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 Aug 19 revised Prove or disprove: $\sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$ added 2 characters in body Aug 19 revised Prove or disprove: $\sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$ added 43 characters in body Aug 19 revised Prove or disprove: $\sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$ added 376 characters in body Aug 19 asked Prove or disprove: $\sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$ Aug 16 comment Area of the lattice generated from $(n, n\sqrt{2} \mod 1)$ @LeeMosher I start out with the line $(t, t \sqrt{2}) \in \mathbb{R}^2$ and mod the y-coordinate by $1$, $(x,y) \mapsto (x, y \mod 1)$ so it's wrapping around a cylinder $\mathbb{R}\times S^1$. Additionally $t \in \mathbb{Z}$ so although I started with a line in the plane, it really looks like a 2D lattice on the cylinder. Aug 16 asked Area of the lattice generated from $(n, n\sqrt{2} \mod 1)$ Aug 16 answered Proof of $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$ (not standard proof) Aug 16 revised Moebius band not homeomorphic to Cylinder. added 149 characters in body Aug 16 comment Moebius band not homeomorphic to Cylinder. @ThomasAndrews sure I can; I am taking the closure of a subset of the cylinder/Mobius band in the relative topology. Aug 15 comment Proof of $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$ (not standard proof) Also $\sum k^3 = \left( \sum k \right)^2$. Concidence? Aug 15 revised Moebius band not homeomorphic to Cylinder. deleted 315 characters in body Aug 15 comment Moebius band not homeomorphic to Cylinder. @PyRulez My constructions are fine. If the two spaces where homeomorphic, we could map one meridian circle to the other $S^1 \subset X \leftrightarrow S^1 \subset Y$. Since both spaces fiber over the circle, we can take a closed interval over each point in $S^1$. The result is a closed cylinder on the one hand and a closed Möbius band on the other. Aug 15 revised Moebius band not homeomorphic to Cylinder. added 70 characters in body Aug 15 revised Moebius band not homeomorphic to Cylinder. added 259 characters in body Aug 15 revised Moebius band not homeomorphic to Cylinder. added 259 characters in body Aug 15 answered Moebius band not homeomorphic to Cylinder. Aug 15 comment Area of a Random Polygon I don't think the exact formula is a very exciting thing to compute. There are some interesting formulas in the large $n$ limit. See the papers of John Pardon. arXiv:1110.5656 Central limit theorems for uniform model random polygons. Aug 15 comment Without using Heegner-Stark-Baker, $\mathbb{Q}(\sqrt{-11})$ has class number $1$. Possibly related Dense Packings from Algebraic Number Fields and Codes Shantian Cheng Aug 13 revised Dual Cone Construction $\{z \; | \;z \perp v \text{ for some } v \in \Lambda \}$ added 13 characters in body Aug 13 asked Dual Cone Construction $\{z \; | \;z \perp v \text{ for some } v \in \Lambda \}$