Timeline for Explicit formula for $\sin\frac{\alpha}{3}$ [closed]
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 16, 2015 at 0:52 | review | Reopen votes | |||
| Jan 16, 2015 at 3:03 | |||||
| Jan 11, 2015 at 4:37 | comment | added | Alexander Kuleshov | This question is equivalent to the following: when is it possible to express the real and imaginary part of $\sqrt[3]{a+ib}$ as $f(a,b)$, where $f$ is a "real radical" function? | |
| Jan 11, 2015 at 4:21 | comment | added | Alexander Kuleshov | Yes, of course I meant real radicals: in the paper that I mentioned it is proved that $\sin\displaystyle\Big(\frac{\pi}{n}\Big)$ can be expressed in real radicals over rational numbers iff $\varphi(n)=2^m$ where $\varphi$ is Euler's totient function, so there is no such expression for $n=9$. But my question is a bit more complicated, because I allow not only rational numbers, but "$\sin\alpha$" as an argument too! The easiest example: can $\sin(1/3)$ be expressed as $f(\sin 1)$ where $f$ is a composition of rational powers and algebraic operations? | |
| Jan 11, 2015 at 4:15 | review | Reopen votes | |||
| Jan 11, 2015 at 10:25 | |||||
| Jan 11, 2015 at 3:59 | history | edited | Alexander Kuleshov | CC BY-SA 3.0 |
added 5 characters in body
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| Jan 11, 2015 at 0:50 | history | closed |
Andrés E. Caicedo Michael Renardy Stefan Kohl♦ Dima Pasechnik Andy Putman |
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| Jan 10, 2015 at 22:26 | comment | added | Emil Jeřábek | More generally, $\sin(\pi q)$ is solvable for all rational $q$, being $1/(2i)$ times the difference of two roots of unity. Presumably the question intends to only consider real radicals? | |
| Jan 10, 2015 at 22:02 | review | Close votes | |||
| Jan 11, 2015 at 0:51 | |||||
| Jan 10, 2015 at 22:02 | comment | added | Alex Degtyarev | A cubic equation can be solved in radicals! (Sometimes, they will involve $\sqrt{-1}$, which does not seem to be a very big deal.) So, your statement on $\sin(\pi/3)$ looks doubtful. | |
| Jan 10, 2015 at 21:32 | history | asked | Alexander Kuleshov | CC BY-SA 3.0 |