john mangual
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 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 $\{z \; | \;z \perp v \text{ for some } v \in \Lambda \}$ Aug 13 comment Does $\cos (\pi/5)$ belong to $\mathbb{Q} (\sin(\pi/5))$? Somehow we should exploit: $\cos \frac{\pi}{5} = \sqrt{1 - \sin^2 \frac{\pi}{5}}$ or something. I been looking at these proofwiki.org/wiki/Quintuple_Angle_Formulas Aug 11 revised Number of irreducible quadratic polynomials over a finite field added 264 characters in body Aug 11 comment Number of irreducible quadratic polynomials over a finite field I like your use of "invisible ink" - it's great pedagogical tool. Aug 11 comment Number of irreducible quadratic polynomials over a finite field In $\mathbb{F}_2$, there are only 4 possibilities $x^2 , x^2 + 1=(x+1)^2, \color{blue}{x^2 + x + 1}, x^2 + x = x(x+1)$ Aug 11 answered Number of irreducible quadratic polynomials over a finite field Aug 9 answered Explanation of a method to compute $\sum_{k \le n} k^2$ Jul 31 awarded Nice Question Jul 30 revised Why is $\zeta(1+it) \neq 0$ equivalent to the prime number theorem? added 97 characters in body Jul 30 asked Why is $\zeta(1+it) \neq 0$ equivalent to the prime number theorem? Jul 30 accepted Computing the intersection of two arithmetic sequences $(a\mathbb{Z} + b) \cap (c \mathbb{Z} + d)$ Jul 30 asked Computing the intersection of two arithmetic sequences $(a\mathbb{Z} + b) \cap (c \mathbb{Z} + d)$ Jul 29 accepted Can the numbers $2^m 3^n$ have an infinitely long arithmetic sequence? Jul 29 comment Can the numbers $2^m 3^n$ have an infinitely long arithmetic sequence? See it's not so easy? Dirichlet's theorem was my motivation for this problem. As for the comments above, proving the natural density is 0 might also be hard. Jul 29 asked Can the numbers $2^m 3^n$ have an infinitely long arithmetic sequence? Jul 28 revised If $p$ is a prime number and $p\equiv 1(mod 4)$, (show that) there exist integers $a$ and $b$ such that $a^{2}+b^{2}=p$. added 48 characters in body Jul 25 comment Can $O(\sqrt{x})$ be considered $o(x)$? @user251257 Oh my. What an important question. I guess $\boxed{x \to \infty}$, but $x \to 0$ could be important.