Timeline for For which rational values of $c$ and $d$ are the numbers $\sin{(\pi\cdot c)}$, $\sin{(\pi\cdot d)}$ and $1$ linearly dependent over $\mathbb{Q}$?
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| Jan 16, 2015 at 19:24 | comment | added | Zack Wolske | The sine values for $c=1/10$ and $d=3/10$ differ by $1/2$, so the answer to question 2 is no. | |
| Jan 16, 2015 at 17:06 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Jan 16, 2015 at 16:45 | history | reopened |
GH from MO David E Speyer Gerald Edgar Gerry Myerson Lucia |
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| Jan 16, 2015 at 16:11 | comment | added | Gerry Myerson | Morris Newman found, many years ago, all solutions in rational $a,b,c$ to $\sin\pi a\sin\pi b=c$ (and later I extended this to products of 3 and 4 sines). The methods involve writing it as a vanishing sum of roots of unity (and there's a paper by Conway and Jones about that). I suspect one should be able to cobble together an answer out of those sources and techniques. | |
| Jan 16, 2015 at 12:13 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 16, 2015 at 9:42 | comment | added | math110 | @ToddTrimble,Thank you for help edit it,and seem it is beatifull.+1 | |
| Jan 16, 2015 at 8:52 | comment | added | Todd Trimble | Since you have performed major surgery on this question, I went in and edited further to what I hope is a pretty stable state. Please go ahead and insert the reference to the M.SE question, and perform any other minor edits (e.g., a colon after Question 2), and let's see what reaction this now gets (i.e., after one more edit, let's leave it alone for a while). | |
| Jan 16, 2015 at 8:48 | history | edited | Todd Trimble | CC BY-SA 3.0 |
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| Jan 16, 2015 at 7:21 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 16, 2015 at 7:16 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 16, 2015 at 7:11 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 16, 2015 at 6:50 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 17:00 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 14:45 | comment | added | Hjalmar Rosengren | You can more generally ask for which rational values of $c$ and $d$ the numbers $\sin(\pi c)$, $\sin(\pi d)$ and $1$ are linearly dependent over $\mathbb Q$. If you can solve this for $d=1/18$ you are done. The case $d=0$ is known as Niven's theorem. Maybe you should try rephrasing your question in more general terms. | |
| Jan 15, 2015 at 12:17 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 11:06 | review | Reopen votes | |||
| Jan 15, 2015 at 14:43 | |||||
| Jan 15, 2015 at 10:48 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 10:47 | comment | added | math110 | such this post,mathoverflow.net/questions/130319/… I know this is AME(USA) problem,But don't hold,and my problem A class of transcendental trigonometric equations integer solution of such a situation，Related to the this general $a+b\sin{A}=c+d\sin{B}$ problem?So far I have not seen such a study of this problem this paper | |
| Jan 15, 2015 at 10:31 | comment | added | math110 | why [on hold]? Thank you | |
| Jan 15, 2015 at 10:24 | history | closed |
Will Jagy abx GH from MO Dima Pasechnik Stefan Kohl♦ |
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| Jan 15, 2015 at 10:09 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Jan 15, 2015 at 9:42 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 7:36 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 7:28 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 7:21 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 5:57 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 5:49 | review | Close votes | |||
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| Jan 15, 2015 at 4:37 | history | edited | math110 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 4:19 | history | asked | math110 | CC BY-SA 3.0 |