cactus314
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 45 Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse? 19 Nobody told me that self teaching could be so damaging… 18 How do I sell out with abstract algebra? 17 Studying for the Putnam Exam 13 Is $\sum_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}=\frac{m^2-1}{3}$ true for $m\in\mathbb N$?

### Reputation (11,653)

 +10 $T^2=I$ implies $T$ is diagonalizable +5 Example of a number field with only one complex place +5 what is the value of $\zeta_{\mathbb{Q}(i)}(-1)$? +10 Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?

### Questions (171)

 14 $\pi^4 + \pi^5 \approx e^6$ is anything special going on here? 12 Why is $\zeta(1+it) \neq 0$ equivalent to the prime number theorem? 11 Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p)$ 10 What is the minimum polynomial of $x = \sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6} = \cot (7.5^\circ)$? 10 How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$?

### Tags (310)

 69 trigonometry × 10 31 limits × 17 45 conic-sections × 4 31 summation × 9 44 real-analysis × 40 30 combinatorics × 24 36 self-learning × 2 30 geometry × 16 31 number-theory × 45 29 abstract-algebra × 21

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