First models of the 'impossible triangle' and 'impossible staircase'

First models of the 'impossible triangle' and 'impossible staircase' First models of the 'impossible triangle' and 'impossible staircase' First models of the 'impossible triangle' and 'impossible staircase'

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Creative Commons LicenseThis image is released under a CC BY-NC-SA 4.0 Licence

Buy this image as a print 

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License this image for commercial use at Science and Society Picture Library

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Creative Commons LicenseThis image is released under a CC BY-NC-SA 4.0 Licence

Buy this image as a print 

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License this image for commercial use at Science and Society Picture Library

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Science Museum Group Collection
© The Board of Trustees of the Science Museum

Science Museum Group Collection
© The Board of Trustees of the Science Museum

Science Museum Group Collection
© The Board of Trustees of the Science Museum

First models of the 'impossible triangle' and 'impossible staircase', designed and constructed by Roger Penrose and Lionel Sharples Penrose FRS, England, 1955-1959

First models of the 'impossible triangle' and 'impossible staircase', designed and constructed by Roger Penrose (b. 1931) and Lionel Sharples Penrose FRS (1898-1972), England, 1955-1959

The Penroses were inspired by the Dutch artist M C Escher (1898-1972) and vice versa. In 1954 Roger heard a lecture by Escher, and then drew the impossible triangle in the form with which we are now familiar. It had actually previously been drawn, unknown to him, in another form by the Swedish artist Oscar Reutersvard. The Penroses published in 1958, sending Escher a copy. Escher modelled his lithograph Waterfall on the triangle in 1961, adding polyhedra ‘only because I like them’. While it is easy to draw the impossible triangle in 2D, the Penroses also made a 3D model to be viewed from a certain position.

In the same paper as the impossible triangle, the Penroses introduced the impossible staircase. ‘Actual objects, suitably designed, when viewed from particular angles, can give exactly the same impression as inconsistent drawings.’ This model was photographed so as to give the impression of an impossible staircase. Again, Escher used the concept in his famous Ascending and Descending, published in 1960.

Details

Category:
Mathematics
Object Number:
1982-899
type:
model - representation and optical puzzle
credit:
Newman, M.

Parts

First model of the 'Impossible triangle'

First model of the 'impossible triangle', designed and constructed by Roger Penrose and Lionel Sharples Penrose FRS, England, 1955-1959

More

First model of the 'impossible triangle' one of a series of 'impossible figures' designed and constructed by English geneticist Lionel Penrose FRS (1898-1972) in the 1950s. Penrose's discovery of the 'impossible figure' laid the foundation for the scientific study of illusions and investigations into the psychology of human perception. The Dutch artist M C Escher (1898-1972) was heavily influenced by Penrose's discovery, and incorporated an 'impossible triangle' into his well known 'Waterfall' lithograph.

Measurements:
overall: Ht 101 mm x W 105 mm, 0.05kg
Materials:
birch plywood , paper (fibre product) and adhesive
Object Number:
1982-899/1
type:
model - representation and optical puzzle
Image ©
The Board of Trustees of the Science Museum

First model of the impossible staircase

First model of the 'impossible staircase', designed and constructed by Roger Penrose and Lionel Sharples Penrose FRS, England, 1955-1959

More

First model of the 'impossible staircase' one of a series of 'impossible figures' designed and constructed by English geneticist Lionel Penrose FRS (1898-1972) in the 1950s. Penrose's discovery of the 'impossible figure' laid the foundation for the scientific study of illusions and investigations into the psychology of human perception. The Dutch artist M C Escher (1898-1972) was heavily influenced by Penrose's discovery, and incorporated an 'impossible triangle' into his well known 'Waterfall' lithograph.

Measurements:
overall: Ht 95 mm x W 101 mm x D 101 mm, 0.261kg
Materials:
birch plywood , paper (fibre product) and adhesive
Object Number:
1982-899/2
type:
model - representation and optical puzzle
Image ©
The Board of Trustees of the Science Museum