Dan Klain's Publications
Articles

A probabilistic proof of the spherical excess formula
[full text]
American Mathematical Monthly, 128 (2021), no. 1, 7072.

Volume bounds for shadow covering
[full text]
[alternate]
with Christina Chen and Tanya Khovanova,
Transactions of the American Mathematical Society, 366 (2014), no. 3, 11611177.

Steiner symmetrization using a finite set of directions
[full text]
[alternate]
Advances in Applied Mathematics, 48 (2012), no. 2, 340353.

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, 869873.

On the equality conditions of the BrunnMinkowski theorem [full text]
[alternate]
Proceedings of the American Mathematical Society, 139 (2011), no. 10, 37193726.

If you can hide behind it, can you hide inside it? [full text]
[alternate]
Transactions of the American Mathematical Society, 363 (2011), no. 9, 45854601.

Containment and inscribed simplices [full text]
[alternate]
Indiana University Mathematics Journal, 59 (2010), no. 4, 12311244.

Covering shadows with a smaller volume
[full text]
[alternate]
Advances in Mathematics, 224 (2010), no. 2, 601619.

Angles as probabilities
[full text]
[alternate]
with David V. Feldman,
American Mathematical Monthly, 116 (2009), no. 8, 732735.
 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 1820, 2008.

Bonnesentype inequalities for surfaces of constant curvature
[full text]
[alternate]
Advances in Applied Mathematics, 39 (2007), no. 2, 143154.

Isometry invariant valuations on hyperbolic space
[full text]
[alternate]
Discrete and Computational Geometry,
36 (2006), no. 3, 457477.

An error estimate for the isoperimetric deficit [full text]
[alternate]
Illinois Journal of Mathematics,
49 (2005), no. 3, 981992.

An intuitive derivation of Heron's formula [full text]
[alternate]
American Mathematical Monthly,
111 (2004), no. 8, 709712.

The Minkowski problem for polytopes [abstract]
[full text]
Advances in Mathematics,
185 (2004), no. 2, 270–288.

Continuous and profinite combinatorics [full text]
with Joseph P. S. Kung,
in
GianCarlo 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
[abstract]
[full text]
Discrete Mathematics,
218 (2000), 109119.

Even valuations on convex bodies [abstract]
[full text]
Transactions of the American Mathematical Society,
352 (2000), no. 1, 7193.

An Euler relation for valuations on polytopes [abstract]
[full text]
Advances in Mathematics, 147 (1999), no. 1, 134.

Kinematic formulas for finite vector spaces [abstract]
[full text]
Discrete Mathematics, 179 (1998), 121132.

Kinematic formulas for finite lattices [abstract]
[full text]
Annals of Combinatorics, 1 (1997), no. 4, 353366.

A continuous analogue of Sperner's theorem [abstract]
[full text]
with GianCarlo Rota,
Communications on Pure and Applied Mathematics, 50
(1997), no. 3, 205223.

Invariant valuations on starshaped sets [abstract]
[full text]
Advances in Mathematics, 125 (1997), no. 1, 95113.

Star valuations and dual mixed volumes [abstract]
[full text]
Advances in Mathematics, 121 (1996), no. 1, 80101.

A short proof of Hadwiger's characterization theorem
[abstract]
[full text]
Mathematika, 42 (1995), no. 2, 329339.
 Several of my preprints are also available at
arXiv.org
Books

Essentials of Number Theory,
draft preprint version, 2019.
Expository Articles and Notes

DehnSommerville relations for triangulated manifolds
[pdf]

The Minkowski problem for polygons [pdf]

The Minkowski problem for simplices [pdf]

The Minkowski condition and divergence [pdf]

Lecture notes on the simplex method [pdf]

Lecture notes on matrix exponentials [pdf]

Lecture notes on orthogonal matrices [pdf]

Lecture notes on projection matrices [pdf]

Lecture notes on rotation matrices [pdf]
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"I don't want to achieve immortality through my work.
I want to achieve it through not dying."
 Woody Allen