SLATES, SLIDERULES AND SOFTWARE - TEACHING MATH IN AMERICA

The World Stage

The World Stage

From the 1870s, Americans began to play a larger role in discovering new mathematical principles. Some studied abroad, especially in Germany, and a few American universities began to offer graduate degrees in mathematics.

Mathematicians purchased teaching equipment linked to recent advances in their discipline. They and others also introduced devices to help the rapidly growing number of high school students.

WELLESLEY COLLEGE MATH CLASS

From ancient times, mathematicians had studied regular solids like the tetrahedron, the cube, and the octahedron. In the 1850s, the Swiss mathematician Ludwig Schläfli described the six regular figures, or polytopes, that can exist in four-dimensional space.

In 1880, W. I. Stringham, a fellow at Johns Hopkins University, wrote his Ph.D. dissertation on these figures. A few years later, the German mathematician and model maker Ludwig Brill published models of projections of polytopes. These examples on the right were purchased and displayed by Wesleyan University in Connecticut.

GEOMETRIC MODELS
OF POLYTYPES

College students studied figures that could be generated by the motion of straight lines. This model shows two such surfaces, the cone on the inside and the hyperboloid on the outside. Surfaces of this sort had been discovered by the Swiss mathematician Leonhard Euler (1707-1783), and were useful in engineering education.

GEOMETRIC MODEL--
ELLIPTIC CONE AND HYPERBOLOID
OF ONE SHEET

Americans also began to build geometric models that reflected recent discoveries. Richard P. Baker, an English-born mathematics professor, did advanced work at the University of Chicago and then taught at the University of Iowa. He designed and sold several models of surfaces discovered by the German mathematician G. F. Bernhard Riemann and his students.

GEOMETRIC MODEL--
RIEMANN SURFACE

In 1900, Edgar J. Townsend returned from advanced studies in Germany and became director of the mathematics department at the University of Illinois. He promptly arranged for the university to extend its collection of German geometric models and introduced a graduate program in mathematics.

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E. J. Townsend and students - Click To Enlarge

E. J. TOWNSEND AND STUDENTS AT THE UNIVERSITY OF ILLINOIS