2 citations · 3 across the 3 of their papers we have counts for
7 papers
The Nash manifold of four-point configurations modulo similarity subgroups
Bruce Olberding, Elaine A. Walker
We construct and study the Nash manifold of four-point configurations in the real plane modulo the action of a Nash subgroup of the group of similarity transformations. We do so by…
Bisector fields and projective duality
Bruce Olberding, Elaine A. Walker
Working over a field of characteristic , we study what we call bisector fields, which are arrangements of paired lines in the plane that have the property tha…
Bisector fields of quadrilaterals
Bruce Olberding, Elaine A. Walker
Working over a field of characteristic other than , we examine a relationship between quadrilaterals and the pencil of conics passing through their vertices. Asymptotically, suc…
Bisector fields and pencils of conics
Bruce Olberding, Elaine A. Walker
We introduce the notion of a bisector field, which is a maximal collection of pairs of lines such that for each line in each pair, the midpoint of the points where the line crosses…
Rectangles conformally inscribed in lines
Bruce Olberding, Elaine A. Walker
A parallelogram is conformally inscribed in four lines in the plane if it is inscribed in a scaled copy of the configuration of four lines. We describe the geometry of the three-di…
Paths of rectangles inscribed in lines over fields
Bruce Olberding, Elaine A. Walker
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…
The conic geometry of rectangles inscribed in lines
Bruce Olberding, Elaine A. Walker
We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in…