Tetrahedra with congruent facet pairs[full text], The Mathematical Intelligencer, published online: 30 November 2022
A probabilistic proof of the spherical excess formula [full text], American Mathematical Monthly, 128 (2021), no. 1, 70-72.
Volume bounds for shadow covering [full text] [alternate], with Christina Chen and Tanya Khovanova, Transactions of the American Mathematical Society, 366 (2014), no. 3, 1161-1177.
Steiner symmetrization using a finite set of directions [full text] [alternate], Advances in Applied Mathematics, 48 (2012), no. 2, 340-353.
A countable set of directions is sufficient for Steiner symmetrization [full text] [alternate], with Gabriele Bianchi, Erwin Lutwak, Deane Yang, and Gaoyong Zhang, Advances in Applied Mathematics, 47 (2011), no. 4, 869-873.
On the equality conditions of the Brunn-Minkowski theorem [full text] [alternate], Proceedings of the American Mathematical Society, 139 (2011), no. 10, 3719-3726.
If you can hide behind it, can you hide inside it? [full text] [alternate], Transactions of the American Mathematical Society, 363 (2011), no. 9, 4585-4601.
Containment and inscribed simplices [full text] [alternate], Indiana University Mathematics Journal, 59 (2010), no. 4, 1231-1244.
Covering shadows with a smaller volume [full text] [alternate], Advances in Mathematics, 224 (2010), no. 2, 601-619.
Estimation of Euler characteristic from volumetric data [proceedings full text (pdf)], with K. Rybnikov, K. Daniels, B. Jones, and V. Durante, Proceedings of the Fourth International Symposium on 3D Data Processing, Visualization, and Transmission, Georgia Institute of Technology, June 18-20, 2008.
Bonnesen-type inequalities for surfaces of constant curvature [full text] [alternate], Advances in Applied Mathematics, 39 (2007), no. 2, 143-154.
Isometry invariant valuations on hyperbolic space [full text] [alternate], Discrete and Computational Geometry,36 (2006), no. 3, 457-477.
An error estimate for the isoperimetric deficit [full text] [alternate], Illinois Journal of Mathematics,49 (2005), no. 3, 981-992.
An intuitive derivation of Heron’s formula [full text] [alternate], American Mathematical Monthly,111 (2004), no. 8, 709-712.
The Minkowski problem for polytopes [full text], Advances in Mathematics,185 (2004), no. 2, 270–288.
Continuous and profinite combinatorics [full text], with Joseph P. S. Kung, in Gian-Carlo Rota on Analysis and Probability, edited by Jean Dhombres, Joseph Kung and Norton Starr. (Boston: Birkhäuser Verlag, 2003).
Free polygon enumeration and the area of an integral polygon [full text], Discrete Mathematics, 218 (2000), 109-119.
Even valuations on convex bodies [full text], Transactions of the American Mathematical Society, 352 (2000), no. 1, 71-93.
An Euler relation for valuations on polytopes [full text], Advances in Mathematics, 147 (1999), no. 1, 1-34.
Kinematic formulas for finite lattices [full text], Annals of Combinatorics, 1 (1997), no. 4, 353-366.
A continuous analogue of Sperner’s theorem [full text], with Gian-Carlo Rota, Communications on Pure and Applied Mathematics,50 (1997), no. 3, 205-223.
Invariant valuations on star-shaped sets [full text], Advances in Mathematics, 125 (1997), no. 1, 95-113.
Star valuations and dual mixed volumes [full text], Advances in Mathematics, 121 (1996), no. 1, 80-101.
A short proof of Hadwiger’s characterization theorem [full text], Mathematika, 42 (1995), no. 2, 329-339.
Several of my preprints are also available at arXiv.org
