Mathematics Problem Archive

Consider two nested convex plane domains, and let $T_1,T_2$ be their billiard ball maps on the oriented lines intersecting both domains. If $T_1\circ ...

Let $f(x,y)$ be a polynomial for which $0$ is a nonsingular value, let $\gamma$ be an oval component of $f(x,y)=0$, and assume that $\gamma_\varepsilo...

Assume the origami hyperbolic-paraboloid pattern has invisible straight folds along a chosen diagonal of each elementary trapezoid. What is the shape ...

Find conceptual proofs and possible generalizations of the new projective-geometry configuration theorems described in the source. In particular, prov...

For a fixed combinatorial dissection of a square into $n$ triangles, the ordered triangle areas satisfy a polynomial relation depending only on the co...

Does the three-dimensional cube admit a triangulation into tetrahedra all of whose dihedral angles are acute?...

Is there a near-linear-time algorithm to construct the straight skeleton of a simple polygon? Determine the optimal complexity, including for polygons...

Given motorcycles moving simultaneously along fixed rays and crashing upon reaching another track, determine the motorcycle graph in near-linear time....

Given a sufficiently dense sample of points on a surface (technically, an $\epsilon$-sample), reconstruct a surface homeomorphic to the original....

An optimization problem that naturally arises in the study of ``swarm robotics'' is to wake up a set of ``asleep'' robots, starting with only one ``aw...

There almost surely exists a horofunction h such that lim n→∞ − 1 n h(xn) = A, where A = lim n→∞ 1 n d(x0, xn). A theorem of Karlsson states that ∀ϵ >...

Prove that the pictured standard triple soap bubble is the least-perimeter way to enclose and separate three given volumes in $\mathbb{R}^3$....

Is every Laplacian algebra of polynomials maximal?...

Does every curve bounding a surface of positive curvature in 3-space have (at least) four points where the torsion vanishes?...

Does connectedness of the shadows imply that f(M) is convex?...

Does every convex polyhedron have Rupert's property?...