Re: Another little puzzle

From	Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups	comp.programming
Subject	Re: Another little puzzle
Date	2023-01-08 19:43 +0000
Organization	A noiseless patient Spider
Message-ID	<87ilhgx152.fsf@bsb.me.uk> (permalink)
References	(5 earlier) <87o7rlhtsv.fsf@bsb.me.uk> <878rioifnh.fsf@bsb.me.uk> <868rinskhk.fsf@linuxsc.com> <87zgb3giu6.fsf@bsb.me.uk> <86cz7pnji2.fsf@linuxsc.com>

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Tim Rentsch <tr.17687@z991.linuxsc.com> writes:

> Ben Bacarisse <ben.usenet@bsb.me.uk> writes:
<cut>
>> The "other" average, minimises the sum of the of the angular
>> distances.
>
> I think you mean it minimizes the sum of the squares of the
> angular distances.

Yes thanks.  I originally thought I'd write an abbreviation but then I
convinced myself I would not forget any of the "squares of"s.  Proof
reading might have been useful too.

>>> and the center of mass is never on the unit
>>> circle (not counting the case when all the time values are the
>>> same).  Even so it's an interesting way to view the distinction.
>>
>> It's more interesting because it really is about chords!
>
> I don't buy the "really" here.  The center of mass is fundamental
> and always well-defined.  Furthermore it works for collections of
> points that are not all on the same circle or sphere.  Looking at
> the problem in terms of chords seems somewhat artificial, or at
> least less fundamental.

There are other ways for something to be interesting (at least to me).
When you plot the two averages, and look at the chords vs the arcs, it
becomes clear why one average "looks" more average than the other.

-- 
Ben.

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Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-12-30 01:00 +0000
  Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-29 23:25 -0800
    Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-12-30 14:04 +0000
      Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-12-31 00:24 +0000
        Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-31 06:42 -0800
          Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-12-31 17:04 +0100
            Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-01 01:24 +0000
            Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2023-01-08 07:45 -0800
              Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2023-01-08 17:17 +0100
                Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-08 20:41 +0000
                Re: Another little puzzle Richard Heathfield <rjh@cpax.org.uk> - 2023-01-08 21:14 +0000
                Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2023-01-08 22:31 +0100
                Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-09 03:25 +0000
                Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2023-01-09 11:22 +0100
                Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-09 20:37 +0000
                Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2023-01-10 09:06 +0100
                Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-11 02:41 +0000
                Re: Another little puzzle "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2023-01-11 10:01 +0100
                Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-12 01:00 +0000
                Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2023-01-10 23:36 -0800
                Re: Another little puzzle Y A <ya00000100000@yahoo.com> - 2023-01-11 02:39 -0800
          Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-01 01:10 +0000
            Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2023-01-08 07:17 -0800
              Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-08 19:43 +0000
                Re: Another little puzzle Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-01-08 19:59 +0000
                Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2023-01-10 23:25 -0800
      Re: Another little puzzle Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-31 06:20 -0800
        Re: Another little puzzle Augǝl <angel0000000001000000000000@mail.ee> - 2022-12-31 10:23 -0800

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