Geometry in Our Modern World

Applications of mathematics, specifically geometry, to electoral redistricting and the challenge of combatting gerrymandering is a current topic of study among many mathematicians, pioneered by Professor Moon Duchin of Tufts University. Multiple gerrymandering cases have been heard in recent years by the Supreme Court, and shaping district boundaries has social, political, and economic impacts on society.

Mathematically, gerrymandering touches on an old mathematical problem called the isoperimetric problem, which relates the perimeter of a region to its area. Students studied this problem, as well as different ways one can mathematically assess gerrymandering. They took a hands-on approach to gerrymandering and explored software that allowed them to attempt to equalize representation among existing districts in their state.

To highlight several modern applications of geometry, Taback arranged a series of special lectures given by experts from MIT, Colby, and other institutions.

The first, by YouTuber CodeParade, was on implementing a hyperbolic world in a video game context.

The second, by MIT professor Octavian Ganea, described cutting-edge work in machine learning using hyperbolic geometry to obtain embeddings of hierarchical data sets.

The third, by Colby College professor Scott Taylor, discussed how hyperbolic geometry can be used to model large data sets, such as the router connections underlying the world wide web.

Finally, curator Kevin Adkisson from the Cranbrook Center for Collections and Research gave an inspiring talk on geometry in architecture. This lecture was delivered from a Frank Lloyd Wright house, and Adkisson was able to tour the house over Zoom, highlighting Wright’s innovative use of geometry in real time.

Some of Taback’s students from Math 2404 shared their impressions of the course:

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