query: Is $\pi$ a rational multiple of e?
positive_passages.docid: 147363
positive_passages.text: Is $\large \frac {\pi}{e}$ rational, irrational, or trandescendal?
negative_passages.docid: 125096
negative_passages.text: Minimal polynomial of $\alpha=\sqrt 2e^\frac{2\pi i}{3}$
negative_passages.docid: 40837
negative_passages.text: Why $e^{i(π/3)} \ne -1$?
negative_passages.docid: 75731
negative_passages.text: Significance of $\pi$ in physics
negative_passages.docid: 148576
negative_passages.text: Origin of rapidly converging sequence for $e^\pi$
negative_passages.docid: 138355
negative_passages.text: Improper rational/trig integral comes out to $\pi/e$
negative_passages.docid: 158235
negative_passages.text: Laurent Series for $\cot(\pi z)$
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 81150
negative_passages.text: Positive integer multiples of an irrational mod 1 are dense
negative_passages.docid: 7500
negative_passages.text: $\arctan$ of a square root as a rational multiple of $\pi$
negative_passages.docid: 114379
negative_passages.text: Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
negative_passages.docid: 49444
negative_passages.text: Why isn't $e^{2\pi xi}=1$ true for all $x$?
negative_passages.docid: 40087
negative_passages.text: Using Modularity Theorem and Ribet's Theorem to disprove existence of rational solutions
negative_passages.docid: 2786
negative_passages.text: The staircase paradox, or why $\pi\ne4$
negative_passages.docid: 11935
negative_passages.text: Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
negative_passages.docid: 67768
negative_passages.text: How to determine the group structure of $E(\mathbb{R})$ for an elliptic curve $E/\mathbb{R}$
negative_passages.docid: 37642
negative_passages.text: Why is $\pi$ irrational if it is represented as $C/D$?