Model of a Riemann Surface by Richard P. Baker, Baker #411Z

The mathematician R. P. Baker believed that models were essential for the teaching of mathematics. This model, which he constructed in about 1930, represents a Riemann surface defined by the equation w3=z, where the variables w and z represent complex numbers, i.e., numbers of the form a + bi where i is the square root of -1. Riemann surfaces are named after the 19th-century German mathematician, Bernhard Riemann. They are different from surfaces in three dimensions, such as spheres, that are defined by equations in three variables, all of which represent real numbers.
Real and complex numbers behave differently. For example, any non-zero complex number has three distinct cube roots. For 1 the three cube roots are 1, (-1 + √3) / 2, and (-1 + √3 i) / 2 while for i the three cube roots are -i, (√3 + i) / 2, and (-√3 + i) / 2 .
In this model, the bottom level represents the w plane, a plane of complex numbers that is not part of the Riemann surface. That surface is represented by the other three levels and rectangles connecting them. There are three levels because there are three different values of w that produce the same value of w cubed. The coloring of the surfaces indicates the connections between the values of w on the bottom level and the points that satisfy the equation w3=z on the surface.
Currently not on view
Object Name
geometric model
Baker, Richard P.
Physical Description
wood (overall material)
metal (overall material)
other, cardboard (overall material)
red (overall color)
green (overall color)
yellow (overall color)
blue (overall color)
bolted and soldered. (overall production method/technique)
average spatial: 24.6 cm x 24.7 cm x 25.4 cm; 9 11/16 in x 9 3/4 in x 10 in
place made
United States: Iowa, Iowa City
ID Number
accession number
catalog number
Science & Mathematics
Women Mathematicians
See more items in
Medicine and Science: Mathematics
Women Mathematicians
Data Source
National Museum of American History, Kenneth E. Behring Center
Credit Line
Gift of Frances E. Baker
general reference
Baker, Robert P.. Mathematical Models

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