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Painting - One Surface and One Edge (Möbius)

National Museum of American History

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Object Details

referenced
Moebius, August Ferdinand
painter
Johnson, Crockett
Description
Most geometric surfaces have a distinct inside and outside. This painting shows one that doesn’t. Take a strip of material, give it a half-twist, and attach the ends together. The result is a band with only one surface and one edge. Mathematicians began to explore such surfaces in the nineteenth century. In 1858 German astronomer and mathematician August Ferdinand Möbius (1790–1868), who had studied theoretical astronomy under Carl Friedrich Gauss at the University of Goettingen, discovered the one-sided surface shown in the painting. It has come to be known by his name. As often happens in the history of mathematics, another scholar, Johann Benedict Listing, had found the same result a few months earlier. Listing did not publish his work until 1861.
If one attaches the ends of a strip of paper without a half twist, the resulting figure is a cylinder. The cylinder has two sides such that one can paint the outside surface red and the inside surface green. If you try to paint the outside surface of a Möbius band red you will paint the entire band red without crossing an edge. Similarly, if you try to paint the inside surface of a Möbius band green you will paint the entire surface green. A cylinder has an upper edge and a lower edge. However, if you start at a point on the edge of a Möbius band you will trace out its entire edge and return to the point at which you began. Since Möbius's time, mathematicians have discovered and explored many other one-sided surfaces.
This painting, #34 in the series, was executed in oil on masonite and is signed: CJ65. The strip is shown in three shades of gray based on the figure’s position. The shades of gray, especially the lightest shade, are striking against the rose-colored background, and this contrast allows the viewer to focus on the properties of the Möbius band. The painting has a wooden frame.
Crockett Johnson's painting is similar to illustrations in James R. Newman's The World of Mathematics (1956), p. 596. However, the figures are not annotated in the artist's copy of the book.
Location
Currently not on view
Credit Line
Ruth Krauss in memory of Crockett Johnson
1965
ID Number
1979.1093.23
catalog number
1979.1093.23
accession number
1979.1093
Object Name
painting
Physical Description
masonite (substrate material)
wood (frame material)
Measurements
overall: 65 cm x 65 cm x 1.3 cm; 25 9/16 in x 25 9/16 in x 1/2 in
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Crockett Johnson
Art
National Museum of American History
Record ID
nmah_694647
Metadata Usage (text)
CC0
GUID (Link to Original Record)
http://n2t.net/ark:/65665/ng49ca746a5-1b71-704b-e053-15f76fa0b4fa

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One Surface and One Edge (Moebius)
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