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Impossible staircase

Penrose stairs.

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.

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