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math.MG2026
Qualitative convexity and universal cross-sections
David Victor Feldman
We study a family of questions in convexity in which \emph{size does not matter}: one records a convex cross-section only up to translation and scaling, so that the data attached t…
math.MG2026
Arranging convex bodies for maximum intersection volume: the sharp efficiency of centroid alignment
David Victor Feldman
Given finitely many compact convex bodies in , one seeks translates maximizing the volume of their common intersection. A lazy solver merely translates each body so as to pla…
math.MG2008
Angles as probabilities
David V. Feldman, Daniel A. Klain
We use a probabilistic interpretation of solid angles to generalize the well-known fact that the inner angles of a triangle sum to 180 degrees. For the 3-dimensional case, we show…