Dynamics, Geometry, and Botany of Continued Fraction Expansions

Wake Forest University
Department of Mathematics & Statistics

Colloquium

Thursday, October 14, 11:00 AM
In Person Event: 121 Manchester Hall

Dynamics, Geometry, and Botany of Continued Fraction Expansions
Dr. Patrick Shipman, Colorado State University

Variations on the idea of representing a number by its continued fraction expansion (CFE) have appeared throughout history and cultures. 2300+ years ago, Euclid’s The Elements provided an early recorded version of CFE’s. Gauss developed a dynamical systems view of CFE’s in the early 1800’s, and in the early 1900’s Klein provided a geometric interpretation. All the while, plants across the globe have been illustrating all of these views in what we call phyllotactic patterns—the arrangement (taxis) of leaves (phylla) and the associated tilings of plant surfaces. This talk will lead us through some of the history of CFE’s and their phyllotactic realization, starting off with the following question: Can well can one tile a cone by quadrilaterals?

Host: John Gemmer (gemmerj@wfu.edu) *In person host: Leandro Lichtenfelz (lichtel@wfu.edu)

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