Optimal unrestricted containment of one regular polygon in another
Determines the largest regular polygon that fits inside another when rotation and translation are allowed, including the optimal configurations and their contact geometry.
Geometry
Research on polytope containment and related areas.
Published manuscripts
Optimal nestings of all regular polygons
Determines optimal orders for nesting every regular polygon inward or outward, and explains why attaining the optimum requires infinite blocks joined at limiting circles.
How One Polytope Fits Inside Another: An Illustrated Monograph
Develops polytope containment through illustrated examples, optimal placements, contact forces, motion and stability, with exercises and reproducible sources.
Sharp mixed-potential Fourier pairs and planar universal optimality
Studies planar energy minimization using sharp Fourier auxiliaries, with quantitative estimates relating small excess energy to local triangular order in periodic configurations.