2024/05/31 by Rebecca M. Bowen, Bowen, Rebecca M., Sadie Pruitt +3
Engineering · Materials Science · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Structural Analysis and Optimization #Textile materials and evaluations
paper · pdf · doi:10.48550/arxiv.2405.20793
openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are quarter-circles, but Tangles comprised of thirds and sixths of circles are introduced. Together, these three families of Tangles are related to the three regular tilings of the plane by squares, regular hexagons, and equilateral triangles. This relationship is harnessed to prove results about the number of links comprising a Tangle and the area that it encloses.