1 citations · 2 across the 9 of their papers we have counts for
12 papers
What's for dessert?
Tanya Khovanova, Daniel A. Klain
Two people meet in a coffeehouse and decide to share one dessert from a menu of several possible choices. How should they choose which one? A method is presented that is intended t…
Tetrahedra with congruent face pairs
Daniel A. Klain
If the four triangular facets of a tetrahedron can be partitioned into pairs having the same area, then the triangles in each pair must be congruent to one another. A Heron-style f…
A probabilistic proof of the spherical excess formula
Daniel A. Klain
This note offers a probabilistic proof of Girard's angle excess formula for the area of a spherical triangle, based on the observation that an unbounded 3-dimensional convex cone,…
Volume bounds for shadow covering
Christina Chen, Tanya Khovanova, Daniel A. Klain
For n >= 2 a construction is given for a large family of compact convex sets K and L in n-dimensional Euclidean space such that the orthogonal projection L_u onto the subspace u^\p…
A countable set of directions is sufficient for Steiner symmetrization
Gabriele Bianchi, Daniel A. Klain, Erwin Lutwak +2
A countable dense set of directions is sufficient for Steiner symmetrization, but the order of directions matters.
Steiner symmetrization using a finite set of directions
Daniel A. Klain
Let be a finite set of unit vectors in $\RR^n$. Suppose that an infinite sequence of Steiner symmetrizations are applied to a compact convex set in $\RR^n$, whe…