A Gallery of Gaussian Periods
Ellen Eischen and Stephan Garcia

Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture
Pages 243–248
Regular Papers

Abstract

Gaussian periods are certain sums of roots of unity whose study dates back to Gauss’s seminal work in algebra and number theory. Recently, large scale plots of Gaussian periods have been revealed to exhibit striking visual patterns, some of which have been explored in the second named author’s prior work. In 2020, the first named author produced a new app, Gaussian periods, which allows anyone to create these plots much more efficiently and at a larger scale than before. In this paper, we introduce Gaussian periods, present illustrations created with the new app, and summarize how mathematics controls some visual features, including colorings left unexplained in earlier work.

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