##
Women Mathematicians and NMAH CollectionsFrances Baker: Daughter of a Mathematical Model Maker

Image of Frances Baker, ca 1957. Gift of Frances E. Baker. (2006.3037.02) |

Frances Ellen Baker (1902–1995) is one of many women mathematicians who had a close relative who was also a mathematician. Her father was the England-born mathematician Richard Philip Baker, who is best known in the mathematical community for constructing mathematical models. Frances Baker spent most of her career teaching at women’s colleges, Mount Holyoke and Vassar. She was particularly involved with honor students, both by directing honor’s papers and through local chapters of the honor societies Phi Beta Kappa and Sigma Xi.

Questionnaires for both Bakers are preserved in the collection honoring American women in mathematics. In addition, the mathematics collections also include several objects donated by Frances Baker. Among these are the two doctoral hoods from the University of Chicago that she and her father received when they were awarded their PhD’s and a large number of mathematical models constructed by her father.

Riemann Surface. R. P. Baker Model #411z (w^{3}=z). Gift of Frances E. Baker. |

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

- Description
- 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
*w*^{3}=*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*w*^{3}=z on the surface.

- Location
- Currently not on view

- maker
- Baker, Richard P.

- ID Number
- MA*211257.074

- accession number
- 211257

- catalog number
- 211257.074

- Data Source
- National Museum of American History, Kenneth E. Behring Center