''Waterfall'' ( nl, Waterval) is a lithograph by the Dutch artist M. C. Escher, first printed in October 1961. It shows a

perpetual motion machine Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can do work infinitely without an external energy source. This kind of machine is impossible, a ...

where water from the base of a

waterfall A waterfall is a point in a river or stream where water flows over a vertical drop or a series of steep drops. Waterfalls also occur where meltwater drops over the edge of a tabular iceberg or ice shelf. Waterfalls can be formed in severa ...

appears to run downhill along the water path before reaching the top of the waterfall. While most two-dimensional artists use relative proportions to create an illusion of depth, Escher here and elsewhere uses conflicting proportions to create a visual

paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

. The

watercourse A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long large streams a ...

supplying the waterfall (its aqueduct or

leat A leat (; also lete or leet, or millstream) is the name, common in the south and west of England and in Wales, for an artificial watercourse or aqueduct dug into the ground, especially one supplying water to a watermill or its mill pond. Othe ...

) has the structure of two

Penrose triangle The Penrose triangle, also known as the Penrose tribar, the impossible tribar, or the impossible triangle, is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing, but cannot e ...

s. A Penrose triangle is an

impossible object An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two- dimensional figure which is instantly and naturally understood as representing a projection of a three-d ...

Description

The image depicts a watermill with an elevated aqueduct and waterwheel as the main feature. The aqueduct begins at the waterwheel and flows behind it. The walls of the aqueduct step downward, suggesting that it slopes downhill. The aqueduct turns sharply three times, first to the left, then to the right, and finally to the left again. The viewer looks down at the scene diagonally, which means that from the viewer's perspective the aqueduct appears to be slanted upward. The viewer is also looking across the scene diagonally from the lower right, which means that from the viewer's perspective the two left-hand turns are directly in line with each other, while the waterwheel, the forward turn and the end of the aqueduct are all in line. The second left-hand turn is supported by pillars from the first, while the other two corners are supported by a tower of pillars that begins at the waterwheel. The water falls off the edge of the aqueduct and over the waterwheel in an impossible infinite cycle; in his notes on the picture, Escher points out that some water must be periodically added to this

to compensate for evaporation. The use of the Penrose stairs is paralleled by Escher's ''

Ascending and Descending ''Ascending and Descending'' is a lithograph print by the Dutch artist M. C. Escher first printed in March 1960. The original print measures . The lithograph depicts a large building roofed by a never-ending staircase. Two lines of identicall ...

'' (1960), where instead of the flow of water, two lines of monks endlessly march uphill or downhill around the four flights of stairs. The two support towers continue above the aqueduct and are topped by two compound

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ...

, revealing Escher's interest in mathematics as an artist. The one on the left is a compound of three cubes. The one on the right is a stellation of a

rhombic dodecahedron In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron. Properties The rhombic dodecahed ...

(or a compound of three non-regular

octahedra In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet a ...

) and is known as Escher's solid. Below the mill is a garden of bizarre, giant plants. This is a magnified view of a cluster of moss and lichen that Escher drew in ink as a study in 1942. The background seems to be a climbing expanse of

terraced In agriculture, a terrace is a piece of sloped plane that has been cut into a series of successively receding flat surfaces or platforms, which resemble steps, for the purposes of more effective farming. This type of landscaping is therefore ...

farmland.

References

External links

Escher's Solid—from Wolfram MathWorld
Includes a great deal of metric data

from

George W. Hart George William Hart (born 1955) is an American sculptor and geometer. Before retiring, he was an associate professor of Electrical Engineering at Columbia University in New York City and then an interdepartmental research professor at Stony B ...

{{Optical illusions Mathematical artworks Works by M. C. Escher 1961 paintings Impossible objects Water in art

Description

See also

References

External links