Strange Surfaces

After the First World War, changes in the direction of mathematics and economic upheaval brought an end to surface building on a grand scale.


The models were often used to illustrate concepts in physics such as the shape of wave surfaces in acoustics and optics. Some surfaces related to ancient disciplines such as architecture, while others explored emerging fields such as topology, the geometry of India -rubber figures.

Felix Klein, a German mathematician, introduced one of the best known surfaces, the Klein bottle, in 1882. It has no edge, no inside or outside, and cannot be constructed properly in 3 dimensions.

In 1995 Alan Bennett, a retired glass-blower, became interested in Klein bottles and was in a unique position to satisfy his curiosity. From simple beginnings his researches produced a variety of beautiful and mathematically sophisticated forms.


The sculptor Henry Moore attended the Royal College of Art in South Kensington between 1921 and 1924. He was an avid museum-goer and was particularly struck by the mathematical models here. In the late 1930s he made a series of carved wood and string forms based on these surfaces and in 1960 an edition of 10 bronze forms. One of these, 'Stringed Figure 1938/60', is at the Tate Gallery.


Mathematical surface models provided ideal material for the Surrealists. In 1936 they held a mould-breaking exhibition in London. The catalogue cover for this exhibition included illustrations of three surface models available in the late 19th century.

Max Ernst, a well-known surrealist, frequently used mathematical surface models in unusual contexts, these have been identified recently by Gabriele Werner.

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