The Penrose stairs is an impossible object devised by Lionel
Penrose and his son Roger Penrose and can be seen as a variation on his 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, where it is incorporated into a monastery where
several monks do penance by ascending continuously, but are allowed to turn
around and descend occasionally.
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