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Dublin Core
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Senior Showcase 2017
Description
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Oral and poster presentations from Senior Showcase held on April 18, 2017 at Ripon College.
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Ripon College Lane Library
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Ripon College Seniors 2017
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Title
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Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun
Subject
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Mathematics
Creator
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Mitchell Eithun
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Senior Showcase Oral Presentation
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Ripon College
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April 18, 2017
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Majors: Mathematics and Computer Science
Minor: Music
New London, Wisconsin
Description
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A semidiscrete curve-shortening flow continuously deforms a polygon in the direction of an inward normal until it shrinks to a point. We are interested in the long-time behavior of polygons under such flows. Is there a semidiscrete flow under which all polygons become asymptotically regular? This is an open question, but we provide numerical evidence to suggest that the recent β-polygon flow of Glickenstein and Liang produces regular polygons. It is known that triangles become regular under the β-polygon flow. Using a rescaled flow in which a regular polygon is a fixed point, we note how side lengths and angles evolve under the β-polygon flow and conjecture that all quadrilaterals become rhombic and polygons with more than 5 vertices become regular.
circulant matrices
curve-shortening
Discrete Differential Geometry
Euler’s Method
Mathematics
rescaled geometric flows