query: Is this a valid mathematical proof that $\pi = 4\sqrt{\sqrt{5/4}-\sqrt{1/4}}$?
positive_passages.docid: 145466
positive_passages.text: Is this a valid mathematical proof?
negative_passages.docid: 95145
negative_passages.text: Does $\exp(2ir\pi)$ equal $1$? What's wrong?
negative_passages.docid: 3098
negative_passages.text: How are first digits of $\pi$ found?
negative_passages.docid: 28771
negative_passages.text: Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
negative_passages.docid: 58284
negative_passages.text: How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
negative_passages.docid: 22767
negative_passages.text: How to prove $3^\pi>\pi^3$ using algebra or geometry?
negative_passages.docid: 36366
negative_passages.text: Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
negative_passages.docid: 120953
negative_passages.text: Show that, $2\arctan\left(\frac{1}{3}\right)+2\arcsin\left(\frac{1}{5\sqrt2}\right)-\arctan\left(\frac{1}{7}\right)=\frac{\pi}{4}$
negative_passages.docid: 97011
negative_passages.text: Proving that $\prod_{k=1}^{n}\tan\left(\frac{\pi k}{2n+1}\right)=\sqrt{2n+1}$ using geometry
negative_passages.docid: 140949
negative_passages.text: Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
negative_passages.docid: 12401
negative_passages.text: Is it standard to say $-i \log(-1)$ is $\pi$?
negative_passages.docid: 96328
negative_passages.text: Proving $e^{i\pi} = -1$ without proving $e^{ix} = \cos x + i\sin x$
negative_passages.docid: 50777
negative_passages.text: Prove that $4\sin\frac{2\pi}{7}- \tan\frac{\pi}{7}= \sqrt{7}$ .
negative_passages.docid: 81750
negative_passages.text: $4 \sin 72^\circ \sin 36^\circ = \sqrt 5$
negative_passages.docid: 132928
negative_passages.text: Digits of $\pi$ forming primes?
negative_passages.docid: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
negative_passages.docid: 48086
negative_passages.text: Why is this series of square root of twos equal $\pi$?