### Answers (417)

 54 Conjectures that have been disproved with extremely large counterexamples? 34 Why is this trigonometric identity true? 20 Number of equations needed to define a rectangle? 19 Is there any integral for the Golden Ratio? 18 Dog bone-shaped curve: $|x|^x=|y|^y$

### Reputation (16,118)

 +80 Conjectures that have been disproved with extremely large counterexamples? +10 Generalization of Dirichlet integral +35 Evaluating $\int_1^\infty \sin \frac{1}{x^2} dx$ +10 Evaluation of $\sqrt{\frac12+\sqrt{\frac14+\sqrt{\frac18+\cdots+\sqrt{\frac{1}{2^n}}}}}$

### Questions (274)

 103 All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$ 56 Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them? 49 Crazy pattern in the simple continued fraction for $\sum_{k=1}^\infty \frac{1}{(2^k)!}$ 38 Prove inequality $\arccos \left( \frac{\sin 1-\sin x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$ 38 Closed form for $\left(1+\left(\frac{1}{2}+\left(\frac{1}{3}+\left(\frac{1}{4}+\cdots\right)^2\right)^2\right)^2\right)^2$?

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