Timeline for Degrees of trigonometric numbers
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2023 at 12:09 | comment | added | Gerry Myerson | Had a look at those references, Joonas? | |
| Oct 13, 2023 at 6:25 | comment | added | Gerry Myerson | See also Theorem 3.9, attributed to Lehmer, in Niven, Irrational Numbers. | |
| Oct 13, 2023 at 6:21 | comment | added | Gerry Myerson | Also math.stackexchange.com/questions/822547/… and math.stackexchange.com/questions/460930/… and Heaven knows how many more. | |
| Oct 13, 2023 at 6:15 | comment | added | Gerry Myerson | Also math.stackexchange.com/questions/239425/… and math.stackexchange.com/questions/237515/… and math.stackexchange.com/questions/239316/… | |
| Oct 13, 2023 at 6:08 | comment | added | Gerry Myerson | Degree of $\cos(p\pi/q)$ is discussed at math.stackexchange.com/questions/3441626/… See also math.stackexchange.com/questions/1947835/… and math.stackexchange.com/questions/1693198/… and math.stackexchange.com/questions/3815786/… | |
| Oct 12, 2023 at 18:31 | comment | added | Emil Jeřábek | Furthermore, if $r$ is not an integer, then $\mathbb Z(e^{ir\pi})$ is a proper extension, so $\deg(z)\le\phi(q)/2$. More precisely, the degree must be one of $\phi(q)/4$ or $\phi(q)/2$. | |
| Oct 12, 2023 at 16:08 | comment | added | Aleksei Kulikov | $z\in \mathbb{Z}[e^{ir\pi}]$, so $deg(z) \le deg(e^{ir\pi})=\phi(q)$. On the other hand, since adding $cos(r\pi)$ and $i$ are both quadratic extensions, $deg(z) \ge \frac{\phi(q)}{4}$. | |
| Oct 12, 2023 at 16:08 | comment | added | Conrad | note that $\sin p \pi/q=\cos (\pi (1/2-p/q))=\cos (\pi (q-2p)/(2q))$ so any results about cosine apply to sine too | |
| Oct 12, 2023 at 15:59 | history | asked | Joonas Ilmavirta | CC BY-SA 4.0 |