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I know from two sources that it is (or at least was) unknown whether there are infinitely many geometrically distinct closed geodesics for every Riemannian metric on $S^3$, the 3-sphere (Weinberger, C …

I ran across this recurrence relation in a paper by Medina and Zeilberger [MZ] (who got it from [CR]): $$f(h,t) = \max \left( \frac{1}{2} f(h+1,t) + \frac{1}{2} f(h,t+1) ,\frac{h}{h+t} \right) \;.$$ T …

I heard it claimed that there is, in some sense, only one random metric on $\mathbb{S}^2$. I would appreciate any pointer to literature that explicates this intriguing claim. So far my own searches ha …

View a plane tree drawn in $\mathbb{R}^2$ as a joining of geometric (straight) segments at endpoints such that (a) they avoid intersecting one another (except where they share a vertex), and (b) they …

I have a graph $G$ whose minimum vertex degree is $\delta=7$. I am seeking an upper bound on the domination number $\gamma(G)$ in terms of the number of vertices $n$ of $G$. I found a paper by Edwin C …

This is a simple bibliographic request that I have been unable to pin down. Max Dehn's solution to Hilbert's 3rd problem is: Max Dehn, "Über den Rauminhalt." Mathematische Annalen 55 (190x), no. 3, …

Is there a classification of the equivalent of a "developable surface" in $\mathbb{R}^4$? Analogous to: planes, cylinders, cones, and tangent developables in $\mathbb{R}^3$? Edit: Here I am imagining …

Is there a simple proof for the 4-color theorem when restricted to (finite) maps all of whose (internal) regions are pentagons? I am in fact most interested in convex pentagons, if that additional st …

Let $G$ be a (large) graph and $W$ another (smaller) graph. $W$ is what I call a walker. Let me use "vertices" and "edges" for $G$ and "nodes" and "arcs" for $W$. $W$ has a distinguished node, its ce …

Pardon my naivety, but I wonder if much use has been found for trigonometric functions defined in terms of a centrally symmetric convex curve $K$ replacing the circle $C$. For example, here is the equ …

Say that a string of $n$ digits, each from $\lbrace 0,1,2,\ldots,b-1 \rbrace$, is foldable if, were each digit on its own stamp in a sequence of connected stamps, one could fold the stamps so that lik …

Let $\gamma$ be a simple (non-self-intersecting) open curve in $\mathbb{R}^3$. I am seeking a measure of its degree of "entangledness," some measure that accords with the intuition one senses with a t …

Q. Do there exist De Bruijn tori in dimension $d > 2$? A De Bruijn torus is a two-dimensional generalization of a De Bruijn sequence. A De Bruijn sequence is, for two symbols, a cyclical bit-str …

John Horton Conway is known for many achievements: Life, the three sporadic groups in the "Conway constellation," surreal numbers, his "Look-and-Say" sequence analysis, the Conway-Schneeberger $15$-th …

Thales semicircle theorem says that an angle inscribed in a semicircle is a right angle. Q1. Does a cone with apex on a hemisphere and encompassing the circular base have a solid angle independe …