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Acknowledgements To my advisor, John Shareshian. I am grateful for our many conversations and the chance to experience your viewpoint of learning and doing mathematics. Thank you for inspiring me and forming me into a better mathematician. To Jesús De Loera, from whom I learned about my thesis problem. You have been a constant source of encouragement and(More)
There are many unanswered questions about the evolution of the ancient 'Silk Roads' across Asia. This is especially the case in their mountainous stretches, where harsh terrain is seen as an impediment to travel. Considering the ecology and mobility of inner Asian mountain pastoralists, we use 'flow accumulation' modelling to calculate the annual routes of(More)
In this paper, we classify and compute the convex foldings of a particular rhombus that are obtained via a zipper folding along the boundary of the shape. In the process, we explore computational aspects of this problem; in particular, we outline several useful techniques for computing both the edge set of the final polyhedron and its three-dimensional(More)
This paper develops techniques for computing the minimum weight Steiner triangulation of a planar point set. We call a Steiner point P a Steiner reducing point of a planar point set X if the weight (sum of edge lengths) of a minimum weight triangulation of X ∪ {P } is less than that of X. We define the Steiner reducing set St(X) to be the collection of all(More)
We obtain a complete classification of all simple closed geodesics on the eight convex deltahedra by solving a related graph coloring problem. Geodesic segments in the neighborhood of each deltahedron vertex produce a limited number of crossing angles with deltahedron edges. We define a coloring on the edge graph of a deltahedron based on these angles, and(More)
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