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Aug
19
accepted Prove or disprove: $ \sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$
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