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Talk:Averages/Mean angle: Difference between revisions
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:::Not so ridiculous. If you have flashes at a distance that you think are localized then you could measure their bearing and want some numerical number that indicates where they are likely to be coming from. An average of the individual, circular, bearings would help. I have to read a bit more about opposite directions but there was something about the size of the radius of the resultant for me to grasp. --[[User:Paddy3118|Paddy3118]] 08:28, 10 July 2012 (UTC)
:::: That's one problem of the task: given an angle a and an integer n, equation n x == a doesn't have a unique solution for x. Which one you pick depends on what use scenario you want, converting angles to unit vectors, averaging them and converting back is simply not a universal solution. Suppose you see three of your flashes and want to choose a heading so you can get closer to investigate; if the degrees of the angles were 10, 20 and 30, you can head to 20 and that's that, but if then angles were 0, -95 and 95, there's no intuitive way to say which direction to go. By your math you'd be going to 0, but you'd be getting closer to one source while getting further away from the other two (I'm not saying you should go the opposite dirction: it depends on what kind of "getting closer to the sources" you really want). Another thing, as currently specified, you average vectors, then keep the angle and discard the amplitude from the result, thus losing relevant information, which just can't be a good way to do things. As a result, you end up with singularities when the result vector is small, and a potential arbitrary "mean value".--[[User:Ledrug|Ledrug]] 03:24, 12 July 2012 (UTC)
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