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this is my first post on the mathematics node of stack exchange, so please forgive me if I'm not posting an appropriate question, but I'm not sure where else to address this. I'm trying to figure out what equation might generate the following pattern. (keep in mind the numbers might be slightly off, not exact)

 0  :: 0, 0  10 :: 19, -16 (0.17453)  20 :: 41, -28 (0.34906)  30 :: 64, -37 (0.52359)  40 :: 89, -41 (0.69813)  50 :: 113,-41 (0.87266)  60 :: 138,-37 (1.04719)  70 :: 162,-28 (1.22)  80 :: 182,-16 (1.392)  90 :: 201, 0  (1.570)  100:: 217,19 (1.745)  110:: 229,41 (1.919)  120:: 238,64 (2.094)  130:: 241,89 (2.268)  140:: 241,113 (2.443)  150:: 238,138 (2.617)  160:: 229,162 (2.792)  170:: 217,182 (2.792)  180:: 201,201 (2.967)  190:: 182,217 (3.316)  200:: 162,229 (3.490)  210:: 138,238 (3.665)  220:: 113,241 (3.839)  230:: 89,241 (4.0142)  240:: 64,238 (4.188)  250:: 41,229  260:: 19,217  270:: 0,201  280:: -16,182  290:: -28,160  300:: -37,137  310:: -41,113  320:: -41,89  330:: -37,64  340:: -28,41  350:: -16,19  360:: 0,0 

as you math wizez may have guessed it has to do with adjusting coordinates for rotation around an axis. Any help would be great!

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    This kind of thing has been tackled several times before on the site: [here](http://math.stackexchange.com/q/121332/264), [here](http://math.stackexchange.com/q/12852/264), [here](http://math.stackexchange.com/q/82357/264), and [here](http://math.stackexchange.com/q/11502/264). The upshot is that there are infinitely many functions that would produce any given finite collection of data, and so there is no single "answer"; but if you have information or assumptions about the function, then there are methods that can produce interpolating functions with those properties.2012-06-23
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    It would be rather helpful to know how you came across this set of data. Also, Zev, I'm not sure the point you're making with those examples.2012-06-23
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    @Eric: I think this question qualifies as an *abstract* duplicate (this doesn't necessarily mean the question will be closed though). But providing links to relevant earlier questions seems helpful regardless.2012-06-23
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    @Zev: I think there's a qualitative difference from the examples you link to. In the typical questions that your criticism applies to there is only a few (up to 7 in your examples) data points, which isn't enough to decide the general shape of a fit with any degree of accuracy. But with 37 data points, as here, there is a good chance that someone with mathematical experience can look at a plot and see a solution type that can fit the data better than other solutions _of comparable simplicity_, whereas an OP with less experience perhaps can't. That makes it a _good_ question in my opinion.2012-06-23

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Just plot your data and make a guess.

Let $f(x) = 142 \sin \frac{\pi (t -45)}{180}+100$. Then your data is reasonably well approximated by $\{t, f(t), f(360-t)\}_{t\in \{0,\cdots,360\}}$.

Here is a plot of $f$ and the first two columns of the data above:

enter image description here

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    I dare guess that your $142$ might actually be $100\sqrt2$.2012-06-23
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    You might be right. All the data (at least the first 3 columns) are integers, so I would guess there was some rounding. The $2$-norm with $100 \sqrt{2}$ is slightly larger than with 142, but this may be due to rounding (I'm treating the data as a vector in $\mathbb{R}^{360}$).2012-06-23
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    brilliant! Thank you so much!2012-06-23