Paths of rectangles inscribed in lines over fields
arXiv:2006.14424
Abstract
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.
30 pages, 10 figures. A number of revisions have been made to the first version, including a title change and the addition of Sections 3 and 9. Comments welcome