon of visual perception. When one fixates a particular point, after about 20 seconds or so, a stimulus away from the fixation point, in peripheral vision, will fade away and disappear. The effect is enhanced if the stimulus is small, is of low contrast or equiluminant, or is blurred. The effect is enhanced the further the stimulus is away from the fixation point. Troxler’s fading was discovered by Ignaz Paul Vital Troxler in 1804.

Troxler’s fading has been attributed to adaptation of neurons in the visual system vital for perceiving a stimulus. It is part of the general principle in sensory systems that an unvarying stimulus soon disappears from our awareness.

The Penrose stairs, also dubbed as the impossible staircase, is an impossible object created by Lionel Penrose and his son Roger Penrose. It can be seen as a variation on the Penrose triangle. It is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three dimensions; the two-dimensional figure achieves this paradox by distorting perspective.

The best known example of Penrose stairs appears in the lithograph Ascending and Descending by M. C. Escher in 1961, where it is incorporated into a monastery where several monks ascend and descend the endless staircase.

The staircase had also been discovered previously by the Swedish artist Oscar Reutersvärd, but neither Penrose nor Escher were aware of his designs.

In terms of sound, the Shepard tone is a similar illusion.