Paths of rectangles inscribed in lines over fields

Bruce Olberding; Elaine A. Walker

Paths of rectangles inscribed in lines over fields

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arxiv 2006.14424 v2 pith:KRG36X5A submitted 2020-06-25 math.MG

Bruce Olberding , Elaine A. Walker This is my paper · ORCID

classification math.MG

keywords rectangleslinespathsaspectinscribedotherratioslope

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We study rectangles inscribed in lines in the plane by parametrizing these rectangles in two ways, one involving slope and the other aspect ratio. This produces two paths, one that finds rectangles with specified slope and the other rectangles with specified aspect ratio. We describe the geometry of these paths and its dependence on the choice of four lines. Our methods are algebraic and work over an arbitrary field.

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The conic geometry of rectangles inscribed in lines
math.MG 2019-08 conditional novelty 6.0 of 10

The locus of centers of rectangles inscribed in two pairs of lines is generically a hyperbola, and every hyperbola occurs as such a locus.

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